THE ROLE OF TRAIT ACHIEVEMENT MOTIVATION AND ABILITY IN
PREDICTING ACADEMIC PERFORMANCE TRAJECTORIES
By
Matthew C. Reeder

A THESIS
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
MASTER OF ARTS
Psychology
2010

ABSTRACT
THE ROLE OF TRAIT ACHIEVEMENT MOTIVATION AND ABILITY IN
PREDICTING ACADEMIC PERFORMANCE TRAJECTORIES
By
Matthew C. Reeder
In the organizational and educational domains, student and employee performance are
central outcomes to applied psychologists, practitioners, and policymakers alike. In each
of these domains, sizable literatures have been devoted to research on individual
differences in cognitive ability and motivation as performance determinants, that is, how
between-persons variability in ability and motivational characteristics contributes to
between-persons variability in performance measured at a given point in time. However,
it is commonly acknowledged that performance is not a static phenomenon; rather, how
an individual performs varies in systematic and substantively meaningful ways over time.
One method of describing these patterns of change in performance over time is through
the analysis of performance trajectories. In two studies, the influence of ability and traitlike motivational characteristics on undergraduate academic performance trajectories was
examined. Results suggest that individuals high in ability and need for achievement tend
to perform better initially. However, relationships between change over time and both
ability and need for achievement were not consistent across samples.

ACKNOWLEDGEMENTS
I would like to express my appreciation to Dr. Neal Schmitt for the advice,
feedback, support, and discussions that guided me through this process. I‟m extremely
grateful for the ideas and suggestions that he offered throughout the duration of the
project – they contributed greatly to my thesis and I‟ve learned a lot as a result. Similarly,
I would like to thank Drs. Ann Marie Ryan and Rick DeShon for their ideas, suggestions,
and guidance. This thesis strongly benefited from the conceptual and methodological
advice provided by both of you. To my committee as a whole, I appreciate the
conversations that we had throughout the process of proposal and defense. Those
discussions are what I had imagined graduate school would be like when before I came to
Michigan State, and it‟s made for a truly wonderful and insightful experience.
Finally, I would like to express my appreciation to my family, notably my mother
and father, for their continued support leading up to and during the process of working on
my thesis. Mom: thanks for the boxes of chocolate that helped keep me up late at night
working on this. Dad: you‟ve been in my thoughts and have been a constant source of
inspiration - I wish you were here, and I hope I‟d have made you proud.

iii

TABLE OF CONTENTS

LIST OF TABLES ............................................................................................................. vi
LIST OF FIGURES ......................................................................................................... viii
INTRODUCTION ...............................................................................................................1
ABILITY AND MOTIVATION AS INDIVIDUAL DIFFERENCE DETERMINANTS
OF PERFORMANCE ..........................................................................................................7
Ability...............................................................................................................................7
Ability and Performance ..............................................................................................9
Theoretical Explanations for the Role of Ability in Performance .............................11
Motivation ......................................................................................................................15
The Growth and Decline of Need for Achievement ..................................................16
Renewed Interest in Trait Conceptualizations of Achievement Motivation ..............22
Validity of Need for Achievement / Trait Achievement Motivation .........................25
The Interaction Hypothesis: M + A or M × A? .............................................................28
Theoretical Perspectives Relevant to the Interaction Hypothesis ..............................30
Empirical Evidence Pertaining to the Interaction Hypothesis ...................................32
Critique of Extant Research Relating to the Interaction Hypothesis .........................35
DYNAMIC CRITERIA AND THE STUDY OF TRAJECTORIES IN PERFORMANCE
............................................................................................................................................42
Dynamic Criteria: Initial Research, Theory, and Debate ...............................................42
Evidence for Dynamic Criteria ..................................................................................43
Theoretical Perspectives on Dynamic Criteria ..........................................................45
From Dynamic Criteria to Individual Differences in Performance Trajectories............50
Cognitive Predictors of Performance Trajectories .....................................................52
Non-Ability Predictors of Performance Trajectories .................................................54
Integrating the Interaction Hypothesis into the Study of Trajectories in Performance .....59
Individual Difference Determinants of Academic Performance Trajectories ................61
Predictors of Initial Performance ...............................................................................61
Predictors of Performance Trajectories .....................................................................64
METHOD ..........................................................................................................................72
Sample and Procedures ..................................................................................................72
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Sample 1: MSU-Only ................................................................................................72
Sample 2: Multi-Institution ........................................................................................74
Measures: MSU-Only Sample .......................................................................................77
Predictor Measures.....................................................................................................77
Criterion Measures .....................................................................................................80
Measures: Multi-Institution Sample ...............................................................................80
Predictor Measures.....................................................................................................80
Criterion Measures .....................................................................................................82
Convergent Validity of Achievement Motivation Measures .....................................84
Analytic Strategy ............................................................................................................88
Phase 1: Descriptive and Static Analyses ..................................................................89
Phase 2: Model Building and Model Test..................................................................89
Hypothesis Evaluation. ..............................................................................................97
RESULTS: MSU-ONLY SAMPLE ................................................................................101
Descriptive and Static Analyses ...................................................................................101
Latent Trajectory Models .............................................................................................102
Y-measurement model .............................................................................................102
Structural model .......................................................................................................105
RESULTS: MULTI-INSTITUTION SAMPLE ..............................................................109
Descriptive and Static Analyses ...................................................................................109
Latent Trajectory Models .............................................................................................110
Y-measurement model .............................................................................................110
Structural model .......................................................................................................113
DISCUSSION ..................................................................................................................119
Study Findings..............................................................................................................119
Strengths and Limitations.............................................................................................123
Future Research ............................................................................................................128
Conclusion ....................................................................................................................130
REFERENCES ................................................................................................................165

v

LIST OF TABLES

Table 1. Listing of achievement motivation items employed in MSU-Only Sample .....132
Table 2. Achievement Motivation Biodata Inventory (AM BIO-15) items ...................133
Table 3. Listing of Achievement Motivation Biodata Inventory (AM BIO-15) items,
College Board biodata dimensions, and convergent validities with achievement
motivation scales in pilot sample .....................................................................................134
Table 4. Descriptive statistics and intercorrelations for achievement motivation measures
..........................................................................................................................................135
Table 5. Differences between analysis sample and excluded subjects on demographic
and background categorical variables (MSU-Only Sample) ...........................................136
Table 6. Differences between analysis sample and excluded subjects on demographic
and background categorical variables (Multi-Institution Sample)...................................137
Table 7. Differences between analysis sample and excluded subjects on continuous
variables (MSU-Only Sample) ........................................................................................138
Table 8. Differences between analysis sample and excluded subjects on continuous
variables (Multi-Institution Sample) ................................................................................139
Table 9. Summary of y-measurement models evaluated in MSU-Only and MultiInstitution Samples...........................................................................................................140
Table 10. Descriptive statistics and intercorrelations among study measures ................141
Table 11. Global model fit statistics for measurement model (MSU-Only Sample)......142
Table 12. Unstandardized Model Parameters for Unconditional Measurement Model
(MSU-Only Sample) ........................................................................................................143
Table 13. Global model fit statistics for structural model (MSU-Only Sample) ............144
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Table 14. Local model fit statistics for structural model (MSU-Only Sample)..............145
Table 15. Global model fit statistics for measurement model (Multi-Institution Sample)
..........................................................................................................................................146
Table 16. Local model fit statistics for unconditional measurement model (MultiInstitution Sample) ...........................................................................................................147
Table 17. Global model fit statistics for structural model (Multi-Institution Sample) ...148
Table 18. Local model fit statistics for structural model (Multi-Institution Sample) .....149

vii

LIST OF FIGURES

Figure 1. Equations describing relationship between performance and time (withinsubjects) and person-specific change parameters to subject characteristics (betweensubjects) ...........................................................................................................................151
Figure 2. Conceptual path diagram of predictors of latent trajectory parameters
(intercept, slope) ..............................................................................................................154
Figure 3. Plot of unconditional performance trajectory for MSU-Only Sample ............155
Figure 4. Plot of ability main effects (low: -1 SD, high: +1 SD) on latent performance
trajectories (MSU-Only Sample) .....................................................................................156
Figure 5. Plot of motivation main effects (low: -1 SD, high: +1 SD) on latent
performance trajectories (MSU-Only Sample) ................................................................157
Figure 6. Plot of motivation conditional effects on latent performance trajectories at low
ability (MSU-Only Sample).............................................................................................158
Figure 7. Plot of motivation conditional effects on latent performance trajectories at high
ability (MSU-Only Sample).............................................................................................159
Figure 8. Plot of unconditional performance trajectory for Multi-Institution sample ....160
Figure 9. Plots of ability main effects (low: -1 SD, high: +1 SD) on latent performance
trajectories (Multi-Institution Sample) ............................................................................161
Figure 10. Plots of motivation main effects (low: -1 SD, high: +1 SD) on latent
performance trajectories (Multi-Institution Sample) .......................................................162
Figure 11. Plots of motivation conditional effects on latent performance trajectories at
low ability (Multi-Institution Sample) .............................................................................163
Figure 12. Plots of motivation conditional effects on latent performance trajectories at
high ability (Multi-Institution Sample) ............................................................................164

viii

INTRODUCTION
It is intuitive to conceive that indicators of performance, whether at the level of
the individual, the team, or the firm, should display the characteristic of varying in a
systematic manner with the passage of time. To imagine otherwise, that performance is
indefinitely stable or even highly resistant to change, seems conceptually illogical,
antithetical to many of the interventions commonly employed in organizational practice
to influence performance (e.g., training, strategy intervention), and counter to everyday
observation (e.g., financial reports indicating firm performance varying over time as a
function of dynamics in macroeconomic conditions). Consequently, the study of
variability in performance over time, and the determinants of such variability, has long
interested researchers in a variety of fields across various levels of analysis.
One infamous example in the history of statistics pertains to Secrist‟s analysis of
firm performance over time throughout the 1920s (Secrist, 1933, as cited in Stigler,
2002). Secrist believed he had discovered a fundamental law in economic activity,
namely that competitive pressures lead to mediocrity, or an averaging out, in firm
financial performance over the course of time. Unbeknownst to him, Secrist had
(unwittingly) re-discovered the principle of regression toward the mean, first observed by
Galton more than 45 years earlier (Galton, 1886). More recent, and perhaps less
unfortunate, examples of research investigating determinants of organizational
performance or productivity over time have focused on a variety of factors, with human

1

resource management (HRM) practices receiving a sizable amount of attention (Birdi,
Clegg, Patterson, et al., 2008; Collins & Smith, 2006; Wang & Shyu, 2009).
In addition to the examples cited above, applied researchers have not ignored
temporal dynamics in performance at the individual level of analysis. Indeed, as noted
more than 40 years ago by MacKinney (1967) in a discussion of temporal variability in
individual-level job performance, “change is fashionable” (p. 9). Evidence of the
popularity surrounding the study of temporal variability in human performance is
reflected in the body of research on the topic of dynamic criteria, which amassed steadily
throughout the latter half of the twentieth century. Defined broadly, the concept of
dynamic criteria refers to the relative variability or instability of measures of performance
over the course of time (Deadrick & Madigan, 1990; Steele-Johnson, Osburn, & Pieper,
2000). Dating to the 1950s (e.g., Worbois, 1951), the dynamic nature of criterion
measures employed in organizational psychology and related fields has been the subject
of much theoretical conceptualizing, empirical testing, and heated debate in light of
ongoing research pertaining to the more general issue of the criterion problem
acknowledged in applied psychology (Austin & Villanova, 1992; Barrett, Caldwell, &
Alexander, 1985; Ghiselli, 1956). That the topic of dynamic criteria has been the center
of a great deal of research activity is not surprising, given the potential implications of
temporal variability in performance and performance measures for domains such as
personnel psychology (e.g., personnel selection: choice of predictor constructs, validation
study design and need to continually validate predictor measures, estimation of utility;
training: aptitude-by-treatment interactions), organizational behavior (e.g., the role of
state-like and trait-like motivational determinants of performance, employee

2

socialization), educational psychology (e.g., similar concerns as those expressed above
regarding personnel selection), and other areas within the general auspices of the applied
social sciences.
Researchers investigating the dynamic nature of performance have posited a
number of theoretical explanations for the phenomenon. Many of these perspectives
focus on the temporally-varying importance of performance determinants in the ability
and motivational individual difference domains (e.g., Ackerman, 1988; Alvares & Hulin,
1973; Helmreich, Sawin, & Carsrud, 1986; Kanfer & Ackerman, 1989; Murphy, 1989).
In brief, these explanations postulate that constructs important for the prediction of initial
or early performance may not be the same constructs important for the prediction of later
performance. This shift in importance is often attributed to factors such as skill
acquisition and dissipating task novelty, changes which alter the means by which ability
and motivational constructs contribute to task performance. Researchers incorporating
both ability and motivational constructs into theories of dynamic performance have
generally postulated that, while individual differences in general cognitive ability may be
more predictive of performance initially (early in the performance period or in one‟s
tenure), ability-performance correlations should dissipate over time as the core job tasks
become well learned. Conversely, correlations between individual difference
motivational constructs and performance are expected to rise over time as the initial
novelty of the task and job dissipates (e.g., Helmreich et al., 1986; Murphy, 1989).
Much of the empirical research from which these models and theories are drawn
has focused on how predictor-criterion correlations change over time. However, research
dating to the early 1990s has largely shifted to a focus on examining individual

3

differences in performance trajectories over time, an approach that focuses on how
performance develops across a period of time and what factors account for differences
between persons in developmental trajectories. This body of research has examined how
between-persons variability in trajectories can be accounted for by both stable, trait-like
constructs (e.g., Ployhart & Hakel, 1998; Thoresen, Bradley, Bliese, & Thoresen, 2004;
Voelkle, Wittmann, & Ackerman, 2006; Zyphur, Bradley, Landis, & Thoresen, 2008), as
well as more proximal or situationally-specific constructs (Chen & Mathieu, 2008; Yeo
& Neal, 2006, 2008).
Another line of research with a roughly parallel chronological lineage to that of
dynamic criteria has developed around what has been referred to as the interaction
hypothesis (Mount, Barrick, & Strauss, 1999), or the notion that job performance can be
viewed as a multiplicative function of constructs in the domains of task-relevant ability
and motivation. The interaction hypothesis, often attributed to Maier (1955), has been
integrated into models of both work motivation (e.g., Dachler & Mobley, 1973) and static
models of job performance (McCloy, Campbell, & Cudeck, 1994; Vroom, 1964).
Traditional research on the interaction hypothesis, which has been conducted in both
applied settings (e.g., Lawler & Suttle, 1973; Sackett, Gruys, & Ellingson, 1998; Wright,
Kacmar, McMahan, & Deleeuw, 1995) and lab settings (e.g., Fleishman, 1958; French,
1958; Locke, Mento, & Katcher, 1976), seeks to address whether interactions between
constructs in the ability and motivational domains add incrementally to the prediction of
performance at a given time beyond the main effects attributed to either ability and
motivation.

4

Despite the similar chronological paths of these two streams of research (viz.,
dynamic criteria and the interaction hypothesis) and the debate and research that each has
generated, it is noteworthy that there has been little attempt at formally integrating the
two into a single, coherent theoretical framework applicable to performance in applied
domains. For the dynamic criteria literature, ability and motivation have both been jointly
evoked in predominant theories put forth to account for the existence of dynamic criteria
(e.g., Helmreich et al., 1986; Murphy, 1989). However, such treatments have generally
focused on additive main effects of individual differences in ability and motivation,
without much consideration for the form of the relationship between these determinants
and performance in a time-varying context. With respect to the literature focusing on the
interaction hypothesis, performance (albeit in a static perspective) has been the primary
criterion utilized in empirical research. In addition, as previously mentioned, the
interaction hypothesis has been incorporated into models of job performance utilized
within the field of organizational psychology. Thus, while a connection between these
two literatures seems a logical next step, it remains a step yet to be taken.
As such, the purpose of the present study is to integrate the literature on dynamic
performance with prior theorizing and empirical research on the interaction hypothesis.
The intention underlying this integration is to arrive at a formal analysis of the functional
form of the relationships between performance trajectories and individual differences in
the ability and motivational domains, so as to derive hypotheses about such relationships
that can be tested empirically. To this end, the report is outlined as follows. First, prior
research on individual difference determinants of performance and the interaction
hypothesis will be reviewed in order to (a) explicate the primary implications derived

5

from the interaction hypothesis; (b) summarize empirical research that has been
conducted to test the feasibility of the interaction hypothesis, and; (c) elucidate
theoretical justifications put forth for the interaction hypothesis with the aim of noting
how such justifications may be extended from a focus on performance as a static concept
to performance as a dynamic construct. Second, prior research on dynamic criteria will be
reviewed in order to (a) derive its primary implications from both practical and
theoretical perspectives; (b) examine relevant theoretical perspectives as they relate to
individual difference predictor constructs in the ability and motivational domains, and;
(c) highlight empirical research that has investigated relationships between individual
difference predictor constructs and performance trajectories. Third, stemming from the
literature in these two domains, a model describing determinants of performance
trajectories will be put forth that attempts to explain how ability and motivation might
account for inter-individual variation in such trajectories within a given applied context,
with a specific focus on comparing additive versus multiplicative models. Fourth, results
from a study conducted in order to test the aforementioned model will be presented.
Finally, results from the present study will be discussed in light of (a) theoretical
implications for the dynamic criteria and interaction hypothesis literatures, separately, as
well as for how these two bodies of research may be more fully integrated into a model of
determinants of performance trajectories; (b) practical implications stemming from the
present findings, and; (c) limitations of the present study and suggestions for future
research.

6

ABILITY AND MOTIVATION AS INDIVIDUAL DIFFERENCE DETERMINANTS
OF PERFORMANCE
Historically, conceptualizations of human performance within
industrial/organizational psychology have treated constructs in both the ability and
motivational domains as fundamental determinants of performance. Examples include
Kanfer and Ackerman‟s resource allocation model (Kanfer & Ackerman, 1989),
Campbell and colleagues‟ model of job performance (Campbell, McCloy, Oppler,&
Sager, 1993; McCloy et al., 1994), the task performance/contextual performance
distinction proffered by Borman and Motowidlo (Borman & Motowidlo, 1993;
Motowidlo, Borman, & Schmit, 1997), and variants of expectancy models of motivation
(e.g., Lawler & Suttle, 1973). One issue that predates most current models of
performance, however, is the recurrent question of how ability and motivation work in
tandem to influence performance, that is, the functional form of the relationship between
performance, on the one hand, and ability and motivation on the other. In order to
understand how this question has been addressed in the literature, previous research on
ability and motivation as separate predictors of performance is first reviewed.
Consideration is then given to prior theoretical and empirical treatments of ability and
motivation as joint determinants of performance.
Ability
Ability has been defined as interindividual variability in the maximum levels of
task difficulty at which individuals exhibit successful performance on a given class of

7

tasks, where tasks are differentiated according to the modalities or resources required for
performance (e.g., cognitive, psychomotor, perceptual; Carroll, 1993). Within the
differential psychology literature, one of the most widely accepted frameworks of the
structure of human cognitive abilities is the Cattell-Horn-Carroll (CHC) model. In the
CHC model, the domain of human cognitive abilities is structured hierarchically into
three strata: stratum-I narrow abilities, stratum-II broad content abilities, and stratum-III
general ability, or g (Carroll, 1993). Each higher-order stratum reflects an increasing
degree of generality within the domain of cognitive ability. Stratum I is characterized by
specialized abilities reflecting experience and the acquisition of task-specific strategies
relevant to performance. Stratum-I factors load onto stratum-II factors similar to those
suggested by Cattell and Horn (e.g., Cattell, 1963; Horn & Cattell, 1966), characterized
by broad content abilities indicative of general domains of behavioral performance (e.g.,
fluid intelligence, crystallized intelligence, general visual perception, cognitive speed,
memory and learning). These stratum-II factors, in turn, load on stratum-III g, indicating
the general factor common to performance across the various cognitive subdomains.
Stratum-III g has also been interpreted as general mental ability (Schmidt & Hunter,
1998) or general intelligence (Sheppard & Vernon, 2007).
Differential psychologists and applied measurement researchers have speculated
as to the conceptual interpretation of g within the structure of human abilities. These
considerations have resulted in three nonexclusive perspectives: psychometric g,
pertaining to general intelligence and its foundation within the factor-analytic tradition in
psychological measurement, primarily among researchers espousing simple structure;
physiological/biological g, pertaining to the neurological, physiological, and biological

8

substrates of general intelligence and its relation to various genetic phenomena (e.g.,
inbreeding depression, hybrid vigor), and; psychological/behavioral g, pertaining to the
relation between general intelligence and performance in various domains of everyday
life, including both academic and employment (e.g., Gottfredson, 1997, 2002; Jensen,
1986, 1998; Ree & Carretta, 2002; Schmidt, 2002). This third perspective would also
encompass relationships between g and performance on basic information-processing
components tasks employed in differential psychology (e.g., Kyllonen, 1993; Kyllonen &
Christal, 1990; Sheppard & Vernon, 2007). Although there is no generally agreed upon
definition of g (Jensen, 1986) and new perspectives continue to emerge (e.g., Van der
Maas, Dolan, Raoul, Grasman, Wicherts, Huizenga, & Raijmakers, 2006), researchers
have emphasized the importance of general intelligence as a determinant of performance
in situations calling for complex information processing, fast and efficient learning, and
adaptability in responding to novel environmental stimuli across situations.
Ability and performance. The vast majority of research in applied psychology
examining human abilities as predictors of performance, particularly large-scale reviews
and meta-analyses, has focused on general cognitive ability. The present review on ability
correlates of performance summarizes these findings, while not discounting the potential
importance of specific abilities in certain situations. A large body of literature speaks to
the predictive efficacy of general cognitive ability in both the work and academic
domains (Kuncel, Hezlett, & Ones, 2004). In the work domain, g is hypothesized to be a
stronger predictor of core technical components of task performance, as opposed to
behaviors categorized as contextual performance or citizenship behavior where weaker
relationships are hypothesized (Gottfredson, 2002; Motowidlo et al., 1997). Supporting

9

this hypothesis, research in personnel psychology has consistently shown general
cognitive ability to be a moderate to strong predictor of job knowledge (Colquitt, LePine,
& Noe, 2000; Hunter, 1983; Schmidt, Hunter, & Outerbridge, 1986), training
performance and skill acquisition (Colquitt et al., 2000; Hunter, 1986; Hunter & Hunter,
1984; Olea & Ree, 1994; Ree & Earles, 1991, 1992), and various measures of job
performance (Hunter, 1986; Hunter & Hunter, 1984; Kuncel et al., 2004; Ree, Earles &
Teachout, 1994; Schmidt & Hunter, 1998). Collectively, these findings indicate that
general intelligence is a robust, pervasive determinant of technical aspects of task
performance; as Olea and Ree (1994) note, “from jelly rolls to aileron rolls, g predicts
occupational criteria” (p. 848).
Recent meta-analyses and large-scale studies have explored the relationship
between academic performance and general intelligence, often measured as a composite
score derived from standardized examinations used in college admissions (e.g., ACT,
SAT). Mirroring the results found in the personnel domain, results suggest that g is a
moderate to strong predictor of student performance for both the undergraduate (Robbins,
Lauver, Le, Davis, Langley, & Carlstrom, 2004; Sackett, Kuncel, Arneson, Cooper, &
Waters, 2009; Tracey & Robbin, 2006) and graduate (Kuncel et al., 2004) populations. In
the undergraduate domain, these studies have yielded validities in the range of .35 to .53,
depending on the measurement and statistical artifacts corrected for. Kuncel and
colleagues‟ (2004) meta-analysis revealed that the validity for general intelligence may
be slightly weaker in the graduate domain than in the undergraduate domain ( = .27,

operational = .36 following corrections for restriction and criterion measurement error).

10

Theoretical explanations for the role of ability in performance. A number of
theories have been put forth in the industrial/organizational psychology literature to
account for the observed relationship between stable individual difference constructs and
job performance. These theories vary in both the level of detail used to describe the role
of ability, as well as the extent to which the propositions set forth have been empirically
tested. Two prominent perspectives that have received a great deal of empirical
examination are Hunter‟s theory (e.g., Hunter, 1983, 1986; Schmidt et al., 1986) and
Ackerman‟s theory (e.g., Ackerman, 1987, 1988; Ackerman & Ciancolo, 2000; Kanfer &
Ackerman, 1989; Voelkle et al., 2006).
Hunter (1986) presented a theory describing the role of ability as a determinant of
performance that was influenced by the classic learning perspective of E. L. Thorndike
(see also Hunter, 1983). As described by Hunter (1986), the classic learning perspective
postulates that performance on complex tasks is strongly determined by prior learning
and that learning is strongly determined by general intelligence. Therefore, performance
on complex tasks is determined by general intelligence mediated through learning and the
accumulation of knowledge. Hunter (1986) noted two types of learning relevant for
performance within the workplace, formal training and on-the-job learning. Both types
of learning lead to the accumulation of declarative and procedural knowledge, each of
which yields increases in task performance (Hunter, 1983). Within a given learning
situation, those high in general intelligence are believed to acquire more job knowledge
and acquire it faster than those low in general intelligence (e.g., Schmidt, 2002). In
addition, Hunter (1986) suggested that although performance is bounded by the amount
of task-relevant knowledge held by the employee, performance may also require the

11

employee to extend beyond the amount of knowledge already held. This state of affairs
arises in situations where effective performance places demands on the worker requiring
the allocation of higher-order cognitive processing to the task (e.g., problem solving,
planning, memory, etc.; see Hunter, 1983). Because of these demands for higher-order
cognitive processing, general intelligence will not only predict performance as mediated
by learning (knowledge), but it will also have a direct effect on performance (Hunter,
1983).
Hunter (1983) meta-analyzed correlations among measures of cognitive ability,
job knowledge, work sample performance, and supervisor performance ratings from both
military and civilian samples. The meta-analytic correlations were used to create path
models to test the aforementioned propositions regarding the influence of ability on
performance. As hypothesized by Hunter, ability exhibited an indirect effect on
performance through job knowledge, such that individuals with greater ability tended to
have greater job knowledge, and those with greater job knowledge also exhibited higher
performance on the work sample measure. Furthermore, ability demonstrated a direct
effect on work sample performance beyond the mediated effect through job knowledge;
however, the indirect effect was almost twice as large as the direct effect (.34 versus .19).
Schmidt and colleagues (1986) extended upon Hunter‟s (1983) study by incorporating
job experience as an antecedent to job knowledge, with experience exhibiting effects
parallel to those of general intelligence. Finally, Borman, White, Pulakos, and Oppler
(1991) tested Hunter‟s theory using a sample of first-term soldiers in nine military
occupations derived from the Project A dataset. Borman and colleagues (1991) confirmed
the theorized indirect effect of ability on work sample performance through job

12

knowledge; however, no evidence was found for a direct effect between ability and work
sample performance in this study. Similar findings were reported by Borman, White, and
Dorsey (1995).
Ackerman (e.g., 1987, 1988; Kanfer & Ackerman, 1989; Voelkle et al., 2006)
presented a theory of skill acquisition integrating perspectives from the differential
psychology, human information-processing, and skilled performance literatures.
Ackerman‟s theory suggests that, as an individual acquires experience on a task that
permits for consistent information processing, he or she passes through three qualitatively
distinct stages of skill acquisition that correspond to the manner in which knowledge is
acquired or used at a given stage. These stages are labeled declarative knowledge,
knowledge compilation, and procedural knowledge, respectively (Kanfer & Ackerman,
1989; see also Anderson, 1982). These stages correspond largely to Schneider and
Shiffrin‟s controlled-automatic processing distinction (Schneider & Shiffrin, 1977;
Shiffrin & Schneider, 1977; see also Schneider & Chein, 2003). During the declarative
knowledge stage, the individual attempts to understand the task environment and
specifications, store rules for effective performance, and derive effective performance
strategies. Because of the novelty imposed on the leaner by the task environment at this
stage, substantial demands are made on the individual‟s attentional resources, resulting in
slow and error-prone performance. During the knowledge compilation stage, sequences
of cognitive and motor processes are integrated, resulting in performance that is faster,
more accurate, and less resource-intensive. Finally, during the procedural knowledge
stage, the skill has been automatized and can be performed largely outside the

13

individual‟s attention; attentional demands are reduced sharply, with performance being
fast, efficient, and accurate.
Ackerman‟s theory suggests that the types of ability relevant for performance
during skill acquisition can be mapped onto the three stages described above (Ackerman,
1988; Kanfer & Ackerman, 1989). At the declarative knowledge stage, general
intelligence and content abilities corresponding roughly to Carroll‟s stratum-II broad
factors are the primary determinants of performance, with demands on general
intelligence being invoked by the high attentional requirements confronting the learner
and task content determining the relevance of the broad content abilities. As the
individual progress to knowledge compilation, demands on perceptual speed ability
increase as the learner attempts to compile production rules into fast, efficient
performance sequences; concurrently, the demand on general intelligence wanes as
attentional load decreases. Finally, as the individual progresses in the procedural
knowledge stage, performance is determined largely by individual differences in
psychomotor ability that influences task execution and speed; demands on general
intelligence and perceptual speed reduce. Together, both of the theories described above
provide largely complimentary and congruent treatments of the role of general
intelligence in performance. Both theories suggest that general intelligence leads to the
accumulation of procedural and declarative knowledge that leads to subsequent increases
in performance. The one area where the two theories would likely diverge pertains to the
type of abilities involved (i.e., the exclusive focus on general intelligence in Hunter‟s
theory versus the differential importance of abilities at varying levels of generality in
Ackerman‟s theory).

14

The separate models of Hunter and Ackerman provide useful and unique
perspectives on the determinants of human performance in work settings, although both
have certain limitations relevant to the present study. Hunter‟s model has largely received
support in the various empirical examinations of it as reported by both Hunter and
colleagues and Borman and colleagues. However, the model contains an inherent time
precedence that has been thus far neglected; no true longitudinal examinations of the
model exist in the published literature that test key propositions (e.g., tests of the
proposition that learning mediates the ability-knowledge relationship). Furthermore, the
direct effect of ability on performance remains uncertain, as results have not been entirely
consistent across studies. Ackerman‟s theory focuses explicitly on the skill learning
process. It was not intended to be a theory of higher-order task performance measured
over long-run time sequences as is the case in much of the job and academic performance
research referred to elsewhere herein, a point that Ackerman acknowledges (Kanfer &
Ackerman, 1989). Furthermore, the theory‟s propositions regarding the differential
importance of various ability constructs throughout skill acquisition have not always
found clear support in empirical examinations (e.g., Voelkle et al., 2006). However, the
theory is useful for present purposes due to its specification of the role of cognitive
abilities in determining performance at a level of detail that is lacking in other individual
difference models of job performance.
Motivation
The present focus restricts the domain of motivational constructs in two ways.
First, consideration is restricted to constructs relevant to the domain of achievement
motivation. The achievement domain includes settings within which behavior is

15

evaluated in light of some standard of excellence and where motivation serves the
purpose of energizing and directing affect, behavior, and cognition tied to one‟s
competence in meeting such standards (Cooper, 1983; Elliot, 1999). Broadly speaking,
the domain of interest (e.g., interpersonal, achievement, etc.) can be viewed as reflecting
those specific affective, behavioral, and cognitive manifestations that are adaptive for
performance within that domain; motivational processes, both internal and external to the
individual, undergird these manifestations. Using an academic setting as a specific
instance of an achievement setting, such manifestations include being ambitious in
establishing one‟s goals, being highly involved in and maintaining control of one‟s
performance and progress, and being persistent and hard working (e.g., Nonis &Wright,
2003). In this sense, achievement motivation is viewed as being an appetitive construct
(Kanfer & Heggestad, 1997).
Second, the present focus is on stable individual difference constructs in the
domain of achievement motivation. State-like or malleable constructs are relevant insofar
as they can be considered manifestations tied to distal individual difference attributes or
that represent characteristic responses (cognitive, affective, or otherwise) to an
environmental stimulus or set of stimuli. Such malleable constructs can be viewed as the
means by which distal, stable characteristics ultimately influence behavior in a given
context. Individual difference characteristics associated with achievement motivation
become relevant only in the presence of appropriate environmental incentives and when
goal choice and pursuit is not constrained (Kanfer & Heggestad, 1997).
The growth and decline of need for achievement. One construct that has played a
central role in achievement motivation research over the past 60 years is need for

16

achievement (also commonly referred to as nAch, the achievement motive, achievement
motivation, or achievement orientation). The concept of need for achievement has
historical roots in early psychological thinking, including William James, Narziss Ach,
and Henry Murray (Fineman, 1977). McClelland and colleagues (e.g., Atkinson, 1957;
McClelland, 1985; McClelland, Atkinson, Clark, & Lowell, 1953; McClelland, Koestner,
& Weinberger, 1989) developed the conceptual domain of achievement motivation
around the need for achievement construct by describing the construct‟s developmental
origins, the role of environmental stimuli in causing it to become manifest in a given
setting, and the construct‟s basis in affective arousal.
Atkinson (1957) defined need for achievement as a stable, trait-like disposition
associated with strivings for achievement and success. This trait was assumed to be latent
or dormant until activated by environmental or contextual cues indicating the
instrumentality associated with high achievement (Atkinson, 1953, 1957). Murray (1938,
as cited in Fineman, 1977) emphasized a number of characteristics associated with high
need for achievement: the tendency to do things quickly and as well as possible, the
desire to accomplish difficult tasks, to overcome challenges, and to improve oneself and
to surpass others. High standing on need for achievement is associated with competition
against standards of excellence, preferences for difficult or challenging tasks, striving to
attain high levels of competence, and preferences for feedback information about
competence levels (Puca & Schmalt, 1999). These characteristics share in common an
adaptive, appetitive form of motivation that is hypothesized to be beneficial in
achievement contexts.

17

Early theorizing from the program of research initiated by McClelland and
Atkinson highlighted a number of cognitive manifestations believed to be associated with
high standing on need for achievement, including initial selection of moderately difficult
tasks (Atkinson, 1957; Cooper, 1983; DeCharms & Davé, 1965; Karabenick & Youssef,
1968), selection of novel and more difficult tasks as previous tasks are mastered
(Atkinson, 1957), heightened subjective probabilities of success (Atkinson, 1957), recall
of incomplete tasks when performance is interrupted (Atkinson, 1953), choice behavior
leading to patterns of persistence when confronted with failure (Cooper, 1983; Feather,
1961), and tendencies toward the delay of gratification (Mehrabian, 1968). Furthermore,
affect was posited as the primary driver underlying need for achievement (McClelland et
al., 1953). High standing on need for achievement is associated with feelings of positive
affect or satisfaction derived from striving and the anticipation of success in
achievement-related endeavors; conversely, low standing on need for achievement is
associated with feelings of defensiveness and a fear of failure stemming from the
anticipation of poor performance (McClelland et al., 1953). Rooted in the hedonic
principle, this distinction between approach and avoidance motivation has been adopted
by psychologists as diverse as E. L. Thorndike, Tolman, Hebb, Maslow, and Eysenck
(Elliot, 1999) and remains a central premise in many contemporary theories of
motivational psychology (Higgins, 1997).
Atkinson (1957, 1974) integrated the construct of need for achievement into a
model of achievement motivation that attempted to account for action selection, exertion,
and persistence in achievement settings. This model was, in essence, an integration of
trait-based and cognitive-motivational perspectives, viewing the tendency to achieve

18

success (Ts) as multiplicative function of need for achievement (Ms), the strength of the
individual‟s expectancy, or subjective probability, for achieving success (Ps), and the

attractiveness, or valence, associated with achieving success (Is; Atkinson, 1974). Based
on this formulation, Atkinson hypothesized many of the cognitive manifestations
associated with need for achievement listed previously. Subsequent researchers sought to
verify and extend upon the propositions laid out in Atkinson‟s theory (e.g., DeCharms &
Davé, 1965; Feather, 1961; Karabenick & Youssef, 1965; Raynor, 1969, 1970).
Over the years, the predominant stream of research in the domain of achievement
motivation has shifted (Elliot, 1999). With the introduction of cognitive and sociallearning perspectives into achievement motivation research between the 1950‟s and
1970‟s, interest in trait-based perspectives declined. The shift was evident early on
among researchers studying need for achievement, as the construct was merged into
models comprising constructs derived from the cognitively-oriented perspectives.
Subsequent researchers in the social psychological and educational disciplines redirected
their efforts to the study of attributional processes (e.g., Kukla, 1972a, 1972b; Weiner &
Kukla, 1970), self-perceptions of ability and beliefs regarding the determinants of
outcomes in achievement situations (e.g., Bandura, 1977; Dweck & Leggett, 1988;
Rotter, 1990), and goals in achievement environments (e.g., Duda & Nicholls, 1992;
Dweck, 1986; Harackiewicz & Elliot, 1993). Over the same time period, cognitive
perspectives were pervasive in many theories of work motivation, as reflected in research

19

on goals and intentions (e.g., Locke, 1968; Locke, Shaw, Saari, & Latham, 1981) and
expectancy theory (e.g., Lawler & Suttle, 1973; Vroom, 1964).
While a number of factors likely lead to the declining interest in need for
achievement, one area that has caused considerable controversy has been the
measurement of the construct. Over the years, need for achievement has been
operationalized using projective measures (e.g., the Thematic Apperception Test [TAT],
Iowa Picture Interpretation Test, Test of Insight), self-report measures (e.g., Mehrabian,
1968; Steers & Braunstein, 1976), and hybrid measurement systems incorporating
projective and self-report components (e.g., Puca, 2005; Puca & Schmalt, 1999). Until
the 1970s, projective measures were the most widely used means of operationalizing
need for achievement (Hermans, 1970; Klinger, 1966), with McClelland, Atkinson, and
colleagues relying primarily on the TAT.
Early research and reviews of the literature suggested that projective measures
exhibited poor internal-consistency and test-retest reliability, a near-absence of
convergence between projective measures of need for achievement, and low criterionrelated validity (e.g., Entwisle, 1972; Klinger, 1966). Fineman (1977) concluded that
there can be little “confidence that the TAT is measuring any unitary psychological
construct, let alone nAch,” (p. 8; see also Hermans, 1970). Other criticisms levied against
projective measures of need for achievement included concerns regarding the impact of
the motive-arousing instructions used to activate latent motives prior to administration of
the TAT (Klinger, 1966), arguments that scores on projective measures are likely
contaminated by ability (Entwisle, 1972), and suggestions that projective measurement is

20

not amenable to applied settings due to the difficulty associated with administration and
the likely elicitation of poor test-taker reactions (Fineman, 1977).
Due to the logistical and measurement problems discussed with respect to
projective measurement, a large number of self-report measures of need for achievement
have proliferated throughout the literature (Fineman, 1977). These scales exist as
components of larger personality inventories (e.g., CPI, PRF, NEO PI-R), as well as
stand-alone measures developed explicitly to assess need for achievement (Kanfer &
Heggestad, 1997). Estimates of internal-consistency have often been quite low (e.g.,
Geiger & Cooper, 1995; Slade & Rush, 1991; Williams & Woodward, 1980; Yukl &
Latham, 1978). However, convergent validities among self-report measures of nAch and
similar constructs have been stronger than those obtained with projective measures (e.g.,
Mehrabian, 1969; Miller, Woehr, & Hudspeth, 2002; Steers & Braunstein, 1976;
Steinmayr & Spinath, 2009; although see Entwisle, 1972; Fineman, 1977; Wotruba &
Price, 1975). Researchers have lamented the lack of similarity between various selfreport measures of need for achievement with regard to item content (Fineman, 1977),
suggesting that these measures may be tapping distinct constructs or subfacets of the
higher-order need for achievement construct (Cassidy & Lynn, 1989).
Given the concerns listed above, it is not surprising that projective and self-report
measures of need for achievement have failed to exhibit convergence with one another
(e.g., Klinger, 1966), with large-scale studies and meta-analyses yielding estimated
correlations between projective and self-report of .08 and .15 (Fineman, 1977; Spangler,
1992). The lack of convergence between projective and self-report measures of need for
achievement has long been acknowledged. Throughout much of his career, McClelland

21

(1985; McClelland et al., 1953; McClelland et al., 1989) argued for the use of projective
measurement in research on need for achievement (ironically, proponents of projective
measurement for assessing need for achievement have frequently used self-report
measures to assess fear of failure, the avoidance component of achievement motivation).
McClelland‟s arguments were based on several grounds, often tied to the level of
conscious accessibility associated with motives and the theoretical foundation of need for
achievement in affect. These included: (1) projective measures assess unconscious
motives, while self-report measures assess conscious motives; (2) projective measures
assess affective bases of need for achievement, while self-report measures tap cognitive
aspects of the construct; (3) many people are not capable of accurately reporting their
motives or will distort their responses, and; (4) implicit motives reflect a general
orientation toward certain types of goals, while explicit motives combine with explicit
goals associated with doing well in a particular achievement domain (e.g., academics,
employment; McClelland, 1985; McClelland et al., 1989). These arguments have not
always been met with acceptance (e.g., Fineman, 1977; Locke & Latham, 2004).
However, the implicit-explicit motive distinction is one that still carries use in current
research and theorizing on achievement motivation (e.g., Kehr, 2004; Thrash & Elliot,
2002).
Renewed interest in trait conceptualizations of achievement motivation. During
the same period that interest in need for achievement waned in social psychological and
educational circles, researchers within social/organizational psychology attempted to
integrate the construct into various theoretical and empirical frameworks. Thus,
researchers interested in job design (Orpen, 1985; Steers & Spencer, 1977), leadership

22

(Arvey & Dewhirst, 1976), organizational attraction (Turban & Keon, 1993), and
entrepreneurial behavior (e.g., Collins, Hanges, & Locke, 2004) have examined the
construct in an attempt to highlight the role of individual differences in various social
processes within organizations. Similarly, goal-setting researchers have long viewed need
for achievement as a potentially important individual difference construct (e.g., Locke,
Shaw, Saari, & Latham, 1981; Matsui, Okada, & Kakuyama, 1982; Steers, 1975;
Wofford, Goodwin, & Premack, 1992; Yukl & Latham, 1978).
In addition to growing interest in organizational psychology, recent attempts to
develop trait-based perspectives of achievement motivation have been influenced greatly
by classic conceptualizations of need for achievement. For example, Cassidy and Lynn
(1989) developed a 49-item scale based on a faceted perspective of need for achievement
incorporating seven lower-order constructs: work ethic, pursuit of excellence, mastery,
status aspiration, competitiveness, acquisitiveness for money and material wealth, and
dominance. Story, Hart, Stasson and Mahoney (2009) presented a two-factor theory
extending upon the Cassidy and Lynn (1989) structure, with the facets divided into
intrinsic motivation (work ethic, pursuit of excellence, and mastery) and extrinsic
motivation (acquisitiveness for money and wealth, dominance, competitiveness, and
status aspiration). Story and colleagues‟ perspective is particularly useful, in that it
distinguishes between aspects of trait-based need for achievement arising from both
internal and external cues and stimuli.
In the industrial/organizational psychology literature, Kanfer and Heggestad‟s
(2000; Kanfer & Ackerman, 2000) conceptualization of motivational traits illustrates a
recent example of a modern trait-based perspective of achievement motivation. Based on

23

a review of the need for achievement and avoidance motivation/test anxiety literature and
several empirical studies, Kanfer and Heggestad (2000) developed the Motivational Trait
Questionnaire (MTQ), a multidimensional measure of trait motivation comprising three
distinct higher-order factors: Personal Mastery, Competitive Excellence, and
Achievement Anxiety. Kanfer and Ackerman (2000) described Personal Mastery as an
appetitive motivational trait based on the facets Desire to Learn and Mastery.
Competitive Excellence includes both Other Referenced Goals (a combination of
approach and avoidance-related characteristics) and Competitiveness (approachoriented). Achievement Anxiety was described as including both two avoidance-related
tendencies, Worry and Emotionality, associated with negative cognition and emotionality
in evaluative contexts.
Finally, recent theoretical frameworks in motivational psychology often include
need for achievement as a key distal individual difference trait. For example, Elliot and
colleagues‟ (e.g., Elliot, 1999; Elliot & Church, 1997; Elliot & Thrash, 2001; Thrash &
Elliot, 2002) hierarchical model of achievement motivation positions trait achievement
motivation as a distal predictor of achievement goals (i.e., performance-approach,
mastery-approach, performance-avoid, mastery-avoid). Payne, Youngcourt, & Beaubien
(2007) also view need for achievement as an antecedent to goal orientation along with
several other individual difference characteristics (e.g., cognitive ability, general selfefficacy, self-esteem). Steel and König‟s (2006) temporal motivational theory includes
needs broadly, and need for achievement in particular, as dispositional characteristics
impacting upon people‟s perceptions of outcome evaluation. In the training literature,
Colquitt and colleagues‟ (2000) model of training motivation views achievement

24

motivation as a dispositional antecedent to several proximal characteristics, including
pre-training self-efficacy, valence, and job/career constructs. Finally, more recent models
associated with goal-setting constructs have also included need for achievement as a
stable antecedent (e.g., Campbell, 1982; Phillips & Gully, 1997).
Validity of need for achievement/trait achievement motivation. Need for
achievement has been examined as an antecedent of many proximal mediating constructs
in both applied and basic motivational research. This research highlights a number of
outcomes associated with high standing on need for achievement likely to be beneficial
for task performance. The most consistent outcomes of need for achievement that have
been recently examined are individuals‟ achievement goals. Need for achievement, or
facets of it, has been found to be a consistent positive predictor of mastery goals (Bipp,
Steinmayr, & Spinath, 2008; Durik, Lovejoy, & Johnson, 2009; Elliot & Church, 1997;
Elliot & Murayama, 2008; Harackiewicz, Barron, Tauer, & Elliot, 2002; Payne et al.,
2007; Steinmayr & Spinath, 2009; Thrash & Elliot, 2002; VandeWalle, 1997), with
uncorrected correlations commonly in the upper .30s for global need for achievement
scales and evidence of stronger correlations for facet scales. Although somewhat weaker
in magnitude, consistent positive correlations have also been found with performanceapproach goals (Bipp et al., 2008; Durik et al., 2009; Elliot & Church, 1997; Elliot &
Murayama, 2008; Steinmayr & Spinath, 2009; Thrash & Elliot, 2002; VandeWalle, 1997;
however, see Payne et al., 2007). Need for achievement also appears to be a negative
predictor of both work avoidance and performance avoidance goals (Bipp et al., 2008;
Harackiewicz et al., 2002; Payne et al., 2007; Steinmayr & Spinath, 2009; VandeWalle,
1997).

25

In addition, need for achievement has been found to predict self-efficacy and
similar constructs (e.g., subjective probabilities of success, generalized expectancy for
success, self-reported competence; Elliot & Church, 1997; Kirk & Brown, 2003; Puca,
2005; Steel, Mento, Davis, & Wilson, 1989; Steinmayr & Spinath, 2009; Story et al.,
2009), goal and task difficulty (Matsui et al., 1982; Puca & Schmalt, 1999; Yukl &
Latham, 1978), behavioral, physiological, and self-report measures of effort allocation
(Capa, Audiffren, & Ragot, 2008a, 2008b; Geiger & Cooper, 1995), and learning
strategies and academic-related skills (Busato, Prins, Elshout, & Hamaker, 1999, 2000;
Robbins et al., 2004). Finally, need for achievement has been found to be positively
related to interest and task-relevant positive affect (Barron & Harackiewicz, 2001;
Harackiewicz et al., 2002; Puca & Schmalt, 1999) and self-reported feedback seeking
behavior (VandeWalle, 1997) and negatively related to procrastination (Steel, 2007).
Although many of these studies were conducted more than 50 years after McClelland and
colleagues‟ initial theorizing on need for achievement (and Murray‟s theorizing before
that), the pattern of results conforms quite well to early descriptions of characteristics
associated with high standing on the trait.
With regard to behavioral outcomes, a large number of studies have examined
need for achievement as a predictor of performance in both educational and work
environments. Early research on the relationship between need for achievement and
ratings or objective measures of job performance produced inconsistent results, often
resulting in nonsignificant relationships and correlations that appeared to vary greatly
between studies (e.g., Fineman, 1975; Steers, 1975; Steers & Braunstein, 1976; Steers &
Spencer, 1977; Tziner & Elizur, 1985; Yukl & Latham, 1978). However, much of this

26

research was characterized by small sample sizes and measures of need for achievement
with questionable psychometric characteristics. Recent results from large-scale studies
and meta-analyses indicate that measures of need for achievement/achievement
motivation have yielded relatively weak correlations with measures of job and task
performance (in the mid .10s; Dudley, Orvis, Lebiecki & Cortina, 2006), although
estimates for training performance have been more favorable (r = .33; Hough, Eaton,
Dunnette, Kamp, & McCloy, 1990).
Recent large-scale studies and meta-analyses on the relationship between
achievement motivation and performance have also been conducted in the academic
domain. Robbins and colleagues (2004) reported a mean uncorrected correlation of .257
between achievement motivation and performance (90% CI = .221,.292, 90% CV =
.136,.471). The researchers also found a weaker non-zero relationship with retention
(mean r = .105; 90% CI = .042,.168), although the 90% credibility interval overlapped
with zero (-.083–.214). Lievens, Ones, and Dilchert (2009) reported increasing
operational validities for achievement motivation in predicting medical school GPA
across seven years. Aside from the first year (.14), estimates were .31 or higher, reaching
a maximum of .48 during the sixth year of school. Durik and colleagues (2009) reported a
negative correlation between the Work Mastery subscale of Spence and Helmreich‟s
(1983) achievement motivation measure and diversity in course selection. Durik and
colleagues hypothesized that the negative relationship was due to a tendency for highly
motivated students to either direct their interests into specific areas of study or to enter
into college with plans that were more solidified than those who were less motivated.

27

Summary. Research has shown need for achievement to be associated with a
number of beneficial outcomes likely to result in strong performance in work and
educational environments. Validities for need for achievement in predicting training and
academic performance have been promising, although relationships with job and task
performance have been relatively weak. Given recent advances with regard to conceptual
models of performance (e.g., Borman & Motowidlo, 1993; Campbell et al., 1993) and the
measurement of individual differences in trait motivation (e.g., Cassidy & Lynn, 1989;
Kanfer & Heggestad, 2000), additional research is warranted to examine whether these
estimates still hold.
Thus far, the discussion has focused on ability and trait motivation as isolated
predictors of performance in applied settings. Both domains stem from a relatively long
theoretical tradition and, for each, empirical research has demonstrated outcomes
(affective, behavioral, or cognitive) beneficial for task performance in educational and
work settings. However, in many cases, theorizing and research has tended to emphasize
one domain (e.g., ability) to the relative exclusion of the other, despite the commonlyheld position that both ability and motivation are both fundamental determinants of
performance. The next section transitions to a review of research that has attempted to
explain how individual differences in ability and motivation function together to explain
inter-individual variability in performance in applied contexts.
The Interaction Hypothesis: M + A or M × A?
Among researchers interested in ability- and motivation-based determinants of
performance, one issue that has let to persistent controversy pertains to the functional
form of the relationship between performance on the one hand, and ability and motivation

28

on the other (Locke et al., 1978). Two opposing viewpoints have been prominent in this
debate (Mount et al., 1999), namely an additive-model perspective and a multiplicativemodel perspective. Those subscribing to an additive-model perspective suggest that
motivation and ability contribute to performance in an isolated manner, with each
determinant having positive, independent effects upon performance (Mount et al., 1999).
This perspective implies that the influence of one domain (e.g., motivation) on
performance is constant across varying levels of the other domain (e.g., ability).
Those subscribing to a multiplicative-model perspective suggest that motivation
and ability function interactively in determining performance, such that constructs in one
domain (ability) are expected to exert a stronger effect on performance among individuals
who are higher in the other domain (motivation; Lawler, 1966; Sackett et al., 1998;
Wright et al., 1995). Dating to researchers in the 1950s and 1960s (e.g., Gagné &
Fleishman, 1959; Maier, 1955; Vroom, 1964), the multiplicative-model perspective
implies the notion that, regardless of one‟s standing on the latent ability construct(s)
relevant to the performance on the task at hand, one cannot exhibit high performance if
one does not also put forth effort in applying his or her ability to that task (e.g., French,
1958). The concept can be framed with motivation as the referent construct, as well;
regardless of one‟s level of motivation to perform, high levels of performance cannot be
expected if one does not have the requisite ability needed to perform at a certain level.
These additive and multiplicative perspectives jointly form what Mount and colleagues
(1999) referred to as the interaction hypothesis, with the multiplicative-model perspective
referring to the alternative hypothesis and the additive-model perspective referring to the
null hypothesis.

29

Theoretical perspectives relevant to the interaction hypothesis. A number of
explanations have been put forth to explain why a multiplicative model should be a valid
account of how ability and motivation influence performance. Unfortunately, many
applied researchers have posited “person-on-the-street” accounts, much like those
described in the previous paragraph, for why such an interaction should exist. Although
these descriptions provide a lay-oriented heuristic that is easy to communicate and grasp,
they carry no theoretical utility, as there is no attempt to describe the intervening
processes that explain why such explanations would hold true. This has often been the
case for researchers who attempt to integrate ability into expectancy-theory models (e.g.,
Dachler & Mobley, 1973). As noted by Campbell and Pritchard (1976), the lack of detail
provided in explanations for such an ability-motivation interaction in expectancy models
was likely a primary cause for the recurrent nonsignificant findings observed for
interactive effects, as will be discussed below.
Kanfer and Ackerman (1989) went beyond a simplistic description and
justification for why ability and motivation should interact to influence task performance.
Kanfer and Ackerman‟s (1989) resource allocation theory relates the concepts of ability
and effort to attentional resources (see also Humphreys & Revelle, 1984 for a similar
perspective). According to this perspective, ability denotes inter-individual variability in
the total amount of attentional capacity that is available to be allocated to a given task.
Effort denotes the proportion of attentional resources allocated. During the declarative
stage of skill acquisition, the task taxes the individual‟s attentional resources by
confronting him or her with a novel task environment within which task strategies, rules,
and instructions for performance must be learned. Thus, on a moderately difficult task,

30

the declarative stage is both ability- and effort-intensive. From a within-persons
perspective, the individual then progresses through the remaining stages of skill
acquisition, assuming a task with consistent information-processing demands, which
subsequently leads to a reduction in the amount of effort that must be invested toward the
task to achieve a given level of performance. However, from a between-persons
perspective, individual differences in ability explain the rate at which different people
progress through these stages. Other factors held constant, individuals high in ability will
proceed at a faster rate than those who are low in ability. Therefore, for those high in
ability, the relationship between effort and performance should decrease at a faster rate
than for those low in ability.
Other researchers have provided explanations of the joint role of ability and
motivation in determining performance, although these have generally been less
formalized than that posited by Kanfer and Ackerman‟s resource allocation theory. For
instance, Bell and Kozlowski (2002) suggested that ability moderates the relationship
between goal orientation and both performance and knowledge. According to this
perspective, learning goal orientation should be positively related to both performance
and knowledge among high-ability individuals, but negatively related to performance and
knowledge among low-ability individuals. The rationale for this hypothesis was that
individuals who adopt learning goals tend to use complex learning strategies and engage
in more effortful information processing when confronting a novel task. Individuals high
in ability should have the necessary resources needed to apply and benefit from such
learning strategies. Conversely, those who are low in ability may be impeded by
attempting to use strategies that are difficult to implement. Bell and Kozlowski further

31

hypothesized that performance goal orientation should be negatively related to
performance and knowledge among high-ability individuals, but positively related to
performance and knowledge for low-ability individuals. High-ability individuals who
adopt performance goals constrain their development by utilizing simpler task strategies,
while low-ability individuals may benefit from applying less complex strategies by
reducing the extent to difficulty associated with learning.
Empirical evidence pertaining to the interaction hypothesis. Results from field
studies in work settings testing the interaction hypothesis have been quite inconsistent.
Several studies have found evidence for a significant interaction between ability and
motivation in predicting performance (e.g., Hollenbeck, Brief, Whitener & Pauli, 1988;
Lawler, 1966; Wright et al., 1995). For example, Hollenbeck and colleagues (1988)
tested the significance of ability-motivation interactions involving measures of both selfesteem and locus of control in one sample of employees and self-esteem in a second
sample. In the first sample, a significant interaction was found between locus of control
and ability (SAT); no evidence was found for an interaction with self-esteem. In the
second sample, a significant interaction was found between self-esteem and ability (the
Aptitude Index Battery).
Lawler (1966) divided a sample of state employees into high- and lowcontingency groups, where contingency was defined with respect to the degree to which
pay was perceived as being contingent upon job performance. Lawler found support for
an interactive effect between the two variables. For those low in ability, perceptions of
pay-performance contingency were not related to performance, with reported correlations
in the low .10s. For those high in ability, contingency did correlate with performance.

32

Those who perceived a high pay-performance contingency had stronger performance,
with observed correlations reported at .35 and .30 for self- and supervisor ratings,
respectively.
Wright and colleagues (1995) investigated the significance of interactive effects
between cognitive ability (a four-test composite that included the Wonderlic) and the
need for achievement scale from the PRF for a sample of warehouse employees. Zeroorder correlations between performance and both ability and need for achievement were
not significant; however, the interaction between ability and need for achievement was,
accounting for an additional nine percent of performance variance beyond the main
effects. The form of the interaction was such that need for achievement was positively
related to performance among those high in ability, but negatively related to performance
among those low in ability.
In addition to the studies cited above, there are also a number of other field
studies failing to find evidence for interactive effects. Several of these studies were in the
expectancy theory stream of research (e.g., Dachler & Mobley, 1973; Galbraith &
Cummings, 1967; Lawler & Suttle, 1973; for reviews, see Campbell & Pritchard, 1976;
Heneman & Schwab, 1972); others were not, focusing on interactions between self-report
personality scales and ability measures (e.g., Mount et al., 1999; Sackett et al., 1998). It
should be noted that several of the expectancy theory studies did not actually test the
interaction hypothesis as intended. For example, Dachler and Mobley (1973) did not
examine the hypothesis in either of their samples; ability scores were available for only a
subset of employees in one sample and ability was uncorrelated with performance for the
second sample. Galbraith and Cummings (1967) set out to test the interaction between

33

ability and motivation in predicting performance; however, they operationalized ability
using tenure. Because a host of other factors likely serve to influence tenure, it would
seem unlikely that this variable would provide a construct valid measure of ability. These
examples characterize the quality of research on the interaction hypothesis within the
expectancy-theory stream of research. In many cases, hypotheses were tested on small
samples using crude methods employed on unreliable measures or questionable proxies
for the constructs of interest.
Mount and colleagues (1999) and Sackett and colleagues (1998) each conducted
multiple-sample studies to assess the feasibility of the interaction hypothesis. In each
case, results were largely disconfirmatory. In three studies, Mount and colleagues (1999)
found no evidence of interactive effects between PCI Conscientiousness and scores on
the Wonderlic, with negligible incremental variance in performance explained by the
interaction. In four studies, Sackett and colleagues (1998) reported largely
disconfirmatory evidence for the interaction hypothesis using different measures of
ability and two personality characteristics (dependability, need for achievement) and
various criteria.
In addition to the field studies cited above, a number of researchers have tested
the interaction hypothesis in lab and educational settings. Compared to field research in
organizational contexts, studies conducted in academic settings have often resulted in
findings supporting the interaction hypothesis (e.g., Edwards & Waters, 1981; Ganzach,
Saporta, & Weber, 2000; Hirschfeld, Lawson, & Mossholder, 2004; Nonis & Wright,
2003; Rosopa & Schroeder, 2009). Semester, yearly, or cumulative GPA has generally
served as the criterion measure, with self-report measures of personality and ability tests

34

serving as predictor measures. In most cases, the form of the relationship has been such
that high standing on trait motivational characteristics increases the validity of ability for
predicting performance (e.g., Edwards & Waters, 1981; Hirschfeld et al., 2004; Nonis &
Wright, 2003; Rosopa & Schroeder, 2009) or that high standing on ability increases the
validity of motivational attributes for predicting performance (e.g., Hollenbeck et al.,
1988; Nonis & Wright, 2003).
Likewise, studies conducted in laboratory settings, often employing psychomotor
tasks or simulations to operationalize performance, have provided more consistent
evidence for the interaction hypothesis than have field samples in work settings (e.g., Bell
& Kozlowski, 2002; Fleishman, 1958; French, 1958; Kanfer & Ackerman, 1989; Locke
et al., 1978; Yeo & Neal, 2004), although there are exceptions (Terborg, 1977). The types
of ability-performance interactions hypothesized and observed have also differed across
lab studies. Many researchers have focused on examining the incremental validity of a
cross-product term above a set of first-order predictors in a standard fixed-effects OLS
regression. Others have examined cross-level interactions between ability and
motivational variables, where levels differentiate within- and between-persons effects, so
as to better understand how stable individual differences and proximal characteristics
function together to influence how performance unfolds over time (e.g., Kanfer &
Ackerman, 1989; Yeo & Neal, 2004).
Critique of extant research relating to the interaction hypothesis. Looking at the
set of studies reviewed above as a whole, two patterns emerge. First, tests of the
interaction hypothesis in laboratory and academic settings do not necessarily converge
with those found in organizational contexts. Second, tests of the interaction hypothesis

35

conducted within organizational settings have been somewhat contradictory, with some
researchers finding support (e.g., Hollenbeck et al., 1988; Wright et al., 1995) and others
not (e.g., Lawler & Suttle, 1973; Mount et al., 1999; Sackett et al., 1998). A number of
potential reasons can be put forth to explain the variability in findings that have emerged.
First, much of the research on the interaction hypothesis is characterized by poor
measurement of the predictor domain, as reflected in varying definitions of attributes in
the motivational and abilities domains. With regard to motivational characteristics, a host
of constructs have been examined: expectancy-theory characteristics (e.g., Lawler &
Suttle, 1973), goal orientation (Bell & Kozlowski, 2002), need for
achievement/achievement motivation (French, 1958; Hirschfeld et al., 2004; Sackett et
al., 1998), dependability (Sackett et al., 1998), effort (Terborg, 1977; Yeo & Neal, 2004),
broad or complex personality characteristics (Mount et al., 1999; Rosopa & Schroeder,
2009), manipulations intended to influence goal characteristics or other state-like
motivational attributes (e.g., Kanfer & Ackerman, 1989; Locke et al., 1978), trait selfesteem (e.g., Hollenbeck et al., 1988), attitudinal variables (e.g., Lawler, 1966), and role
perceptions (Lawler & Suttle, 1973).
In many cases, a rationale for examining a given motivational characteristic is not
explicated by the researcher. This amounts to the implicit assumption that motivation,
whether trait-like or state-like in nature, can be treated as an undifferentiated construct
that should yield comparable results regardless of how it is theoretically or operationally
defined. In addition, questions have been raised about the use of between-subjects
designs to study propositions derived from expectancy theory (Campbell & Pritchard,
1973) and about the predictive utility of expectancy theory in general (Heneman &

36

Schwab, 1972). To the extent that such arguments are true, one must question whether
the general pattern of disconfirming findings from studies using expectancy-value
constructs and operationalizations is of any use at all with regard to the validity of the
interaction hypothesis.
The measurement of ability characteristics in research on the interaction
hypothesis has not always fared much better than has been the case for motivation. Many
researchers have operationalized ability constructs using traditional psychometric ability
tests (e.g., Hirschfeld et al., 2004; Mount et al., 1999; Sackett et al., 1998; Terborg,
1977). However, ability has also been operationalized using measures of questionable
construct validity, including tenure (Galbraith & Cummings, 1967), tests for which no
description of validity or reliability is provided (Dachler & Mobley, 1973), supervisor
rankings (e.g., Lawler, 1966), and performance during early or practice trials of the same
measure used to define criterion performance (Fleishman, 1958; Locke et al., 1978).
Heneman and Schwab (1972) criticized the use of tenure and super rankings as measures
of ability, calling instead for researchers to use standardized tests. Ackerman (1989)
questioned the use of early-trial or practice performance on the same task used to define
criterion performance as a measure of ability.
Questions regarding measurement also arise when examining how researchers
have operationalized the performance side of the equation. Much of the research has
examined traditional measures of performance used in the personnel and education
domains, including supervisory judgments (Lawler, 1966; Mount et al., 1999; Sackett et
al., 1998), objective measures of employee output (Dachler & Mobley, 1973; Galbraith &
Cummings, 1967; Hollenbeck et al., 1988), GPA (Hirschfeld et al., 2003; Hollenbeck et

37

al., 1988; Nonis & Wright, 2003), and graduation (Ganzach et al., 2000). Others have
examined performance on psychomotor or perceptual speed tasks (Fleishman, 1958;
French, 1958; Locke et al., 1978), self-ratings of performance (Lawler & Suttle, 1973),
judgments of performance from the same supervisor providing judgments of ability
(Lawler, 1966), performance on air traffic control or decision-making simulations (Bell
& Kozlowski, 2002; Kanfer & Ackerman, 1989; Yeo & Neal, 2004), managerial level
attained (Sackett et al., 1998), and time spent working on proficiency tests (Terborg,
1977).
Judgments of the appropriateness of a given performance measure will vary
depending on the interests of the researcher; those interested in predicting employee
performance will likely choose different criterion measures from those interested in skill
acquisition. However, it has long been acknowledged that applied psychologists are often
predictor-centric (Ford, Kraiger, & Schechtman, 1986; James, 1973; Jenkins, 1946;
Toops, 1944), placing greater emphasis on the quality of predictor measures while
accepting whatever criterion that happens to be available (Thayer, 1992). This situation is
problematic, given that it is not feasible to design or select appropriate predictor measures
without some clarity as to what performance means in a given context (Kane, 1986).
The present purpose is not to question the reliability or construct validity of
specific criterion measures employed in research on the interaction hypothesis, but to
make explicit the implications that follow from the choices made with regard to
adequately testing the interaction hypothesis. For instance, researchers have examined
distal, trait-like measures of motivation as predictors of both broad, long-run performance
measures (e.g., supervisor ratings) and specific, short-term performance measures (e.g.,

38

simulation performance, performance on psychomotor tasks). However, these same
researchers have not always explicated the rationale for why a given motivational
construct should be relevant to performance at different levels of bandwidth or timeframe
in the performance domain, nor how that construct is theoretically expected to operate in
the context at hand. It is feasible that this mixing of criteria has resulted in the pattern of
inconsistent results observed, given that aggregating measures of behavior over situations
often yields different patterns of results than those obtained on single or short-run
measures of behavior (e.g., Epstein, 1979, 1980).
Finally, Hirschfeld and colleagues (2003) have suggested that one reason for past
inconsistency in research on the interaction hypothesis pertains to the manner in which
trait motivation has been operationalized, specifically with respect to self-report
measures. Researchers interested in trait motivation have often used global, context-free
measures in research on the interaction hypothesis. As Hirshfeld et al. (2003) note, the
theory underlying the interaction hypothesis implies that motivation determines or
reflects the amount of resources allocated to tasks in a given context (e.g., school, work).
Because global trait measures do not provide a frame of reference for respondents to use
in evaluating item content, these respondents may generate responses that reflect a
different frame of reference that does not reflect how the individual behaves or thinks in
the intended context. In support of this argument, Hirschfeld and colleagues found that a
contextualized measure of achievement motivation had higher criterion-related validity
and explained variance above and beyond that of a context-free measure of the same trait
for predicting student GPA. They also found support for the interaction hypothesis with
the contextualized measure, but not the context-free measure.

39

Summary. Theorizing on the interaction hypothesis began with general,
unspecified explanations for why constructs in the ability and motivational domains
should interact in accounting for between-persons variation in performance. Perhaps
unsurprisingly, results from subsequent studies investigating the interaction hypothesis
were largely inconsistent. However, much of the empirical research in this area has
suffered from measurement and conceptual limitations that may account for variability in
results across studies (e.g., operational definitions with questionable reliability and
construct validity, lack of specification or explanation for the relevance of the motivation
construct studied, lack of specification or explanation for the relevance of the predictor
constructs studied with regard to the type of performance in question). More recently,
detailed accounts and explanations of the interaction hypothesis have been put forth and
tested (e.g., Kanfer & Ackerman, 1989). Furthermore, in spite of the unsupportive
evidence discussed above, supportive findings have been reported in various contexts.
The pattern of results has yielded somewhat of a controversy. Some researchers have
concluded that the interaction hypothesis is an unlikely explanation for how ability and
motivation influence performance; others have highlighted the limitations of prior
research and suggest that the interaction hypothesis may still hold in certain situations.
Therefore, a tentative conclusion would be that, although much of the research on the
interactive hypothesis has been unsupportive, an outright rejection of the interaction
hypothesis may be premature at this juncture.
To this point, the review has focused on individual difference determinants of
performance in the ability and motivational domains, considered both in isolation and
together. However, less attention has been placed on the performance domain in question.

40

One perspective particularly relevant for the present paper pertains to the temporally
varying nature of performance, as is often observed when measures of the same
performance construct are collected for the same individuals over several points in time.
Very little research linking the interaction hypothesis to current perspectives of
performance over time has been conducted; the research that has been conducted carries
with it limitations that question its generalizability to long-run performance in
educational and work contexts. So as to provide background for the integration of theory
and research on the interaction hypothesis and performance in a time-varying context, the
next section reviews prior research on dynamic criteria and correlates of performance
trajectories.

41

DYNAMIC CRITERIA AND THE STUDY OF TRAJECTORIES IN PERFORMANCE
Dynamic Criteria: Initial Research, Theory, and Debate
Broadly speaking, the concept of dynamic criteria refers to the relative variability
or instability of worker performance measures over time (Deadrick & Madigan, 1990;
Steele-Johnson et al., 2000). For more than fifty years, questions regarding the existence
of dynamic criteria, the nature of the phenomenon, and the concept‟s implications for
applied measurement practice have appeared in the personnel selection literature. The
notion of dynamic criteria is a component of the larger “criterion problem” in applied
psychology (Ghiselli, 1956), which recognizes that performance measures are not only
temporally dynamic, but also factorially complex, situationally specific, and employed to
serve multiple (sometimes competing) organizational goals and functions (Austin &
Villanova, 1992). This state of affairs arises from the fact that the latent construct space
underlying performance can be measured in multiple ways, but that without a means of
direct comparison among measurement methods, difficulties arise as to ascertaining the
most appropriate method or operationalization to use (Gottfredson, 1991).
Despite recognition that the criterion problem in applied psychology reflects a
measurement problem in large part, it has often been lamented that applied researchers
have neglected or ignored issues associated with performance measurement at the
expense of developing and validating measures of predictor constructs, as noted above
(e.g., Ford et al., 1986; Ghiselli, 1956; Gottfredson, 1991; James, 1973; Jenkins, 1946;
Toops, 1944). Although this may be true, it would be a mistake to conclude that the

42

notion of dynamic criteria has been ignored by selection researchers; quite the opposite,
the topic has been the source of a great deal of controversy and debate (Ackerman, 1989;
Austin, Humphreys, & Hulin, 1989; Barrett & Alexander, 1989; Barrett, Alexander, &
Doverspike, 1992; Barrett, Caldwell, & Alexander, 1985, 1989; Henry & Noon, 1987,
1989).
Evidence for dynamic criteria. Barrett and colleagues (1985) discuss three means
by which dynamic criteria have been operationally defined (a fourth method of
examining dynamic criteria involving exploratory factor analysis of predictor measures
and criterion data gathered over time was also discussed, although this approach has long
been criticized on both methodological and conceptual grounds; Corballis, 1965;
Humphreys, 1960). The first definition pertains to changes in average level of group
performance over time. Barrett and colleagues (1985) dismissed this definition as being
conceptually and operationally weak, primarily due to the obscuring of individual-level
information that results from using mean curves.
The second definition entails changes in the rank-ordering of individuals on a
given criterion measure over time. A frequent observation in examinations of
intercorrelations among measures of a criterion over time is a simplex (Humphreys,
1960) or superdiagonal (Adams, 1987) pattern, characterized by large positive
correlations between measures at adjacent trials (e.g., time t and time t + 1) that become
progressively weaker in magnitude as the size of the interval between measurements
increases. Research addressing this definition has been conducted in both organizational
(e.g., Bass, 1962; Deadrick & Madigan, 1990; Ghiselli & Haire, 1956; Rambo, Chomiak,
& Price, 1983) and educational settings (e.g., Humphreys, 1968; Humphreys & Taber,

43

1973; Lin & Humphreys, 1977). The existence of declining between-trial
intercorrelations appears to be a standard observation; however, results from several field
studies (e.g., Butler & McCauley, 1987) question claims of the phenomenon‟s ubiquity
(Henry and Hulin, 1987).
The third operational definition of dynamic criteria discussed by Barrett et al.
(1985) relates to changes in validity coefficients between a predictor measured at one
point in time and a criterion measured at several points in time. Of the various operational
definitions of dynamic criteria explored in the selection literature, this definition appears
to result in the greatest disagreement and debate, likely due to its direct implications for
selection and admissions practice. Similar to the second definition described above, the
changing-validities phenomenon has been examined extensively in both organizational
(e.g., Bass, 1962; Deadrick & Madigan, 1990; Ghiselli & Haire, 1960; Helmreich et al.,
1986) and educational settings (e.g., Butler & McCauley, 1987; Lin & Humphreys, 1977;
Lunneborg & Lunneborg, 1970); large cross-domain summaries also exist (Barrett,
Alexander, & Doverspike, 1990; Hulin, Henry, & Noon 1990).
Several studies examining test-predictor correlations over time provide evidence
for declining validities (Bass, 1962; Humphreys & Taber, 1973; Lin & Humphreys, 1977;
Lunneborg & Lunneborg, 1970). Other studies provide mixed evidence, indicating that
validities for certain predictor measures appear to decline over time while others remain
consistent or increase as the time between predictor measurement and criterion
measurement increases (Butler & McCauley, 1987; Deadrick & Madigan, 1990; Ghiselli
& Haire, 1960; Helmreich et al., 1986). Mirroring findings obtained from the primary
studies, Hulin and colleagues‟ (1990) summary indicated that validities appeared to

44

decline over time; however, Barrett, Alexander, and Doverspike‟s (1992) reanalyzed
Hulin and colleagues‟ data and questioned the generalizability of the findings on
methodological grounds. Thus, in spite of more than 30 years of research effort invested
into the examination of test-predictor correlations over time in industrial and educational
settings, the picture was as unclear as it was at the outset.
Theoretical perspectives on dynamic criteria. Researchers investigating dynamic
criteria have posited a number of theoretical accounts of the phenomenon in an attempt to
explain empirical findings observed in field and laboratory settings. Broadly speaking,
these theories fall into three categories distinguishable on the basis of the underlying
factor believed to account for performance dynamism: changing persons, changing tasks,
or changing environments. Changing-persons theories postulate that, with practice, the
underlying person characteristics believed to account for performance change; however,
these characteristics‟ relative contribution to performance remains temporally invariant
(Alvares & Hulin, 1973). Alvares and Hulin (1973) frame the prediction of performance
on a given trial using a common-factor model of the form, xij = ∑(ajkyik) + eij + sj

th

(subscripts denoting the i

k

th

person measured on the j

th

trial with contributions from the

common ability factor). The changing-persons perspective thus suggests that

experience results in increases in ability yik with constant loading ajk.
Empirical tests of Alvares and Hulin‟s changing-persons model have yielded
mixed findings. In an early study investigating predictors of aviation training, Alvares
and Hulin (1973) administered pretest and posttest measures of various abilities, some
45

believed to be relevant for performance and impacted by the type of training in question
and others believed to be irrelevant and unaffected by training. Comparisons were made
between an experimental group enrolled in an aviation class and a control group
comprising participants not enrolled in the class. Gain scores, representing change from
pretest to posttest, were examined based on the prediction that gains should be larger for
the experimental group due to transfer effects, but only for relevant abilities likely to be
influenced by training. In addition, correlations between performance and each of the
pretest and posttest batteries were examined based on the prediction that pretest measures
should predict early performance while posttest measures would predict late
performance. Analyses of the gain scores provided some evidence for differential transfer
effects on the posttest ability measures; however, hypotheses regarding the validities
were largely not supported. Other empirical tests bearing on Alvares and Hulin‟s
changing-persons theory have also cast doubt on aspects of the theory (Dunham 1974;
Humphreys & Taber, 1973). The theory is also somewhat at odds with basic assumptions
regarding the stability of individual differences in the cognitive and personality domains
observed over relatively long time periods (e.g., Conley, 1984; Vaidya, Gray, Haig, &
Watson, 2002). However, it may be tenable for relatively specific, lower-order
characteristics that resemble malleable state-like constructs in the personality domain or
trainable skills or knowledge in the abilities domain, although Alvares and Hulin (1973)
explicitly suggested that the distinction between abilities and skills should be abandoned
entirely.
Changing-tasks theories postulate that factors associated with increasing taskrelevant experience (e.g., practice, the accumulation of task-relevant knowledge and

46

skills, reduction in novelty associated with the task, automaticity) change the
fundamental nature of the task itself for the individual. This view suggests that, although
the individual difference characteristics underlying performance may remain relatively
constant over time, those characteristics important for initial performance may not be the
same characteristics that are required for later performance. Alvares and Hulin (1973)
depict the changing-task model as one with temporally dynamic loadings ajk and constant
latent abilities yik. Over time, a large number of changing-task theories have been
postulated by researchers interested in work performance. In addition, many of these
models share quite a bit of commonality. The present treatment focuses largely on those
models developed over the past 30 years. Although not discussed herein, the theory
postulated by Fleishman arising from his program of research (e.g., Fleishman, 1953,
1960; Fleishman & Hempel, 1954, 1955; Fleishman & Parker, 1962; Fleishman & Rich,
1963) shares similarity with several recent frameworks, including Ackerman‟s theory of
skill acquisition.
As previously discussed, Kanfer and Ackerman‟s (1989) theory posits three
primary stages of skill acquisition (declarative knowledge, knowledge compilation, and
procedural knowledge) that differ with regard to the type of knowledge being acquired or
used, the degree of attentional load placed on the individual, and the speed and quality of
performance exhibited by the individual. Because the abilities relevant for performance
during each of these stages varies as a function of the demands placed on the individual
(i.e., declarative knowledge: general intelligence and broad content abilities; knowledge
compilation: perceptual speed; procedural knowledge: psychomotor ability), abilityperformance correlations are also expected to vary across stages.
47

Kanfer and Ackerman‟s (1989) theory does not explicitly address stable
individual differences in the motivational domain, which is somewhat of a limitation of
the theory for the present study. Rather, distal motivational processes in their model focus
on cognitive-motivational decision processes influencing goal choice and intended effort
allocation, while proximal motivational processes pertain primarily to on-task selfregulatory behavior. However, two perspectives put forth in the literature around the
same time as Kanfer and Ackerman‟s theory do take into consideration trait-like
motivational constructs. Helmreich et al. (1986) noted that much of the prior research
examining causes of dynamic criteria as relevant to individual differences focused almost
exclusively on the domain of human cognitive ability. Helmreich and colleagues (1986)
suggested that although predictive validities for measures of ability constructs may
decrease over time, there are several reasons to believe that measures of personality
attributes should increase in predictive validity as experience on the job accrues.
The primary rationale for the temporally increasing validities expected for
personality attributes stems from what Helmreich and colleagues referred to as the
“honeymoon effect,” or the idea that, as the novelty and initial challenge associated with
a job fades with experience, individual differences in task-relevant personality should
subsequently increase in importance. Using subscales derived from measures of
achievement motivation and interpersonal orientation to predict performance measured at
three points in time for a sample of telephone reservation representative incumbents,
Helmreich and colleagues found that three of the subscales (achievement motivation:
work; interpersonal orientation: expressivity, verbal aggression, and submissiveness)
showed significant increases in validity from initial performance to performance on a

48

second performance measurement, with validities appearing to stabilize by the third
performance measurement. Two of the achievement motivation measures (mastery and
competitiveness) did not predict performance, although the researchers noted that
mastery was likely not a relevant predictor for performance in the type of position
examined.
The central premise of Murphy‟s (1989) theory pertains to the distinction between
transition stages and maintenance stages of tenure. Transition stages occur early on in the
individual‟s job tenure or during periods of large change to task-relevant duties or
responsibilities. During transition stages, performance is largely dependent upon
cognitive ability because of the need for the employee to acquire knowledge and because
of the need to make accurate decisions in the absence of task-relevant experience.
Maintenance stages (see also Rambo and colleagues‟ [1983] discussion of maintenance
behaviors) correspond to periods of relative stability where tasks are relatively welllearned and do not impose strong attentional demands on the employee. At this stage,
employees understand how to perform the job‟s primary tasks; in addition, situations
confronting the individual with ambiguous or novel stimuli or demands become less
common. As a result, performance becomes less sensitive to variability in cognitive
ability and more sensitive to variability constructs in the domains of motivation and
personality. Murphy‟s theory has been influential on empirical research examining
cognitive and motivational predictors of job performance, although it seems relatively
difficult to operationalize and measure transitional and maintenance phases of employee
tenure in an unambiguous manner (Thoresen et al., 2004).

49

Finally, changing-environments perspectives highlight the role of dynamic
contextual processes both internal and external to the organization as a causal factor
underlying dynamic criteria. Collectively, these ideas supplement changing-persons and
changing-tasks perspectives by highlighting contextual factors that may also result in
criterion instability. Examples include changes in work-role requirements, tasks, and the
design of jobs (Deadrick & Madigan, 1990; Murphy, 1989), organizational objectives and
goals (Prien, 1966), incentive systems (Rambo et al., 1983), and opportunities and
constraints afforded by co-workers and parties external to the organization (Stewart &
Nandkeolyar, 2007). Hanges, Schneider, and Niles (1990 extended Murphy‟s (1989)
concept of maintenance stages by incorporating ideas derived from interactional
psychology. As previously mentioned, the notion of maintenance stages implies that
performance is likely to stabilize once work tasks are well learned and when changes in
work-relevant tasks and technology are not observed. Hanges and colleagues suggested
that this proposition holds only in the case when employees‟ perceptions of situational
characteristics also remain constant over time.
From Dynamic Criteria to Individual Differences in Performance Trajectories
As of the late 1980s and early 1990s, researchers interested in human
performance had posited various theories and informal frameworks to account for
phenomena associated with performance dynamism. As discussed above, these
perspectives highlighted the roles of changing persons, tasks, and environments. Most
theories attempted to account for change in one of these three areas; few integrative
treatments existed that sought to explain dynamic criteria from all three perspectives in
any type of detailed, comprehensive manner. In spite of the theoretical advancements

50

made in the dynamic criteria literature, however, researchers were still in a state of
disaccord regarding the relevance, interpretation, and implications of empirical research
findings pertaining to dynamic criteria.
Around the same time, Hofmann and colleagues (Hofmann, Jacobs, & Baratta,
1993; Hofmann, Jacobs, & Gerras, 1992) introduced a new perspective into the dynamic
criteria literature by demonstrating the utility of modeling interindividual differences in
performance trajectories over time. Hofmann et al. (1993) noted that an exclusive focus
on the interpretation of correlations and aggregated results fails to adequately describe the
nature of individual change over time (see also Estes, 1956). Although the idea of
examining rate of change over time was not novel within the dynamic criteria literature
(see Ghiselli & Haire, 1960 for an early examination of correlates of linear change in
performance), Hofmann and colleagues solidified the notion by providing a more detailed
treatment of the theoretical significance of examining change over time, by
demonstrating the application of specific analytic methods (e.g., hierarchical linear
modeling) as a means to modeling individual differences in performance trajectories, and
by providing initial evidence that such trajectories are both systematic and capable of
being predicted. Thus, it appeared that the dynamic criteria debate had been largely
resolved (Chen & Mathieu, 2008; Stewart & Nandkeolyar, 2007).
Hofmann and colleagues (1993) acknowledged that both organizational factors
and individual differences would likely influence the rate at which employees would
learn job-relevant tasks and that the importance of various attributes would likely wax
and wane over time. Several studies have examined the influence of contextual and
organizational characteristics on performance trajectories, including organizational

51

socialization (Chan & Schmitt, 2000; Lance, Vandenberg, & Self, 2000) and
opportunities and constraints afforded by other individuals (Stewart & Nandkeolyar,
2007). The present discussion examines the role of person characteristics as correlates of
performance trajectories.
Cognitive predictors of performance trajectories. Subsequent to Hofmann and
colleagues‟ work, researchers began to investigate correlates of individual differences in
performance trajectories. Skill acquisition researchers have examined cognitive
predictors of performance trajectories, although results have not been consistent. Voelkle
and colleagues (2006) found that spatial-numerical ability and perceptual speed were
significant predictors of both initial performance and linear growth on the TRACON air
traffic controller situation. In support of Ackerman‟s theory of skill acquisition, results
suggested that spatial-numerical ability was the stronger predictor of initial performance,
while perceptual speed was the stronger predictor of performance growth. Chen and
Mathieu (2008) examined general cognitive ability (self-reported SAT scores) and
working memory capacity as predictors of trajectories on a computer-based logic game.
Both general ability and working memory significantly predicted initial performance;
however, neither was a significant predictor of linear change in performance over time.
Eyring, Johnson, and Francis (1993) examined general cognitive ability, derived
from scores on the Wonderlic, as a predictor of learning rate on an air traffic control
simulation comparable to that of Kanfer and Ackerman (1989). In this case, withinsubjects variability in performance was modeled using a negative exponential model,
resulting in parameters denoting asymptotic performance and learning rate. Results
suggested that those high in ability began task practice at a higher level of performance,

52

but paradoxically increased at a slower rate compared to those lower in ability. Eyring
and colleagues interpreted this finding as indicating that subsequent increases in
performance are harder to attain for those high in ability because of initial high
performance (i.e., a ceiling effect on performance); therefore, controlling for initial
performance should result in a reversal of the ability-learning rate relationship. After
controlling for initial performance, however, the relationship between ability and learning
rate became nonsignificant. Finally, Yeo and Neal (2004) examined general cognitive
ability (Raven‟s APM) and a self-developed measure of dynamic spatial ability as
predictors of learning on an air traffic control task. Results suggested that although
dynamic spatial ability was significantly related to learning, general cognitive ability was
not.
Cognitive predictors of performance trajectories have also been examined over
time frames longer than that observed in a typical skill acquisition study; again, however,
results have not been entirely consistent. Deadrick, Bennett, and Russell (1997) examined
general cognitive ability and psychomotor ability (both computed from relevant GATB
aptitude scales) as predictors of performance trajectories for a sample of sewing machine
operators over 24 weeks. Results suggested that psychomotor ability predicted initial
performance, while cognitive ability did not; conversely, cognitive ability was a
significant predictor of linear change in performance, while psychomotor ability was not.
Collectively, the ability measures accounted for 12% and 5% in initial performance and
linear change, respectively.
Zyphur et al. (2008) examined general cognitive ability (SAT and ACT scores
obtained from university transcripts) as a predictor of trajectories of students‟ academic

53

performance during their college careers. Results suggested that ability was related to
students‟ initial performance, although the relationship between ability and linear change
was only marginally significant (p < .08). Zyphur and colleagues further hypothesized
that academic performance, as measured by GPA, imposes a limit on the amount that
performance can increase over time. Because high-ability students begin college
performing strongly, initial performance should therefore mediate the relationship
between ability and learning rate, resulting in a negative indirect effect between ability
and the individual-level slope parameters. Results from a mediated model tested by
Zyphur et al. supported this hypothesis. Similar findings regarding the direct effects of
cognitive ability in predicting student performance were reported by Shivpuri, Schmitt,
Oswald, and Kim (2006), with cognitive ability predicting initial performance but not
linear change.
Non-ability predictors of performance trajectories. Researchers interested in skill
acquisition and personnel selection have investigated numerous non-ability predictors of
performance trajectories. Generally, selection researchers have focused more so on
stable, distal individual difference attributes, while skill acquisition researchers have
examined both distal and proximal non-ability attributes. With regard to distal
characteristics, several researchers have examined the role of the Big Five broad
personality traits as predictors of performance trajectories (Thoresen et al., 2004; Yeo &
Neal, 2004; Zyphur et al., 2008).
Thoresen and colleagues (2004) investigated the relationship between the Big
Five and performance trajectories for two samples of sales representatives, one believed
to be in a transitional stage of tenure and the other believed to be in a maintenance stage

54

of tenure. Measures of performance were derived from results-oriented sales criterion
measures (i.e., quarterly territory sales for the maintenance sample, quarterly product
market share for the transition sample). For the maintenance sample, extraversion
emerged as a significant predictor of incumbents‟ initial performance; conscientiousness
was marginally related to initial performance. However, none of the Big Five measures
significantly predicted linear change in performance.
For the transition sample, Thoresen and colleagues found that openness and
agreeableness were both significant predictors of incumbents‟ initial performance. In
addition, emotional stability was marginally related to initial performance, although the
relationship was negative (i.e., those higher in emotional stability had lower initial
performance). With regard to linear change, emotional stability and agreeableness
emerged as significant predictors; however, the relationship between linear change and
emotional stability was again negative. Finally, openness also exhibited a significant
negative relationship with the individual-level quadratic parameter (in the transition
sample, evidence was found for significant individual-level variability in the quadratic
parameter, unlike in the maintenance sample), indicating that those higher in openness
were less likely to experience a plateau in performance during the time period observed.
Zyphur and colleagues (2008) examined the Big Five as predictors of
performance trajectories in a sample of college students using four-year grade point
average as the criterion on which trajectories were modeled. Conscientiousness and
openness both exhibited significant relationships with initial performance, although the
relationship for openness was negative. Neuroticism exhibited a marginally significant
relationship with initial performance (p = .05); however, the relationship in this case was

55

positive. In addition, Zyphur et al. found that conscientious was significantly related to
linear change; the relationship between linear change and neuroticism was marginally
significant (p < .08), although it was also positive in direction. As was the case for
cognitive ability described above, Zyphur and colleagues also found that
conscientiousness had a negative indirect relationship with linear change through initial
performance. Finally, Yeo and Neal (2004) examined the relationship between learning
on an air traffic control task and conscientiousness. Results suggested those higher in
conscientiousness learned at a significantly lower rate compared with those lower in
conscientiousness. This result was hypothesized based on prior researchers in certain
employment and learning contexts.
Several noncognitive constructs outside of the Big Five have also been examined
as predictors of performance trajectories. Two studies (Chen & Mathieu, 2008; Yeo &
Neal, 2004) have examined learning and performance goal orientation in the context of
skill acquisition. Chen and Mathieu (2008) found no evidence that either learning or
performance goal orientation was related to performance intercepts or linear change,
although they did find evidence that goal orientations interacted with type of feedback
and situational goal orientation. Yeo and Neal (2004) found that performance orientation
was negatively related to learning rate, although learning orientation was not.
Ployhart and Hakel (1998) examined three biodata predictors (past sales
commission and salary potential, persuasion, and empathy) of performance trajectories
modeled from gross sales commissions over eight quarters for a sample of national
securities brokerage incumbents. Time was coded such that the intercept parameter for
the trajectories represented performance at one year (four quarters). Results suggested

56

that all three biodata predictors were related to performance at one year, while both
persuasion and empathy were positively related to linear change. Furthermore, persuasion
and empathy were both significant predictors of the individual-level quadratic estimates,
although in opposing directions; those high in persuasion were more likely to decrease in
performance over time, while those high in empathy were less likely to decrease in
performance over time.
Finally, Shivpuri and colleagues (2006) investigated the role of six characteristics
(knowledge of general principles, continuous learning, interpersonal skills, perseverance,
and adaptability) measured via a biodata inventory as predictors of academic
performance trajectories over four semesters for a sample of undergraduates. Knowledge
of general principles was found to be a significant predictor of initial performance.
Adaptability and continuous learning were significantly related to linear change;
however, the relationships were both negative in direction.
Summary. As shown from the studies described above, researchers interested in
human performance have explored a variety of individual difference characteristics as
predictors of performance in numerous settings (laboratory-based skilled performance,
work, education). This body of research affords a number of conclusions regarding the
nature of performance trajectories and predictors of them. First, as has been suggested by
others, we can conclude that performance truly varies over time. Although this
conclusion is intuitive, it was not until researchers began modeling performance
trajectories before agreement existed that performance dynamism reflected more than
unsystematic measurement error. Starting with Hofmann and colleagues‟ research in the
early 1990s, a consistent finding has been that individuals exhibit performance

57

trajectories over time and that between-subjects variability in the parameters underlying
these trajectories has a sizeable systematic component. Second, between-subjects
variability in performance trajectories can be partly accounted for by both distal
individual difference constructs and proximal, malleable characteristics. At present,
greater specificity regarding the particular constructs is not possible; results have not
been entirely consistent across studies and additional replications are needed. Differences
in findings across studies may stem from methodological and contextual differences (e.g.,
differences in how performance is modeled within subjects, the varying nature of the
tasks used in the across laboratory studies, differences in the time frame over which
performance is measured, the potential influence of extraneous characteristics on
performance trajectories, etc.).
Third, constructs that correlate with initial performance are not necessarily the
same constructs that account for variance in change over time. Numerous studies
described above provide examples highlighting this point. In several cases, however,
constructs hypothesized to be significant predictors of change parameters have not
emerged as such on a consistent basis. For instance, with regard to cognitive ability,
several studies show marginal or significant relationships with linear or higher-order
trajectory parameters, while other studies fail to find an effect. Why this is so is not
entirely clear.
At this juncture, research on individual difference determinants of performance
and dynamic criteria has been reviewed. The next section discusses aspects of
educational contexts that highlight the need to modify extant theoretical perspectives on
individual difference determinants of performance trajectories when making predictions

58

regarding correlates of performance over time. Theory and prior research are then
integrated to derive predictions regarding ability and trait motivation as predictors of
college student performance trajectories.

Integrating the Interaction Hypothesis into the Study of Trajectories in Performance
The streams of research reviewed above provide two assumptions that undergird
the present study: (1) human performance in organizational and educational contexts
varies over time, and between-subjects variance in performance trajectories is partly
accounted for by stable individual differences; (2) individual differences in the domains
of human ability and trait motivation are theoretically fundamental to understanding
variation in performance-relevant behavior in organizational and education contexts. The
theoretical issue addressed in the present study pertains to the manner in which individual
differences in ability and motivation contribute to human performance over an extended
time period, that is, during a student‟s undergraduate career. However, although the
literature on individual difference predictors of performance trajectories has grown over
time, there are concerns with respect to generalizing from much of the research that has
been conducted to the issues and questions addressed in the present study.
Zyphur and colleagues (2008) note several aspects of academic performance and
the academic context that make performance in educational contexts a somewhat unique
criterion. First, the shift from high school to life in college, which is initially quite
unstructured, marks a major life transition in the lives of students. This disruption may
lead to difficulties associated with students‟ performance upon entry in college. Although
theoretical accounts exist regarding performance in novel environments (e.g.,

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Ackerman‟s research on skill acquisition, Murphy‟s discussion of transition stages), these
concepts do not explicitly take into consideration the major life changes that occur during
college students‟ entry into post-secondary education.
Second, because time in college is structured on the basis of semesters (or other
similar demarcation), performance periods span several months. The end of each
performance period (semester) brings changes in course content as students enroll in new
classes. Zyphur and colleagues (2008) suggest that because the primary job of students is
to learn information, and because this information is constantly changing across
semesters, this aspect of student performance is similar to Murphy‟s transition stage. At
the same time, many aspects of students‟ skill-based performance (e.g., writing reports)
are relevant across semesters and generally do not change, making this aspect of student
performance comparable to Murphy‟s maintenance stage. As Zyphur and colleagues note,
this state of affairs (i.e., recurrent transition stages undergirded by a constant underlying
maintenance component) results in uncertainty regarding the extent to which models like
those presented by Murphy and Ackerman are accurate descriptions of performance over
time in a college environment.
A third aspect that makes generalization from much of the prior research on
performance trajectories questionable pertains to the level of contingency that is inherent
in college student performance. Unlike much of the research conducted in organizational
or laboratory settings, future academic performance is often dependent on how much the
student has learned in the past because future coursework often builds or extends upon
information learned in more basic courses. This state of affairs provides one reason for
why many post-secondary institutions use prior achievement (high school grade point

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average) as a predictor in the admissions process; students who enter college having
performed well in the past are presumed to have a larger knowledge base that will aid
them in introductory coursework upon entry into college. This situation also means that
students who perform poorly at one time period (e.g., during the second year of college)
are at risk of even poorer performance the following year if the knowledge missed during
the earlier time period is to serve as a foundation for the information to be learned in the
future.
Individual Difference Determinants of Academic Performance Trajectories
Predictors of initial performance. Dating to the theoretical foundations of need
for achievement initially developed by Murray, McClelland, and Atkinson, the construct
has been viewed as a central component in a framework of adaptive tendencies and
characteristics associated with approach motivation that are likely to be of benefit to
students‟ initial performance in college. The first year of college provides both
opportunities and challenges to new students that implicate individual differences in
achievement motivation as a predictor of initial performance. From an opportunities
standpoint, the new student finds him or herself embedded in a novel academic and social
environment that contains features likely to appeal to those who are high in academic
achievement motivation. Examples include clubs and organizations relevant to one‟s
major that provide students the opportunity to meet like-minded individuals who share
similar interests and the availability of faculty members pursuing research in an area that
a student might be interested in learning about. On an even simpler level, college course
scheduling allows students the opportunity to plan what courses they can take over the
course of their college careers. This future oriented activity is likely to cause students to

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think more about where they see themselves over the course of their college career and to
develop academically-relevant goals, likely to have both short-run and long-run benefits,
to ensure that they meet their milestones. Because need for achievement is related to the
adoption of goals that are both challenging (e.g., Matsui et al., 1982; Yukl & Latham,
1978) and are inclusive of both approach-oriented performance and mastery
characteristics (e.g., Elliot & Murayama, 2008), such activities are likely to be beneficial
to those who are initially proactive.
From a challenges perspective, the first year of college is also associated with a
difficult transition period for many students (e.g., Zyphur et al., 2008). Because students
high in achievement motivation are more likely to be both efficacious (e.g., Kirk &
Brown, 2003) and perseverant (e.g., Cooper 1983) and to employ problem-focused
coping strategies (Halamandaris & Power, 1999), such individuals should be wellequipped to deal with the new challenges they face. Conversely, those low in
achievement motivation are more likely to display maladaptive patterns that hinder
academic performance, such as the adoption of avoidance performance goals (Payne et
al., 2007) and an adverse reaction to failure experiences (e.g., Elliot & Church, 1997;
Halamandaris & Power, 1999).
Similarly, the transition to college requires the need to adapt to an unstructured
environment that affords one opportunities to engage activities likely to detract from time
otherwise invested in academic pursuits. First-year students find themselves in a new
location, surrounded by a new social environment, and without any degree of close
supervision to ensure that time is allocated efficiently and focus is maintained on one‟s
coursework. Such circumstances may increase the importance of certain behaviors related

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to achievement motivation (e.g., delaying gratification, avoiding behaviors related to
procrastination; Mehrabian, 1968; Steel, 2007) that are important for ensuring that
adequate attention is paid to one‟s academic performance. Therefore, Hypothesis 1 states:

Hypothesis 1: Individual differences in achievement motivation will be positively
related to initial performance.

Individual differences in cognitive ability are likely to influence initial
performance in at least three ways. First, as noted by Zyphur and colleagues (2008) and
as stated above, the change to college from high school marks a major life change
transition into an unstructured environment that is novel and requires adaptation. Students
who are low in cognitive ability will likely experience greater difficulty adjusting to the
new environment in an adaptive manner; therefore, these students are also more likely to
experience initially poor academic performance than students high in cognitive ability.
Second, cognitive ability will be reflected in the gross amount of knowledge that students
carry with them from high school into college. That is, students high in cognitive ability
have likely learned more in their prior academic endeavors. This greater knowledge base
will afford such students an advantage at the beginning of their college careers. This is
largely the case because students‟ initial course loads are often composed of general,
introductory classes that share greater content similarity with students‟ high school
courses than is the case with courses taken later in college. Third, cognitive ability will be
reflected in the gross amount of knowledge that students learn in their coursework during
the initial time period (i.e., the first year of college); individuals who are higher in

63

cognitive ability gain a larger amount knowledge during their first year of college
compared to individuals lower in cognitive ability. Thus, Hypothesis 2 states:

Hypothesis 2: Individual differences in cognitive ability will be positively related
to initial performance.

Predictors of performance trajectories. Prior research implicates achievement
motivation and its facets as determinants of students‟ use of learning strategies (Elliot &
McGregor, 2001), adaptive learning styles (Busato et al., 1999, 2000), and study
behaviors (Robbins et al., 2004). Relatedly, conscientiousness, of which achievement
motivation is a component, has been found to be related to the amount of time that
students allocate toward studying (Biderman, Nguyen, & Sebren, 2008). This finding
concurs with Zyphur and colleagues‟ (2008) point that individual differences in
conscientiousness, as indicative of motivation, are predictive of performance trajectories
because they reflect characteristics that obtain meaning in the context of time (e.g.,
persistence and striving). When applied to the present study, the findings of Biderman
and colleagues suggest that the skills that undergird students‟ learning strategies and
behaviors are likely to improve over time through experience and application, particularly
for those who are high in achievement motivation. In other words, highly motivated
students‟ use of such strategies and behaviors are likely to strengthen over time,
becoming more efficient and effective, as they experiment with and learn how to better
utilize the skills underlying these strategies and behaviors.

64

As students‟ study skills increase with application and experience, performance
should increase over time, as well, given that study behaviors and strategies are related to
performance in academic contexts (Credé & Kuncel, 2008). Therefore, the present
argument suggests the following: (1) students who are high in achievement motivation
utilize learning strategies and study behaviors to a greater extent than students who are
low in achievement motivation; (2) therefore, the skills underlying these strategies and
behaviors should increase over time with application and experience, particularly for
highly-motivated students that invest greater time on task, and; (3) because these skill
increases should lead to subsequent increases in performance over time, it is thus the case
that grades for high achievement motivation students should increase over time to a
greater extent than is the case for low achievement motivation students.
It should be noted that if achievement motivation is related to higher levels of
initial performance, it may exhibit a negative indirect relationship with linear
performance change if initial performance and performance change are negatively
correlated (Zyphur et al., 2008). This state of affairs would be expected in the present
situation, given that academic performance (GPA) has an upper limit; students who
perform well initially have less room to continue improving compared to students who
initially perform poorly. Therefore, the positive relationship expected between
achievement motivation and linear change should be evident after controlling for initial
performance, as found by Zyphur and colleagues (2008). As such, Hypothesis 3 states:

65

Hypothesis 3: Individual differences in achievement motivation will be positively
related to linear change in performance over time after controlling for initial
performance.

Increases in the skills underlying learning strategies and study behaviors are not
likely to impact performance trajectories in the same way for all individuals, however. As
Bell and Kozlowski (2002) suggest, the use of learning strategies and effortful processing
should result in larger gains for individuals who are high in ability than those who are
low in ability, because individuals who are high in ability have greater resources to invest
when employing such strategies. Therefore, individual differences in cognitive ability
should moderate the relationship between achievement motivation and increases in
grades over time. Again, this relationship is expected to hold only after controlling for
initial performance, for the reasons noted above. Hypothesis 4 states:

Hypothesis 4: Individual differences in cognitive ability will moderate the
relationship between achievement motivation and linear change in academic
performance over time after controlling for initial performance, such that the
relationship will be stronger for individuals high in cognitive ability.

With regard to the role of cognitive ability in predicting linear change in
performance, there are both reasons to expect a positive relationship and reasons to
expect no relationship. Each viewpoint merits further consideration. On the one hand, the
notions of learning and knowledge acquisition are central to the construct of cognitive

66

ability, as reflected in classical definitions of g and in models of job performance
determinants (e.g., Borman & Motowidlo, 1993; Campbell et al., 1993; Hunter, 1983,
1986). Because learning is the primary task for students in an academic context and
because g is theoretically central to learning, one might hypothesize that ability should be
related to linear change in performance over time. This argument is further bolstered by
the fact that advanced-level college courses are often grounded in content learned in basic
or introductory college courses as a foundation, particularly in areas that are strongly
cumulative in nature (e.g., mathematics, physics, medicine). Students who acquire
knowledge in basic or introductory courses are likely to perform more strongly in
advanced-level courses because they have the basic knowledge on which future courses
extend. Those who do not acquire such knowledge are at risk of performing even more
poorly once they reach advanced-level courses because they are deficient in basic
knowledge areas.
On the other hand, it could be argued that, instead of contributing to intraindividual variation in performance, cognitive ability may play a stronger role in
determining individuals‟ mean level of performance throughout college. In other words,
all else held constant, students whose high level of cognitive ability affords them the
advantage of efficient and effective learning during the first year of college are likely to
be those same high-ability students that learn efficiently and effectively during their final
year of college.
This argument stems in part from a closer examination of the nature of GPA as a
measure of performance in academic contexts. In this case, performance is being assessed
using a molar criterion, namely semester or yearly GPA, designed to reflect gross

67

knowledge obtained at the end of a time period, as opposed to the amount, or rate, of
knowledge growth. An example illustrates the difference between these two concepts.
Assume that several tests are administered for a course over the period of a semester on a
bi-weekly basis, starting with the first day of class. Assume also that each test contains a
representative sampling of the entirety of the knowledge domain relevant to that course
for the semester. Each test score for a student reflects the total amount of course-relevant
knowledge that the student holds at a given point in time. Initially, we would expect poor
performance and low variance because students have not yet been exposed to the material
covered later in the course. Ignoring the role of retest effects, as the term progresses, test
score means and variances should increase over time as students are further exposed to
the course‟s knowledge domain and have the opportunity to learn relevant concepts and
skills. If cognitive ability is indeed central to learning, it should be reflected in increases
in students‟ test scores across tests. Thus, if one were to model trajectories from the test
scores, theory would suggest that cognitive ability should be positively related to the rate
of knowledge growth, or the slope of performance regressed on time. This is because the
performance measures themselves allow one to model trajectories that can be interpreted
as a measure of knowledge growth, or learning, in a relatively unambiguous manner.
This, however, is not the nature of semester or yearly GPA as a measure of
academic performance. Even if tests in college courses were similar to the type described
in the example above (imagine how the professor‟s ratings would look if one tried this),
academic scheduling in most U.S. institutions of higher learning is not structured such
that students must take progressively more difficult courses in the same exact content
domain that extend directly upon the courses taken in the previous term. Rather, students

68

are afforded some degree of flexibility regarding whether they take certain classes and if
they take them in a sequential order or not. Therefore, course content is subject to great
variability from semester to semester. This lack of structure precludes the interpretation
of linear trajectories as rates of cumulative knowledge gain, because the content domain
varies. Therefore, cognitive ability is instead reflected in the rate at which students learn
within a semester, which is likely to result in similarly high (low) levels of performance
for individuals high (low) in ability at the end of each semester, as reflected in GPA. For
this reason, cognitive ability should be largely reflected in mean performance (which, in
the present case, will be largely reflected in initial performance), as opposed to linear
change.
This argument is not in conflict with either the theoretical role of g in learning
(e.g., Hunter, 1986) nor the interpretation of g as individual differences in attentional
resources that can be allocated to learning performance (e.g., Ackerman, 1988) or any
other interpretation of the construct. Rather, the argument suggests that the criterion in
question is not a pure measure of (or, perhaps more importantly for the present
discussion, does not allow one to model trajectories that are a pure measure of) the
outcomes to which cognitive ability should be related or the manner in which cognitive
ability should be relevant theoretically. This argument is also not in conflict with the
notion that cognitive ability is an important determinant of both learning and academic
performance in later periods of college tenure. Quite the opposite, learning capacity
should be just as important later in college as it is earlier in college; although the
correlations attenuate somewhat with time, research from the dynamic criteria literature
supports this statement (e.g., Butler & McCauley, 1987; Humphreys, 1968).

69

Finally, this argument is not in conflict with Hypothesis 4, which addressed the
interactive relationship between achievement motivation and ability in predicting linear
performance increases. The role of ability in moderating the motivation-performance
relationship pertains to how ability alters the relationship between strategies and
behaviors and performance over time. Recall that the effective application of such skills
should increase over time because the skills underlying these strategies and behaviors are
also changing over time and because increases in such skills should be reflected in
concomitant increases in performance. Rather, the present argument merely states that the
role of cognitive ability, in isolation, plays a constant, invariant role in students‟
performance over time, as reflected in GPA, because GPA does not allow for the
modeling of trajectories that represent knowledge growth, or rate of learning, over molar
time periods.
In summary, because of the reasons stated above, any relationship between
cognitive ability and linear performance change likely results from factors that are
substantially less salient than those which were used in hypothesizing the role of ability
in predicting initial performance. A strong perspective would be to hypothesize that
cognitive ability should not be related to linear change in performance over time.
However, given that only two studies have examined this relationship in the past in a
college student population (i.e., Shivpuri et al., 2006; Zyphur et al., 2008) and a lack of
pre-existing theoretical evidence to buttress the arguments described above, it is merely
hypothesized that the relationship between cognitive ability and linear performance
change will be weaker than that observed between cognitive ability and initial
performance. Thus, Hypothesis 5 states:

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Hypothesis 5: The relationship between cognitive ability and linear change in
performance over time will be weaker than the relationship between cognitive
ability and initial performance.

The hypotheses stated above integrate the literature streams pertaining to job
performance, dynamic criteria, and performance trajectories with prior research on the
interactive hypotheses to result in a theoretical account of academic performance relevant
to the college student population. The present study tests these hypotheses on two
samples of college students. The first sample comprised students from a single university,
with performance measures representing semester GPA for the first four semesters of a
student‟s tenure. The second sample comprised students from several institutions, with
performance measures representing yearly GPA for the first four years of a student‟s
tenure.

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METHOD
Two samples were included in the primary analyses discussed in the report herein.
For the remainder of the report, these samples will be referred to as „Sample 1: MSUOnly‟ (comprised of Michigan State University undergraduate students) and „Sample 2:
Multi Institution‟ (comprised of undergraduate students from several college and
universities from around the United States).
Sample and Procedures
Sample 1: MSU-Only. Data for participants in Sample 1, referred to hereafter as
the MSU-Only sample, were drawn from a dataset containing predictor and criterion data
on 644 respondents from Michigan State University. Inclusion criteria were limited to the
restriction that respondents must be in their freshman year of college at the time of data
collection. Missing data was addressed via the missing values imputation procedure in
PRELIS. This procedure entails substituting missing values from cases matched on
similar non-missing background variables, where similarity is evaluated with respect to
user-specified variance ratio (the value .5 was chosen for present purposes). In the event
that a case with missing data is not deemed similar to another case in the dataset,
imputation is not performed.
This approach was taken in the present study because of heterogeneity in the
mechanisms underlying missing data for participants, including institutional nonresponse, student attrition from college altogether, or students transferring to other
institutions. Because there was no way to identify the mechanism leading to missingness

72

for any given case, no assumptions can be made regarding the type of missingness
present (e,g., MAR, MCAR) and, thus, the appropriateness of common strategies for
dealing with missing data cannot be evaluated. The matching procedure in PRELIS
makes no assumptions regarding the type of mechanism leading to missing data.
Implementation of the inclusion restriction and subsequent imputation resulted in an
operational sample size of 568 participants (88.2% of the original data file).
Participants in the MSU-Only sample were predominantly female (72.2%).
Average age for participants in the MSU-Only sample was 18.48 (SD=.57). Racioethnic
composition of participants in the MSU-Only sample was as follows: Mexican/Latino
(1.3%), Other Hispanic (.5%), American Indian or Alaskan Native (.2%), Asian (4.9%),
Black/African American (9.2%), White/Caucasian (80.2%), Native Hawaiian or other
Pacific Islander (.5%), and Two or More Races (3.2%). Of the MSU-Only sample
participant, the vast majority (97.3%) were United States citizens, with 98.0% of
participants endorsing English as their primary language. Finally, academic major
composition for participants in the MSU-Only sample was as follows: Business (20.7%),
Engineering (6.4%), Fine Arts/Humanities (6.6%), Social Science (20.5%), Natural or
Physical Science (34.6%), and Other (11.3%).
In order to assess whether there were systematic differences with regard to
background or demographic variables between respondents included in the study and
those not, Table 5 lists proportions and frequencies with regard to gender, racioethnic
status, citizenship status, English speaking status, and academic major for both the

²

analysis sample (MSU-Only) and excluded cases. As indicated by the χ values in Table
5, there was little evidence of differences between those retained and those excluded with
73

²

²

regard to gender, χ (1) = .019, p = .809, citizenship status, χ (2) = .740, p = .691, and

²

English speaking status, χ (5) = 2.481, p = .115.
Although differences were not significant, there was some evidence of differences

²

between the two samples with respect to racioethnic composition, χ (7) = 13.152, p =

²

.068, and academic major, χ (5) = 9.447, p = .093. Compared to respondents who were
excluded, respondents included in the analysis sample were significantly more likely to
identify as being White (80.2% in the analysis subset, 69.4% in the excluded subset; p =
.030) and were significantly less likely to identify as being Mexican / Latino (1.3% in the
analysis subset, 5.9% in the excluded subset; p = .003). In addition, respondents included
in the analysis sample were significantly more likely to be in an academic major affiliated
with the natural or physical sciences (34.6% in the analysis subset, 22.2% in the excluded
subset; p = .030) and were significantly less likely to be in an academic major affiliated
with the social sciences (20.5% in the analysis subset, 33.3% in the excluded subset; p =
.010). As shown in Table 7, the difference in age between the analysis sample and
excluded cases was small and not significant (d = -.163, 95% CI = -.394, .067).
Sample 2: Multi-Institution. Data on participants in Sample 2, hereafter referred to
as the Multi-Institution sample, were drawn from a file containing data on 2,787
respondents from ten public and private institutions across various regions of the
continental United States. Inclusion criteria were limited to the restrictions that
respondents must be in their freshman year of college at the time of data collection and
that the institution they attended agreed to report GPA data for research purposes.
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Imputation was handled in the same manner as that described for the MSU-Only sample.
Following imputation, implementing these restrictions resulted in an operational sample
size of 1,279 participants (45.9% of the original data file) from five institutions.
Participants in the Multi-Institution sample were predominantly female (61.8%).
Average age of participants in the Multi-Institution sample was 18.12 (SD=.39).
Racioethnic composition of participants in the Multi-Institution sample was as follows:
Mexican/Latino (1.3%), Puerto Rican (.2%), Other Hispanic (.9%), American Indian or
Alaskan Native (.1%), Asian (5.7%), Black/African American (8.4%), White/Caucasian
(78.8%), Native Hawaiian or other Pacific Islander (.5%), and Two or More Races
(2.8%). Of the Multi-Institution sample participants, the vast majority (97.5%) had
United States citizenship, with 96.8% of participants endorsing English as their primary
language. Academic major composition for participants in the Multi-Institution sample
was as follows: Business (16.3%), Engineering (11.3%), Fine Arts/Humanities (9.0%),
Social Science (14.3%), Natural or Physical Science (20.2%), Other (14.6%), and
Undeclared (14.3%). University affiliation among participants in the Multi-Institution
sample was as follows: Michigan State University (30.5%), Ohio State University
(20.0%), University of Indiana (7.9%), University of Iowa (20.2%), and University of
Michigan (21.4%).
In order to assess whether there were systematic differences with regard to
background or demographic variables between respondents included in the study and
those not, Table 6 lists proportions and frequencies with regard to gender, racioethnic
status, citizenship status, English speaking status, and academic major for both the
analysis sample (Multi-Institution) and excluded cases. It should be kept in mind while

75

²

interpreting the χ values and associated significance levels that the effective sample for
these analyses was quite large (N = 2,787); thus, differences of a relatively small
magnitude are likely to be identified as significant due to the power afford by the large
sample size. Indeed, as shown in Table 6, significant differences were found between the

²

analysis sample and excluded cases with respect to gender, χ (1) = 4.864, p = .027,

²

²

racioethnic status, χ (9) = 564.985, p < .001, citizenship status, χ (2) = 6.853, p = .032,

²

²

English speaking status, χ (1) = 17.980, p < .001, and academic major, χ (6) = 43.019, p
< .001.
Relative to respondents whose data was retained for analysis, excluded cases were
more likely to be female (61.8% in the analysis subset, 65.9% in the excluded subset; p =
.027). With regard to racioethnic status, respondents included in the analysis sample were
significantly more likely to identify as White (78.8% in the analysis subset, 35.3% in the
excluded subset, p < .001) and were significantly less likely to identify as
Mexican/Latino (1.3% in the analysis subset, 5.8% in the excluded subset; p < .001),
Other Hispanic (.9% in the analysis subset, 2.7% in the excluded subset; p < .001), and
Black/African American (8.4% in the analysis subset, 40.2% in the excluded subset; p <
.001).
Respondents included in the analysis sample were significantly more likely than
excluded cases to have U.S. citizenship (97.5% in the analysis subset, 95.7% in the
excluded subset; p < .001), while excluded cases were significantly more likely than
those in the analysis sample to have non-U.S. citizenship within a country other than
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Canada (2.3% in the analysis subset, 4.0% in the excluded subset; p = .021). Finally,
respondents in the analysis sample were significantly more likely than excluded cases to
have an academic major in the areas of business (16.3% in the analysis subset, 13.9% in
the excluded subset, p = .019) or the natural or physical sciences (20.2% in the analysis
subset, 14.9% in the excluded subset; p < .001). Respondents included in the analysis
sample were also more likely than excluded cases to be undeclared with respect to
academic major (14.3% in the analysis subset, 10.2% in the excluded subset; p < .001).
Conversely, excluded cases were significantly more likely to be in an academic major
within the social sciences (14.3% in the analysis subset, 18.9% in the excluded subset; p
= .012) or within an academic domain other than those listed (14.6% in the analysis
subset, 19.9% in the excluded subset, p = .003). As shown in Table 8, the difference in
age between the analysis sample and excluded cases was small and not significant (d = .064, 95% CI = -.140, .012).
Measures: MSU-Only Sample
Predictor measures. Need for achievement was measured in the MSU-Only
sample via a 10-item composite (hereafter referred to as AM SBF-10; α=.784)
comprising five items taken from the need for achievement scale used by Steers and
Braunstein (1976) and five items taken from the Work Preference Questionnaire used by
Fineman (1975). Where necessary, items were adapted to an academic context in order to
make the content relevant for the sample and purposes at hand. Both of the scales
comprising the AM SBF-10 have been employed in applied research examining
achievement motivation in the work domain (e.g., Steers & Spencer, 1977). The AM

77

SBF-10 was administered to respondents during their first year of college. Items were
rated on 5-point Likert-type scales. Items used in the AM SBF-10 are reported in Table 1.
Ability was measured in the MSU-Only sample via respondents‟ standardized
examination scores. Prior research examining correlates of student performance have
often used standardized examination scores as a measure of student ability (e.g.,
Harackiewicz et al., 2002; Hollenbeck et al., 1988; Kuncel et al., 2004; Nonis & Wright,
2003). Similarly, previous research has demonstrated that such measures are strongly
correlated with general cognitive ability (e.g., Carroll, 1997; Coyle & Pillow, 2008;
Gottfredson, 2002; Jensen, 1998; Koenig, Frey, & Detterman, 2008).
For instance, Koenig and colleagues (2008) reported an uncorrected correlation of
.77 between total ACT and the first factor derived from a principle axis factor analysis of
the 10 ASVAB subtests in the National Longitudinal Survey of Youth 1979 dataset. In
addition, they reported a correlation (corrected for restriction of range) of .75 between
total ACT and scores on the Raven‟s APM in a separate sample of undergraduate college
students. Coyle and Pillow (2008) estimated g-loadings using hierarchical confirmatory
factor analysis for both the SAT and ACT in two samples. In each sample, both the SAT
and ACT exhibited relatively large g-loadings compared to the other indicators included
in the models (for the SAT, .90 and .78; for the ACT, .92 and .75). The large correlations
and path coefficients observed in these studies indicate that both the SAT and ACT
appears to be a relatively good measure of general cognitive ability within the collegeaged population.
In the present study, data on standardized examination scores were collected
during the application process prior to the respondents‟ first year in college. During the

78

informed consent process, participants signed optional data release forms permitting the
researchers to access standardized exam scores from the respondents‟ records stored by
the institutional registrars. All participants included in the MSU-only sample had taken
either the SAT or ACT, with some participants having taken both tests in the process of
applying to different institutions.
To compute the measure of ability used in the present study, either ACT or SAT
scores were used if respondents had completed only one of the two tests; in situations
where respondents had completed both tests, scores were averaged to derive a single
index of ability. Prior to computing the final ability variable, raw ACT composite test
scores were first converted to equivalent SAT scores using a conversion table from
www.collegeboard.com (see also Dorans, Lyu, Pommerich, & Houston, 1997). Among
participants in the MSU-Only sample who had taken both the ACT and SAT (n=123), the
uncorrected correlation between the two measures was .853. Because overall scores were
obtained from the institutional registrars, reliability estimates for ACT and SAT could not
be computed. The interaction term was the cross-product obtained from multiplying the
respondents‟ need for achievement scores with their ability scores. Both predictors were
mean-centered prior to computation of the interaction term; these mean-centered
variables were also used in all analyses examining ability and need for achievement as
predictors.
Table 7 shows mean scores for ability and achievement motivation for both the
analysis sample and cases excluded from analysis. Although respondents in the analysis
sample had higher scores on ability compared to excluded cases by slightly more than
one-fifth of a standard deviation, the difference was not significant (d = .220, 95% CI = -

79

.016, .456). Similarly, there was no evidence for a significant difference with regard to
achievement motivation between the analysis subsample and cases excluded from
analysis (d = .040, 95% CI = -.189, .296).
Criterion measures. During the informed consent process, participants signed
optional data release forms permitting the researchers to access grade point average
(GPA) data from the respondents‟ records stored by the institutional registrars. For
participants in the MSU-only sample, respondents‟ GPAs were obtained for each of the
first four semesters of college (Fall-01, Spring-02, Fall-02, and Spring-03), thus yielding
measures of performance at each of four points in time.
Table 7 shows mean GPA for each time point for both the analysis sample and
cases excluded from analysis. At Times 1 and 2 (i.e., Fall-01 and Spring-02), cases
included in the analysis sample had significantly higher GPA compared with cases
excluded from analysis (GPA1: d = .685, 95% CI = .426, .942; GPA2: d = .787, 95% CI
= .522, 1.050). The number of cases excluded from analysis with GPA data available at
Times 3 and 4 was too small for comparison purposes (8 and 6 cases at Times 3 and 4,
respectively). However, the tendency for mean GPA to continue declining among
excluded cases at Times 3 and 4 (1.84 and .72, respectively) suggests that differences
between the analysis sample and excluded cases remains large.
Measures: Multi-Institution Sample
Predictor measures. Need for achievement was measured in the Multi-Institution
sample using a 15-item biographical data (biodata) inventory (α = .757 within the
analysis sub-sample [n = 1,325]; α = .736 within the entire multi-institution dataset [N =
2,787]), referred to hereafter as the Achievement Motivation Biodata Inventory (AM
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BIO-15). This measure utilized a multiple-choice, self-report format whereby participants
were asked questions regarding their prior experiences or history in the academic domain
and were then presented with either four or five options from which to choose a response.
Items included in the AM BIO-15 were drawn from a pre-existing pool of biodata items
which has been used extensively in prior selection research using college samples (e.g.,
Oswald, Schmitt, Kim, Ramsay, & Gillespie, 2004; Ramsay, Schmitt, Oswald, Kim, &
Gillespie, 2006; Schmitt, Oswald, Kim, Gillespie, Ramsay, & Yoo, 2003; Schmitt,
Oswald, Kim, Imus, Merritt, Friede, & Shivpuri, 2007).
Items from the AM BIO-15 are shown in Table 2. Items were chosen so as to
match, to the extent possible, the item content found in the achievement motivation scale
utilized for the MSU-Only sample and to reflect current conceptualizations of trait
achievement motivation. In doing so, items were drawn from certain motivational
constructs theoretically mapping onto dimensions of college student performance
(Oswald, Friede, Schmitt, Kim, & Ramsay, 2005), namely Perseverance, Knowledge, and
Continuous Learning. Oswald and colleagues (2005) define Perseverance as
“[c]ommitting oneself to goals and priorities set, regardless of the difficulties that stand in
the way,” (p. 155) where goals refer to both short-term (e.g., attending class on a daily
basis) and long-term (e.g., college graduation) outcomes. Knowledge refers to “[g]aining
knowledge and mastering facts, ideas, and theories and how they interrelate and
understanding the relevant contexts in which knowledge is developed and applied,”
(Oswald et al., 2005; p. 154). Although this definition does not explicitly delineate any
specific motivational mechanisms or processes pertaining to the acquisition of
knowledge, content for the Knowledge items included in the AM BIO-15 covers a

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number of motivational concepts relevant to the academic domain, including selfestablished and external standards for performance and effort invested to master relevant
course content and material. Finally, Continuous Learning refers to “[b]eing intellectually
curious and interested in continuous learning,” (p.154), with a specific emphasis placed
on active, self-driven behavior guided towards seeking knowledge in both the declarative
and procedural domains in core and peripheral areas of study.
Ability was measured using scores obtained from standardized examinations
administered as part of the college application process. The procedures used for obtaining
the data and computing the final Ability composite score were identical to those
described for the MSU-Only sample. As was the case in the MSU-Only sample, the
interaction term was the cross-product obtained from multiplying the respondents‟ need
for achievement scores with their ability scores. As above, both predictors were meancentered prior to computation of the interaction term; these mean-centered variables were
also used in all analyses examining ability and need for achievement as predictors.
Table 8 shows mean scores for ability and achievement motivation for both the
analysis sample and cases excluded from analysis. Contrary to the results obtain with
respect to ability differences between cases included for and excluded from analysis in
the MSU-Only sample, the difference favoring the analysis sample with regard to ability
was quite large in the Multi-Institution sample (d = .659, 95% CI = .578, .738). Although
not as large, the analysis sample also had significantly higher scores with respect to
achievement motivation compared to excluded cases (d = .095, 95% CI = .020, .171).
Criterion measures. During the informed consent process, participants signed
optional data release forms permitting the researchers to access grade point average

82

(GPA) data from the respondents‟ records stored by the institutional registrars. For the
Multi-Institution sample, respondents‟ GPAs were obtained for each of the first four
academic years of college (2004-2005, 2005-2006, 2006-2007, and 2007-2008). Thus, as
was the case for the MSU-Only sample, measures of performance were obtained for each
participant at each of four points in time. Unlike the MSU-Only sample, each time point
represented each participant‟s cumulative yearly GPA, encompassing grades from all
institutional time periods (e.g., semesters, trimesters, quarters).
The fact that GPAs were obtained from various institutions in the MultiInstitution sample also resulted in procedural differences pertaining to how GPA was
computed at each time point compared to the MSU-Only sample, where all GPA data
were obtained from the same institution. More specifically, admissions policies at the
various institutions included in the Multi-Institution sample resulted in differential
selectivity on various student characteristics (e.g., high school grade point average,
standardized examination scores). In order to correct for these differences, which are
irrelevant for the present study, GPA was corrected using a procedure employed by the
College Board in conducting validation studies of the SAT in similar situations. The
procedure for correction was as follows. First, a within-institution standardization on
GPA to z-scores was employed. Standardized GPA was then regressed, using the entire
sample, on the measure of ability (i.e., the ACT/SAT composite) along with a set of
dummy variables corresponding to each institution. In this case, the regression
coefficients for the dummy variables indicate variability in GPA that would be expected
for students with comparability ability levels at the various institutions. Finally, GPAs for
students at each institution were adjusted by that institution‟s regression coefficient, such

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that students at institutions with higher average standardized examination scores received
a relatively higher adjusted GPA and, conversely, students at institutions with lower
average standardized examination scores received a relatively lower adjusted college
GPA.
Table 8 shows mean GPA for each time point for both the analysis sample and
cases excluded from analysis. At Times 1 and 2 (i.e., Year 1 and Year2), cases included
in the analysis sample had significantly higher GPA compared with cases excluded from
analysis (GPA1: d = 1.286, 95% CI = 1.134, 1.436; GPA2: d = 1.545, 95% CI = 1.310,
1.777). The number of cases excluded from analysis with GPA data available at Times 3
and 4 was too small for comparison purposes (8 and 5 cases at Times 3 and 4,
respectively). However, the tendency for mean GPA to remain relatively low among
excluded cases at Times 3 and 4 (1.43 and 2.88, respectively) suggests that differences
between the analysis sample and excluded cases remains large.
Convergent validity of achievement motivation measures. Because two different
measures of trait achievement motivation were employed in the two samples included in
the present study, efforts were taken to ensure comparability across the measures with
regard to construct measurement and item content. The items used in the AM SBF-10
scale examined in the MSU-Only sample were adapted from previously established need
for achievement scales with a relatively long track record in the organizational
psychology literature. With respect to the AM BIO-15 scale utilized in the MultiInstitution sample, items were taken from a pre-existing pool of biodata items that have
been used extensively in prior selection research with samples that are similar to those
used in the present study. In addition, care was taken to ensure that the content included
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in the AM BIO-15 items was comparable to that used in the 10-item scale in the MSUOnly sample, while still mapping onto current conceptualizations of trait achievement
motivation. Finally, in line with previous recommendations (Hirschfeld et al., 2004), item
content was contextualized to refer specifically to the academic setting.
However, it is necessary to demonstrate an acceptable degree of convergent
validity between the two measures to ensure that results obtained using one scale are
likely to generalize to those obtained using the other. To this end, a pilot study was
conducted whereby the following measures were administered via an Internet-based
platform to 128 undergraduate college students at Michigan State University: (1) the AM
SBF-10 administered to the MSU-Only sample; (2) the AM BIO-15 administered to the
Multi-Institution sample, and; (3) a 21-item scale comprising the Achievement
Motivation facets of Work Ethic, Excellence, and Mastery from Cassidy and Lynn
(1989). The Cassidy and Lynn (1989) measure, hereafter referred to as AM CL-21, was
administered so as to have data on a more recent conceptualization of need for
achievement that has tended toward a facet-based perspective of the construct.
The initial sample of 128 participants in the pilot sample was reduced to 110
participants after 18 participants were removed for exhibiting careless responding, as
detected by items inserted into the questionnaires designed to assess carelessness (e.g.,
“For this item, please mark „Strongly Disagree.‟”). For the reduced sample, 95.4% of
participants were 21 years of age or younger; 81.5% were female. Year in college was
distributed as follows: freshman (32.1%), sophomore (28.4%), junior (23.9%), senior
(13.8%), and fifth year or later (1.8%). Racioethnic composition of participants in the
pilot sample was as follows: American Indian or Alaska Native (1.0%), Asian (7.6%),

85

Black (1.9%), White (81.9%), Two or More Races (3.8%), and Other (3.8%). Of the pilot
study participants, 99.1% endorsed English as their primary language. Academic major
composition for the pilot study participants was as follows: Undecided (9.2%), Business
(5.5%), Fine Arts/Humanities (4.6%), Social Science (34.9%), Natural/Physical Science
(22.9%), and Other (22.9%).
Table 3 provides correlations between 15 items from the AM BIO-15 with the
AM SBF-10 and Cassidy and Lynn‟s (1989) need for achievement scale (AM CL-21).
All correlations are corrected for unreliability (Cronbach‟s α was .684 and .826 for the
AM SBF-10 and AM CL-21, respectively). For the Cassidy and Lynn facet scales,
Cronbach‟s α was .722, .752, and .715 for Work Ethic, Excellence, and Mastery,
respectively. As originally developed, Cassidy and Lynn‟s (1989) scale is broader than
what is shown in Table 3 and includes facets tied to extrinsic motivation that are not as
relevant for the study of achievement motivation as a determinant of performance among
college students (e.g., dominance, acquisitiveness for money and wealth). The scales
chosen (i.e., Work Ethic, Pursuit of Excellence, and Mastery) correspond to the intrinsic
motivation factor that Story and colleagues (2009) derived from Cassidy and Lynn‟s
(1989) scale.
Most of the AM BIO-15 items correlate at least .15 with AM SBF-10 and AM
CL-21 scales; 12 of the 15 items exhibit correlations of at least .25 with one of the two
scales. Two of the items (e.g., 11 and 12) show correlations below .15 in magnitude with
both scales; however, removal of either item subsequently reduces internal consistency
for the AM BIO-15. Furthermore, despite yielding somewhat low correlations with the
global achievement motivation scales, items 11 and 12 correlate at a level higher than .15

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with relevant facets of Need for Achievement from the Cassidy and Lynn scale (r = .190
and .235, respectively, for Cassidy and Lynn‟s Mastery facet). Therefore, both 11 and 12
were retained for inclusion in the AM BIO-15 scale.
The strongest (dominant) correlation between each AM BIO-15 item and the three
intrinsic motivation facet scales from Cassidy and Lynn is highlighted in bold italicized
font. Dominant correlations ranged from .184 (item 14 with Learning) to .609 (item 2
with Excellence). Many of the AM BIO-15 items had one correlation that was distinctly
higher on a given facet. In several cases, an AM BIO-15 item exhibited correlations that
were comparable in magnitude with two of the Cassidy and Lynn scales (e.g., items 4, 5,
14). That an item might be correlated with multiple facets is not surprising, given
findings from Cassidy and Lynn (1989) showing that the facets are not orthogonal. These
results were replicated in the pilot sample, with positive correlations between Work Ethic
and Excellence (.396), Work Ethic and Mastery (.505), and Excellence and Mastery
(.295.). Corresponding estimates corrected for unreliability were .537, .703, and .402,
respectively.
Table 4 provides descriptive statistics for and intercorrelations among the AM
BIO-15, AM SBF-10, and AM CL-21. Uncorrected correlations between the AM BIO-15
and both of the pre-existing Achievement Motivation measures were .570 for the AM
SBF-10 (95% CI = .443–.697) and .568 for the AM CL-21 (95% CI = .442–695). The
point estimates for the correlations involving the AM BIO-15 are somewhat lower than
the observed correlation between the AM SBF-10 and the AM CL-21 (.637, 95% CI =
.525–.748), although the 95% confidence intervals overlap considerably. Corrected
correlations between the AM BIO-15 and the pre-existing need for achievement measures

87

were .835 for the AM SBF-10 (95% CI = .649–1.000) and .758 for the AM CL-21 (95%
CI = .589–.927). The corrected correlation between the AM SBF-10 and the AM CL-21
was .847 (95% CI = .698–.995). These correlations highlight two points. First, the
correlation between the two scales of primary interest to the present study (the AM BIO15 and the AM SBF-10) are sufficiently strong to suggest that both scales share
considerable overlap with regard to the underlying construct measured. Second, both the
AM BIO-15 and the AM SBF-10 demonstrate comparable correlations with a relatively
recent measure of achievement motivation (the AM CL-21) that is based on a modern
perspective of trait achievement motivation as a multidimensional construct comprising
several lower-order facets.
Analytic Strategy
The aim of the present research is to test the interaction hypothesis with academic
performance trajectories across both semesters (the MSU-Only sample) and academic
years (the Multi-Institution sample) as the outcome of interest. In order to achieve this
outcome, the present analytic strategy can be decomposed into two primary phases:
Descriptive and Static Analyses (Phase 1) and Model Building and Model Testing (Phase
2). As discussed in greater detail below, Phase 1 includes traditional descriptive analyses
of relevant predictor and outcome measures (e.g., description of distributional
characteristics, zero-order correlations). Phase 2 entails analyses subsumed under the
framework of latent growth modeling (LGM) so as to construct an adequate model of
individual difference determinants of performance trajectories and to test hypotheses
concerning relationships within this model.

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Phase 1: Descriptive and static analyses. As mentioned above, Phase 1 entails a
basic descriptive analysis of the predictor and outcome measures central to the present
study (i.e., ability, achievement motivation, GPA across relevant time periods), including
description of the measures‟ distribution characteristics (e.g., means, standard deviations)
and zero-order correlations among the measures. Phase 1 analyses will also include
testing of relationships for both the primary predictor and outcome measures with
relevant student characteristics (e.g., gender, racioethnic status) and academic context
characteristics (e.g., major area, university). Although such student and academic context
characteristics are not a central concern of the present study, results pertaining to such
analyses may provide guidance on potential ancillary variables to be included in the
Phase 2 and Phase 3 analyses described below.
Phase 2: Model building and model testing. Although concern with individual
differences in ability and motivation entails a between-subjects perspective, individual
differences in growth or change in performance is a longitudinal issue. Adopting a
multilevel paradigm, time of performance measurement (time) in this sense can be
viewed as nested within subjects (students). Parameters describing the relationship
between time and performance for each subject depend upon parameters at the betweensubjects level that can, in turn, incorporate subject characteristics (Raudenbush, 2001).
The analytic approach described above has been termed hierarchical linear modeling
(HLM; Bryk & Raudenbush, 1992) and can also be handled flexibly within a structural
equation modeling (SEM) framework, commonly referred to as latent growth modeling
(LGM), latent curve analysis (LCA), or otherwise (Singer & Willett, 2003). Because
LGM encompasses HLM (Bauer, 2003; Curran, 2003) and includes analytic advantages

89

over HLM (e.g., the estimation of global model fit indices in common SEM software),
the present research focuses on growth modeling in an SEM framework.
Modeling the relationship between individual-difference constructs, conceived of
here as time-invariant covariates whose values vary across individuals but are measured
only once, and latent trajectories entails three models: (1) the y-measurement model that
relates the observed outcome measures (in the present case, GPA over four points in
time) to the trajectory parameters used to characterize the form of change over time; (2)
the x-measurement model that relates the observed predictor variables (in the present
case, ability, achievement motivation, and their interaction) to latent factors that
presumably account for variance between subjects in predictor scores, and; (3) the
structural model that represents the hypothesized relationships between the exogenous
predictor factors and the endogenous latent trajectory parameters (Singer & Willett,
2003). The following sections describe each of these models in detail, with equations
borrowed from Singer and Willett (2003). Equations are presented in Figure 1. Elements
in bold typeface are matrices.
Eq. (1) represents the y-measurement model. This model relates the latent
trajectory parameters, η, to the observed outcome measures, Y, via the factor loading
matrix, Λy. In Eq. (1), primary interest with regard to trajectory parameters is on the

intercept, denoting true initial performance (π0i), and the linear slope, denoting the
amount of linear change in GPA associated with a one-unit change in time (i.e., one
semester, one year), represented by π1i. This is illustrated by the inclusion of these two

90

parameters as elements within η in Eq. (2). These elements can be modified to test
hypotheses regarding the form of change over time; this point will be elaborated upon
briefly as it relates to the present study.
The elements in the τy matrix correspond to mean parameters for the observed
indicators in Eq. (1); for present purposes, this matrix is not of interest. The elements
contained in the Λy matrix are fixed factor loadings that represent the relationship
between the underlying latent trajectory parameters, π0i and π1i, and the observed
indicators contained in Y. The first column of Λy, with all elements fixed to unity,

contains the loadings of the indicators onto the latent intercept trajectory parameter (π0i).
The second column Λy contains loadings of the four indicators onto the latent linear
slope trajectory parameter (π1i). Finally, the elements within the diagonal θε matrix are
the estimated residual variances in the observed outcome measures within the ymeasurement model. The form of the θε matrix can be altered to accommodate tests of
hypotheses concerning the error structure underlying the observed indicators with respect
to heterogeneity and autocorrelation. This point is returned to briefly.
As shown in Eq. (3), the trajectory parameters themselves are assumed to be
distributed normally over subjects, with variances

and

, and covariance

. This equation corresponds to the unconditional model for interindividual
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differences in change (Singer & Willett, 2003), permitting individuals (i) to have
different estimates for true initial performance and the degree of linear change over time.
The mean parameters,

and

, correspond to the average unconditional intercept

and linear slope across subjects.
The structural model in Eq. (4) decomposes the latent intercept and slope
parameters in Eq. (3) into average (

and

) and residual (ζ0i and ζ1i)

components. In matrix form, this decomposition can be expressed as per Eq. (5), which
introduces the terms Βη and Γξ. This equation expresses the latent trajectory parameters,
η, as a function of

(trajectory parameter averages;

and

), Βη (relationships

between the latent trajectory parameters, η, with coefficients Β), Γξ (regressions of the
latent trajectory parameters on exogenous latent factors, ξ, via elements in the Γ matrix),
and ζ (a residual matrix). Because exogenous predictors have yet to be introduced, Γ is
set to zero in Eq. (6). For illustration purposes, the latent trajectory parameters are
assumed to be orthogonal (per the zero elements shown in the Β matrix in Eq. [6]).
However, elements in B can also be estimated if there exists an empirical, logical, or
theoretical reason to believe that trajectory parameters are correlated with one another.
As mentioned above, the elements of the ζ matrix (ζ0i and ζ1i) are residuals,
specifically, person-specific deviations of the values π.i about their respective means,
. These residuals, contained in the Ψ matrix shown in Eq. (7), represent individual
differences in (variances) and relationships among (covariances) the latent trajectory
parameters. Significant variance estimates are a prerequisite for examining predictors of
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these parameters; if there is no variance in the trajectory parameters, there is no variance
available to be accounted for. The off-diagonal elements of Ψ in Eq. (7) are covariances
among the latent trajectory parameters. In the two-parameter case (intercept and slope), a
positive relationship suggests that individuals with higher initial status exhibit steeper
increasing slopes in change over time, while a negative relationship suggests that
individuals with higher initial status exhibit steeper declining slopes in change over time.
Collectively, the first seven equations are of interest during the initial process of
constructing the y-measurement model that characterizes change over time. With regard
to the present research, the selection of a y-measurement model to capture change in
GPA over time was conducted in the following manner. For both datasets, 12 models
were tested in an attempt to identify the model that best satisfied relevant criteria (e.g.,
model convergence, acceptable fit to the data as indicated by global fit indices, logical
parameter estimates, and parsimony). The 12 models varied in the following
characteristics: the latent trajectory parameters included (i.e., intercept, linear, quadratic),
the assumption of fixed versus random trajectory components (i.e., intercepts or slopes
that are constant across subjects or are permitted to vary between subjects), the coding of
time (linear and higher-order transformations to capture nonlinear change versus
logarithmic change), and the use of fixed factor loadings versus freely estimated loadings
for the third and fourth performance observations (discussed in greater detail shortly).
These models are listed in Table 9 and discussed in greater detail below.
Model 1 was a random-intercept model. This model assumes that within-subjects
variability in GPA over time can be captured by a person-specific grand average that
varies across subjects (thus, there is no change over time). The next four models (models

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2-5) assumed that a linear slope parameter was also necessary to characterize change over
time in GPA. Model 2 was a fixed-intercept, fixed-slope model. This model assumes that
a single estimate for the slope and linear change parameter holds for all subjects (i.e., all
subjects follow the same trajectory with regard to change over time). Model 3 was a
random-intercept, fixed-slope model, which assumes that individuals vary in initial
performance, but change over time can be characterized using a global estimate
appropriate for all subjects. Model 4 was a fixed-intercept,-random-slope model, which
assumes no variance across individuals with regard to initial performance, but permits for
varying degrees of linear change over time across individuals. Finally, model 5 was a
random-intercept, random-slope model, which assumes that individuals vary with respect
to both initial performance and the degree of linear change over time.
The remaining seven models (models 6-12) allowed for the possibility of
nonlinear change in performance over time. Across these models, nonlinearity was tested
using several different approaches. Models 6 and 7 attempted to accommodate nonlinear
change via the inclusion of a latent quadratic parameter in addition to the intercept and
linear slope parameters. Model 6 was a random-intercept, random-slope, fixed-quadratic
model. This model assumes that individuals vary with respect to both initial performance
and linear change, but that all subjects exhibit the same degree of nonlinear change
characterized by the higher-order quadratic parameter. Model 7, the random-intercept,
random-slope, random-quadratic model, extended model 6 by permitting the quadratic
trajectory parameter to also vary between subjects, thus permitting varying degrees of
inflection in the trajectories across subjects.

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Models 8 and 9 attempted to capture nonlinear change via an intercept parameter
and a slope parameter with the linear elements being transformed into their natural logs to
accommodate logarithmic change. Models incorporating the logarithmic slope parameter
were tested in a manner parallel to that described above with regard to the linear slope
models; thus, model 8 was a fixed-intercept, fixed-slope model, model 9 was a randomintercept, fixed-slope model, and model 10 was a random-intercept, random-slope model.
Finally, models 11 and 12 attempted to capture nonlinearity by relaxing
constraints on the factor loadings between the outcome measures and the latent slope
parameter. Specifically, constraining the loadings to the order [0 1 2 3] forces the latent
slope parameter to assume a linear interpretation. Permitting the estimation of loadings at
certain time points allows for some degree of nonlinearity in the slopes, with the form of
nonlinear change determined empirically. In order for the y-measurement model to be
identified, the first and second loadings are set to 0 and 1, respectively; thus, the
estimated loadings correspond to the third and fourth performance observations. In other
words, nonlinear change was modeled by allowing the vector of loadings on the latent
slope parameter to take the form [0 1 x x], with x denoting estimated loadings. Models 11
and 12 were random-intercept, fixed-slope and random-intercept, random-slope models,
respectively.
For each of the 12 models above, three submodels were evaluated in an attempted
to test hypotheses with regard to the error structure underlying the observed outcome
measures. Submodel 1 made the assumption that the residuals for the outcome measures,
contained in the matrix θε, were homogeneous across measures (i.e.,

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and uncorrelated with one another. Submodel 2 permitted residuals to be
heterogeneous; however, residuals were assumed to be uncorrelated. Submodel 3
permitted residuals to be heterogeneous and permitted residuals between time-adjacent
measures to be correlated, with all correlations constrained to equality (i.e.,
.
Crossing the 12 y-measurement models with the three submodels described above
resulted in 36 models evaluated for each sample. The process for selecting a ymeasurement model will begin by comparing global fit indices across all models for
submodel 1. Models that meet criteria for global fit, discussed shortly, are retained for
examination with respect to local parameter estimates and error structure (comparisons
among submodels 1, 2, and 3). Because the samples differed with regard to the temporal
specificity of the criterion examined (i.e., semester GPA in the MSU-Only sample versus
yearly GPA in the Multi-Institution sample) and the time over which measures were
obtained (two years of college for the MSU-Only sample versus four years for the MultiInstitution sample), it was not assumed that the y-measurement model chosen for one
sample would be the same as that chosen for the other.
The second model of relevance to the present study was the x-measurement
model, which contains the exogenous individual-difference predictors (in this case,
ability, achievement motivation, and their interaction). As shown in Eq. (8), the xmeasurement model parallels the y-measurement model described by Eq. (1) with regard
to form. Composites for ability, achievement motivation, and the cross-product term were
used in the present research. In order for the model to be identified when single-indicator

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latent factors are introduced, elements of the vector-matrices δ (the residual matrix for the
predictor measures) and τx (the intercepts, or means, for the observed predictor
measures) were constrained to zero (Singer & Willett, 2003). Estimates for the predictor
means and variance-covariance matrix were modeled as characteristics of the factors, ξ,
via the κ and Φ matrices, as shown in Eq. (10).
Eqs. (11.a) and (11.b) show cognitive ability (cog), achievement motivation (ach),
and the interaction (int) term as predictors of two latent trajectory parameters, π0i and
π1i. The structural path coefficients, γ, are examined in testing hypotheses concerning
relationships between predictors and trajectory parameters. Eqs. (11.a) and (11.b) are
represented in matrix form in Eq. (5); however, the elements within the matrices now
appear as in (12). The α matrix contains conditional means for the trajectory parameters
adjusting for the influence of the exogenous predictors, Γ contains structural path
coefficients, γ, between the exogenous predictor factors, ξ, and the endogenous latent
trajectory parameters, π. As before, the elements of B in Eq. (12) are set to zero, based on
the assumption that parameter trajectories are uncorrelated for purposes of simplification.
Finally, the Ψ matrix in (13) contains the variances and covariances of the latent
trajectory parameters controlling for the influence of the exogenous predictors. Assuming
that the predictors account for a nonzero amount of variance in the trajectory parameters,
the elements of this matrix will be smaller in magnitude than those in (7).
Hypothesis evaluation. Figure 2 is a conceptual representation of the present
research in path diagrammatic form. In the figure, solid black paths with one-way arrows

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correspond to structural paths, dotted black paths with one-way arrows correspond to
fixed loadings, and grey paths with two-way arrows correspond to latent variances or
covariances. Given the analytic strategy described above, Hypotheses 1through 5 will be
evaluated as follows. Hypotheses 1 and 2 stated that achievement motivation and
cognitive ability would be positively related to initial performance. With respect to
Figure 2, tests of Hypotheses 1 and 2 would entail evaluating the magnitude of the
structural paths γ1 and γ2 relative to their respective standard errors. Positive, nonzero
estimates for γ1 and γ2 would provide support for Hypotheses 1 and 2. Hypothesis 3
stated that achievement motivation would be positively related to linear change in
performance over time. Testing Hypothesis 3 would entail evaluating the magnitude of
the structural path γ5 relative to its standard error. A positive, nonzero estimate for γ5
would provide support for Hypothesis 3. In addition to evaluating the main effects as
described above for Hypotheses 1 through 3, latent trajectories were plotted at low (-1
SD) and high (+1 SD) values of each predictor (see Curran, Bauer, & Willoughby, 2006
for a description of this process), thus permitting visual inspection of the manner in
which each predictor influences performance trajectories.
Hypothesis 4 stated that cognitive ability and achievement motivation would
interact in predicting the linear slope. The hypothesized form of the interaction was such
that the relationship between achievement motivation and linear change would increase
as cognitive ability increases (i.e., the relationship between achievement motivation and
linear change in performance will be stronger in magnitude among high-ability compared
to low-ability students). The evaluation of Hypothesis 4 entails a two-step process. First,
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the magnitude of the structural coefficient γ6 is evaluated; a nonzero coefficient would
provide evidence for an interaction between cognitive ability and achievement motivation
in predicting linear change. Second, simple intercepts and simple slopes were computed
to assess the form of the interaction (Curran et al., 2004; Preacher, Curran, & Bauer,
2006). Simple intercepts and simple slopes were evaluated for low- and high-motivation
students at two levels of ability: low ability and high ability. As before, conditional
values correspond to low and high are -1 SD and +1 SD from each variable‟s respective
mean.
Finally, Hypothesis 5 suggested that the relationship between ability and initial
performance, γ1, would be stronger in magnitude than the relationship between ability
and linear change in performance, γ4. In order to evaluate Hypothesis 5, 95% confidence
intervals were estimated about the structural path estimates γ1 and γ4. Evidence that the
estimate for γ1 was stronger in magnitude than γ4 and the confidence intervals did not
overlap would support Hypothesis 5.
Analyses were conducted in Mplus version 3.01 using maximum likelihood

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estimation (MLE). Global model fit was assessed using the model χ , the comparative fit
index (CFI; Bentler, 1990), the Tucker-Lewis nonnormed index (TLI; Tucker & Lewis,
1973), the root mean squared residual (SRMR; Bentler, 1995) and the root mean square
error of approximation (RMSEA; Steiger, 1990). Because of the relatively large sample

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sizes employed in the present research, the model χ will be overpowered and, hence,
should be interpreted cautiously. Hu and Bentler (1999) suggested the following cutoff
criteria under MLE for the incremental (TLI, CFI) and absolute (SRMR, RMSEA) fit
indices examined herein: CFI > .95, TLI > .95, SRMR < .08, and RMSEA < .06. Browne
& Cudeck (1993) suggested that values for the RMSEA between .05 and .08 indicate
reasonable model fit, and values less than .05 indicate close fit. 90% confidence intervals
about the RMSEA point estimate are reported for interpretation.

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Nested models were compared using the difference in χ between the two models

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(Δχ ), which was evaluated against the difference in degrees of freedom between the two
models (Δdf). Nested and non-nested models were also compared by examining change
in the incremental and absolute fit indices listed above.

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RESULTS: MSU-ONLY SAMPLE
Descriptive and Static Analyses
Table 10 provides descriptive statistics (means, standard deviations, and zeroorder correlations) for the study measures. As mentioned above, ability and achievement
motivation were centered about their respective means (

= 0.00, SDx.cent =

SDx, where x.cent = [x − ]) prior to computing the cross-product term for interpretative
purposes in the subsequent regression analyses. In the MSU-Only sample, ability and
achievement motivation were significantly and negatively related to one another;
however, the magnitude of the correlation was weak (r = -.084, p = .047). With regard to
academic performance, mean GPA increased slightly from the first to second time point
(3.08 to 3.11), and then remained near 3.00 during the final two time points (3.01 and
3.03, respectively). The pattern of standard deviations exhibited for GPA suggested
variance in academic performance was similar for the first and second performance
observations (.65 and .65 at Times 1 and 2) and for the third and fourth performance
observations (.72 and .74 at Times 3 and 4).
Intercorrelations among the four GPA measures yielded some evidence of a
simplex pattern, with intercorrelations being moderate in strength (.600s among timeadjacent elements; .500s and .400s among elements further separate in time). Criterionrelated validities for both predictors showed a decreasing pattern over time, although the
reduction was more severe for achievement motivation (ability: .290, .261, .273, and
.266; achievement motivation: .235, .264, .119, and .132). All predictor-criterion
correlations remained significant through Time 4.
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Latent Trajectory Models
Y-measurement model. Table 11 provides global model fit indices for the
measurement model in the MSU-Only sample. A browsing of the fit indices in Table 11
suggests that all models with fixed intercepts (models 2, 4, 8) yielded an unacceptably
poor fit to the data according to all fit indices. Therefore, any model retained for
consideration would allow for between-subjects variability in initial performance. In
addition, the fit indices suggest that models with variable intercepts, but either no
estimated slopes (i.e., the intercept-only model, model 1) or fixed slope components
(models 3 and 9), yielded CFI values below the .95 cutoff and RMSEA and SRMR
values at or above .08.
Therefore, five models that also permitted random slope parameters were retained
for further consideration: 5 (Random-Intercept, Random-Slope), 6 (Random-Intercept,
Random-Slope, Fixed-Quadratic), 7 (Random-Intercept, Random-Slope, RandomQuadratic), 10 (Random-Intercept, Random-Slope [Logarithmic]), and 12 (RandomIntercept, Random-Slope [Loadings Estimated at Times 3 and 4]). For each of these
models, CFI and TLI values met the .95 cutoff and SRMR values met the .08 cutoff.
However, RMSEA values were above.08 for model 6 (.083), model 7 (.101), model 10
(.089), and model 12 (.086). The only model producing an RMSEA value under .08 was
model 5, the random-intercept, random-slope model (RMSEA = .077, 90% CI = .051,
.104). The remaining fit indices all met relevant criteria (CFI = .973, TLI = .979, SRMR
= .040).
Table 12 provides the local parameter estimates for model 5, submodel 1 (referred
to hereafter as model 5.1). The mean estimated true intercept was 3.090 (SE = .026, 95%

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CI = 3.038, 3.142), which is similar to the observed value for GPA during participants‟
first semester at Time 1 (3.08). Similarly, the mean estimated linear change parameter
was -.023 (SE = .010, 95% CI = -.042, -.004), indicating that GPA decreased by
approximately .02 grade points per semester. Figure 3 provides a plot of the
unconditional mean performance trajectory for the MSU-Only sample including 95%
confidence bands (Curran et al., 2004).
The variances for the latent intercept and slope parameters are both significant
(ψIntercept↔Intercept = .272, SE = .024, 95 CI = .225, .319; ψSlope↔Slope = .019,
SE = .003, 95% CI = .013, .026), indicating meaningful between-subjects variability in
the parameters underlying latent change. The covariance between the latent intercept and
slope parameters was negative, although there was no evidence that the relationship
differed from zero (ψIntercept↔Slope = -.010, SE = .007, 95% CI = -.023, .004). The
standardized covariance between the latent intercept and slope parameters was -.131,
suggesting little between-subjects variance shared between the two trajectory parameters.
Finally, the unstandardized residual variance (θε) estimated for the four performance
measures was .168 (SE = .007, 95% CI = .154, .0182). Standardizing these estimates and

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subtracting them from 1.00 yields R estimates for each indicator, which ranged from
.618 to .698.
Submodel 5.2 relaxes the equality constraint placed on the error variances, thus
permitting heterogeneous error variances for the performance indicators. The nested

²

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model χ estimate comparing the fit of 5.2 against 5.1 was significant, χ (3) = 15.24, p =
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.001, indicating that a model permitting the error variances to vary over indicators
provides a better fit to the data than a model assuming homogeneous variances. Referring
back to Table 11, the mean intercept and linear slope parameters are similar to those
estimated under submodel 5.1 (specifically, 3.092 and -.023, respectively). In addition,
the variances for the latent intercept and slope parameters were again significant
(ψIntercept↔Intercept = .286, SE = .025, 95% CI = .237, .335; ψSlope↔Slope = .019,
SE = .004, 95% CI = .011, .027). Similar to model 5.1, the covariance between the latent
intercept and slope parameters was nonsignificant and negative (ψIntercept↔Slope = .014, SE = .008, 95% CI = -.029, .001; unstandardized ψ: -.190).
Submodel 5.3 permits both heterogeneous and correlated error variances between
time-adjacent indicators, with the time-adjacent correlations constrained to equality over
indicator pairs (i.e., θε(t)↔ θε(t+1) = θε(t+1)↔ θε(t+2)). Introducing the time-adjacent

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correlations in submodel 5.3 significantly improved model fit over 5.2, Δχ (1) = 6.42, p

²

= .011. Despite the significant χ estimate, the improvement in the other global model fit
indices was small (changes in the CFI, TLI, RMSEA, and SRMR were all less than .01 in
magnitude). In addition, introducing the constrained time-adjacent correlation, variability
in the latent slope parameter was no longer significant (ψSlope↔Slope = .010, SE =
.006, 95% CI = -.001, .022). Because the less-parsimonious 5.3 did not appear to yield an
appreciable increase in model fit and because of the nonsignificant variance estimate for

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the linear slope, 5.2 (random-intercept, random-slope with heterogeneous error variances)
was retained to model change in performance over time.
Structural model. In order to examine the contribution of ability and achievement
motivation as predictors of the performance trajectories, the indicator variables
corresponding to ability, achievement motivation, and their interaction were introduced
with structural paths estimated between each of the three predictors and the two latent
trajectory parameters (the intercept and linear change over time). This model will be
referred to as structural model 5.2 from here on. Table 13 provides global model fit
statistics for the structural model described above. All fit indices met cutoff criteria and

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indicated reasonable to good fit, χ (11) = 30.93, CFI = .982, TLI = .970, RMSEA = .057
(90% CI = .034, .081).
Table 14 provides parameter estimates for structural model 5.2. Hypotheses 1 and
2 stated that achievement motivation and ability would be positively related to initial
performance. The structural path between ability and the latent intercept parameter was
.291 (SE = .036, 95% CI = .220, .362, standardized γ = .363); the structural path between
achievement motivation and the latent intercept parameter was .363 (SE = .048, 95% CI =
.270, .457, standardized γ = .347). Both achievement motivation and ability were
positively related to initial performance; thus, Hypotheses 1 and 2 were both supported.
Hypothesis 3 suggested that achievement motivation would be positively related
to linear change over time, that is, individuals who are higher in achievement motivation
would have steeper, positive increases in GPA across the four time points. The estimated
structural path between achievement motivation and the latent slope parameter was -.053
(SE = .019, 95% CI = -.091, -.016, standardized γ = -.197). Although achievement
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motivation was significantly related to the linear change parameter, the relationship was
negative in sign; thus, Hypothesis 3 is not supported. Parenthetically, the path between
ability and the latent linear change parameter was nonsignificant (γ = .006, SE = .015,
95% CI = -.022, .034, standardized γ = .029).
To further illustrate the influence of ability and achievement motivation on latent
trajectories, Figure 4 shows plots of estimated latent performance trajectories at both low
(-1 SD) and high (+1 SD) ability and motivation. Figure 4(a) shows estimated trajectories
for individuals at both low and high ability. In line with the results above, estimated
initial performance for high-ability individuals was much higher than that for low-ability
individuals (low-ability: 2.897, 95% CI = 2.830, 2.964; high-ability: 3.285, 95% CI =
3.218, 3.352). However, the estimated latent slope parameters were negative and similar
in magnitude at low and high ability (low-ability: -.017, 95% CI = -.044, .010; highability: -.025, 95% CI = -.052, .002), as reflected in the roughly parallel trajectories
shown in Figure 4(a). Although the negative linear slope parameter was stronger in
magnitude for high-ability students than for low-ability students, the 95% confidence
bands about the trajectories shown in Figure 2(a) did not overlap. Therefore, there is no
evidence that the estimated latent trajectory at high ability converges with the trajectory
estimated at low ability.
Figure 4(b) shows estimated trajectories at both low and high achievement
motivation. Estimated initial performance was higher at high-motivation compared to
low-motivation (low-motivation: 2.906, 95% CI = 2.839, 2.973; high-motivation: 3.277,
95% CI = 3.210, 3.344). The negative structural coefficient reported above between
achievement motivation and the latent linear slope parameter is reflected in negative

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estimated conditional slope at high-motivation (-.048, 95% CI = -.075, -.021) compared
to the slight positive estimated conditional slope at low-motivation (.006, 95% CI = .021, .033). Figure 4(b) shows that the estimated latent trajectories at low- and highmotivation appear to be approaching convergence over time as indicated by the 95%
confidence bands about the estimated trajectories. Specifically, the lower band for the
high-motivation students intersects the upper band for the low-motivation and slightly
beyond time point 3 (i.e., the third semester in school).
Hypothesis 4 suggested that there would be a significant interaction between
ability and achievement motivation in predicting linear change over time, such that the
relationship between motivation and linear change would be stronger among high-ability
individuals than for low-ability individuals. As shown in Table 14, the structural path
between the interaction term and the latent linear slope parameter was positive and
significant (γ = .062, SE = .027, 95% CI = .009, .115, standardized γ = .162). In order to
assess whether the significant interaction was of the form hypothesized, simple intercepts
and slopes were estimated at low- and high-motivation at both low and high conditional
values for ability.
At low-ability, low-motivation, the estimated simple intercept was 2.693 (SE =
.051, 95% CI = 2.593, 2.793) and the estimated simple slope was .023 (SE = .020, 95%
CI = -.016, .062). At low-ability, high-motivation, the estimated simple intercept was
3.101 (SE = .047, 95% CI = 3.009, 3.193) and the estimated simple slope was -.073 (SE =
.019, 95% CI = -.110, -.036). Thus, at low ability, increases in motivation were
associated with higher estimated initial performance and more negative linear change
over time. At high-ability, low-motivation, the estimated simple intercept was 3.119 (SE

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= .044, 95% CI = 3.033, 3.205) and the estimated simple slope was -.011 (SE = .018,
95% CI = -.046, .024). Finally, at high-ability, high-motivation, the estimated simple
intercept was 3.452 (SE = .049, 95% CI = 3.356, 3.548) and the estimated simple slope
was -.023 (SE = .020, 95% CI = -.062, .016). Thus, at high ability, there was a tendency
for initial performance to increase and for the linear slope to become more negative as
achievement motivation increased.
Estimated trajectories for low- and high-motivation at low- and high-ability are
plotted in Figure 5(a) and 5(b). The hypothesized form of the interaction, that the
relationship between achievement motivation and linear change would become more
positive as ability increased, is not at all evident in the plots. Indeed, the only situation
where a positive slope is found is at low-ability, low-motivation. Thus, hypothesis 4 was
not supported.
Finally, Hypothesis 5 suggested that the relationship between ability and initial
performance would be significantly stronger in magnitude compared to the structural path
between ability and linear change. The 95% confidence interval about the unstandardized
path coefficients were as follows: γAbility→Intercept = .291(95% CI = .220, .362),
γAbility→Slope = .006 (95% CI = -.023, .035). These results suggest that, in the MSUOnly sample, ability was more strongly related to initial performance than linear change
overtime; thus, Hypothesis 5 is supported.

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RESULTS: MULTI-INSTITUTION SAMPLE
Descriptive and Static Analyses
Table 10 provides descriptive statistics (means, standard deviations, and zeroorder correlations) among the study measures. As was done in the MSU-Only sample,
ability and achievement motivation were centered about their respective means (

= 0.00, SDx.cent = SDx, where x.cent = [x − ]) prior to computing the cross-product
term for interpretative purposes in the subsequent regression analyses.
In the Multi-Institution sample, ability and achievement motivation were
positively and significantly related to one another, although the relationship was weak in
magnitude (r = .109, p < .001). With regard to academic performance, mean GPA
decreased across all four time periods at a relatively steady rate (3.45, 3.42, 3.40, and
3.38 for Times 1 through 4, respectively). The pattern of standard deviations exhibited for
GPA suggested a slight tendency for variability in the GPA measures to increase over
time, although the increase was small (standard deviations increasing from .60 to .63 for
Times 1 through 4, respectively).
Intercorrelations among the four GPA measures again yielded evidence of a
simplex pattern, with intercorrelations being stronger in magnitude than that observed
within the MSU-Only sample (.900s among time-adjacent elements; .800s and upper
.700s among elements further separate in time). Criterion-related validities for both
predictors showed a decreasing pattern over time, although the reduction was not overly
large for either predictor (ability: .546, .546, .514, and .461; achievement motivation:

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.191, .185, .180, and .148). All predictor-criterion correlations remained significant
through Time 4.
Latent Trajectory Models
Y-measurement model. Table 15 provides global model fit indices for the
measurement model in the Multi-Institution sample. A browsing of the fit indices in
Table 15 suggests that all models with fixed intercepts (models 2, 4, 8) yielded a poor fit
to the data; thus, any model retained for consideration would allow for between-subjects
variability in initial performance. In addition, a browsing of the fit indices suggests that
models with variable intercepts, but either no estimated slopes (the intercept-only model,
model 1) or fixed slope components (models 3 and 9), yielded values below the cutoff
criteria for CFI, TLI, and RMSEA.
Therefore, five models were thus retained for further consideration: 5 (RandomIntercept, Random-Slope), 6 (Random-Intercept, Random-Slope, Fixed-Quadratic), 7
(Random-Intercept, Random-Slope, Random-Quadratic), 10 (Random-Intercept,
Random-Slope [Logarithmic]), and 12 (Random-Intercept, Random-Slope [Loadings
Estimated at Times 3 and 4]). Note that these are the same five models as those retained
within the MSU-Only sample at this stage of the analysis. For models 5, 6, 10, and 12,
the CFI value was marginal with respect to the .95 cutoff criteria, with values ranging
from .94 to .95; the CFI for model 7 was well above the cutoff (.993). TLI values for all
models were higher than the .95 cutoff. Furthermore, SRMR values across all models
were well below the .08 cutoff. The RMSEA values for all five models were all above the
.08 value suggested by Browne and Cudeck (1993) as indicating reasonable model fit.
For four of the five models (5, 6, 10, and 12), the RMSEA value was greater than .200,

110

while the RMSEA value for model 7 was .109. In addition, model 7 was the only model
where the RMSEA value fell below .08 when various submodels were tested, as shown in
Table 15, with RMSEA values falling to less than .001 for models 7.2 and 7.3. Thus,
model 7 (random-intercept, random-slope, random-quadratic) was retained for further
examination. Aside from the RMSEA value, all other fit indices suggested excellent fit
for model 7 (CFI = .993, TLI = .989, RMSEA = .109, SRMR = .005).
Examining the parameter estimates for model 7.1 under Table 16, the average
trajectory is represented by the following estimates for average change parameters:
intercept = 3.447 (SE = .017, 95% CI = 3.414, 3.479), slope = -.023 (SE = .008, 95% CI =
-.039, -.007), quadratic = .001 (SE = .002, 95% CI = -.004, .005). The estimate for initial
performance was comparable to the observed value for GPA at Time 1 (3.45 under Table
10). The negative slope in tandem with the relatively small mean estimate for the
quadratic change parameter suggests that, on average, GPA tends to decrease over time at
a slightly decreasing rate, as reflected in the change in observed GPA over the four time
points in Table 10 (3.45, 3.42, 3.40, and 3.38 from Time 1 to Time 4). The mean
unconditional academic performance trajectory for the Multi-Institution sample is shown
in Figure 6.
The variance estimates for the latent intercept, slope, and quadratic parameters
were as follows: ψIntercept↔Intercept = .342 (SE = .014, 95% CI = .315, .369),
ψSlope↔Slope = .060 (SE = .004, 95% CI = .053, .067), ψQuadratic↔Quadratic =
.005 (SE < .001, 95% CI = .004, .005). Relative to each estimate‟s standard error, the
observed estimates are large enough to infer meaningful between-subjects variability in
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each of the latent trajectory parameters. The estimated covariances among the latent
trajectory parameters were as followes: ψIntercept↔Slope = -.004 (SE = .005, 95% CI
= -.014, .005, standardized ψ = -.029),ψIntercept↔Quadratic = -.004 (SE = .001, 95%
CI = -.007, -.001, standardized ψ = -.098),ψSlope↔Quadratic = -.015 (SE = .001, 95%
CI = -.017, -.013, standardized ψ = -.863). Similar to the results obtained with the MSUOnly sample, initial performance was not significantly related to linear change in
performance. However, both initial performance and linear change in performance were
related to the latent quadratic change parameter, with a particularly strong relationship
observed between linear and quadratic change.
Despite the high intercorrelation between the linear and quadratic parameters, the
random quadratic component was retained in the measurement model. Compared to
model 6 (random-intercept, random-slope, fixed-quadratic), the fit estimates for all global
fit indices were superior when the quadratic component was permitted to vary over
subjects as opposed to when it was constrained to be invariant. Similar conclusions were
reached when comparing model 7 to model 5 (random-intercept, random-slope), where
no latent quadratic parameter was estimated at all. As shown under submodel 7.1, the
estimated residual variance for the GPA indicators was significant (θε = .011, SE < .001,
95% CI = .010, .012). Across the four GPA indicators, the measurement model specified
in 7.1 accounted for approximately 97% of the observed variance in the GPA indicators.

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Submodel 7.2 permitted the residual variances (θε) to vary across indicators.
Relaxing the equality constraint resulted in a significant improvement in model fit for

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submodel 7.2 compared to submodel 7.1, Δχ (3) = 63.71, p < .001, suggesting that a
measurement model permitting heterogeneous residual variances provided a better fit
than that observed for a model constraining the residual variances to equality.
Furthermore, Table 16 shows that permitting heterogeneous residual variances across
GPA indicators did not substantially alter the local parameter estimates (i.e., latent
variances and covariances, latent means) in the y-measurement model from what was
observed when variances were homogeneous (compare parameter estimates for the
columns corresponding to Submodels 7.1 and 7.2).
Submodel 7.3 (heterogeneous residual variances with correlations among timeadjacent indicators constrained to equality) failed to converge during estimation and,
thus, was not further considered. Therefore, because Submodel 7.2 provided a better fit
compared to Submodel 7.1 without resulting in large changes in the model‟s parameter
estimates, Submodel 7.2 was retained as the model used to capture the latent structure of
performance trajectories for subsequent hypothesis testing.
Structural model. Table 17 illustrates global model fit statistics for structural
model 7.2 with ability, achievement motivation, and their interaction included as
exogenous predictors of the latent change parameters. The estimates for the global fit

²

indices suggested a reasonable fit to the data, χ (4) = 5.65, CFI = 1.000, TLI = .999,
RMSEA = .018, SRMR = .002. Table 18 provides parameter estimates for the structural

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model permitting structural paths between ability, achievement motivation, and their
interactions with the latent trajectory parameters.
Hypotheses 1 and 2 suggested that there would be positive, significant
relationships between both ability and motivation and initial performance. The estimates
for the paths were as follows: γAbility→Intercept = .393 (SE = .017, 95% CI = .359,
.426, standardized γ = .549),γMotivation→Intercept = .176 (SE = .032, 95% CI = .114,
.239, standardized γ = .133). In support of Hypotheses 1 and 2, both ability and
motivation were significantly related to initial performance, such that predicted initial
performance increased as either ability or motivation increased.
Hypothesis 3 suggested that achievement motivation would be positively related
to linear change in performance. The estimated structural path between motivation and
linear change in performance was .012 (SE = .019, 95% CI = -.025, .049, standardized γ =
.024). Although the relationship was in the expected direction, the estimated coefficient
did not reach significance; thus, Hypothesis 3 is not supported. Parenthetically, the
estimated structural path between ability and linear change was .019 (SE = .010, 95% CI
= -.001, .039, standardized γ = .072). In addition, ability was significantly and negatively
related to the latent quadratic parameter (γAbility→Quadratic = -.011, SE = .003, 95%
CI = -.017, -.005, standardized γ = -.156), while the relationship between achievement
motivation and quadratic change was not significant (γMotivation→Quadratic = -.007,
SE = .005, 95% CI = -.018, .004, standardized γ = -.052).

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To illustrate the main effects of ability and motivation on performance
trajectories, simple intercepts and simple slopes were estimated for students both low (-1
SD) and high (+1 SD) in each construct. With regard to the ability, the strong effect on
initial performance discussed above is reflected in the large difference between estimated
initial performance at low and high ability (low-ability: intercept = 3.130, SE = .019, 95%
CI = 3.093, 3.167; high-ability: intercept = 3.763, SE = .019, 95% CI = 3.726, 3.800).
The linear slope parameter was negative in sign for at both low and high ability (lowability: -.037, SE = .012, 95% CI = -.061, -.013; high-ability: -.006, SE = -.006, 95% CI =
-.030, .018). The quadratic parameter was significant and positive at low ability, but
significant and negative at high ability (low-ability: .009, SE = .003, 95% CI = .003, .015;
high-ability: -.008, SE = .003, 95% CI = -.014, -.002).
The estimates reported above are plotted in Figure 7. As shown in Figure 5(a),
estimated initial performance is much higher at high compared to low ability. However,
estimated GPA for both low and high ability shows a tendency toward linear decline. The
positive quadratic parameter at the low ability is reflected in the very slight positive
inflection that appears around Year 3. Conversely, the negative quadratic parameter
observed at high ability is reflected in the increasing rate of GPA decline over time.
Despite the slight trend toward convergence in GPA over time, the 95% confidence bands
suggest that the two groups remain far separated in performance at Year 4. In other
words, there is no evidence that performance trajectories for low- and high-ability
students converge by the final time observed (Year 4).
A somewhat different conclusion is reached with regard to the main effect of
achievement motivation on performance trajectories. Estimated initial performance at

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high motivation is higher than that observed at low motivation (low-motivation: 3.369,
SE = .019, 95% CI = 3.332, 3.406; high-motivation: 3.523, SE = .019, 95% CI = 3.484,
3.562). Furthermore, the slopes at both low- and high-motivation show a slight trend
toward decrease over time, with the magnitude of the negative slope being relatively
similar, albeit weak, at low and high motivation (low-motivation: -.027, SE = .012, 95%
CI = -.051, -003; high-motivation: -.017, SE = .012, 95% CI = -.041, .007). Although the
estimates for the quadratic parameters were not significant (in line with the nonsignificant
effect of motivation on quadratic change noted above), the magnitude of the performance
decline appeared to decrease over time at low motivation, as reflected in the positive
quadratic parameter (.003, SE = .003, 95% CI = -.003, .009). Conversely, the rate of
decline at high motivation appeared to increase over time, as reflected in the slight
negative quadratic estimate (high-motivation: -.002, SE = .003, 95% CI = -.008, .004).
Again, it should be noted that the estimates for the quadratic parameters were relatively
weak, and thus should be interpreted with caution.
Figure 7(b) illustrates the results discussed above with regard to the main effect of
motivation on performance trajectories. Highly motivated students begin college with
relatively higher initial performance compared to low-motivation students. However, the
advantage conferred to highly-motivated students dissipates rather quickly, as reflected in
the overlap in the 95% confidence bands about the estimated trajectories for low- and
high-motivation students slightly after Year 2. In conclusion, although the pattern of main
effects exerted by ability and motivation were similar in form, the magnitude of the
effects for ability resulted in an advantage conferred to high-ability students that
continued on until the fourth year of college. The same could not be said with regard to

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motivation, as discussed above with respect to the overlapping confidence bands about
the estimated trajectories for low- and high-motivation students.
Hypothesis 4 suggested a significant interaction between ability and motivation
with regard to linear change in performance, such that the relationship between
motivation and linear change would be stronger among high-ability students. As shown
in Table 18, the interaction term was not significantly related to the linear change
parameter (-.042, SE = .023, 95% CI = -.087, .004, standardized γ = -.069). Although the
interaction term was not significant, plots of estimated trajectories for low- and highmotivation individuals at both low and high conditional values of ability are shown in
Figure 8(a) and 8(b) for illustrative purposes.
At low ability, the estimates for the simple intercepts and slopes are as follows:
low-motivation: intercept = 3.053 (SE = .026, 95% CI = 3.002, 3.104), slope = -.057 (SE
= .015, 95% CI = -.088, -.026), quadratic = .016 (SE = .005, 95% CI = .006, .026); highmotivation: intercept = 3.207 (SE = .029, 95% CI = 3.150, 3.264), slope = -.017 (SE =
.017, 95% CI = -.050, .016), quadratic = .003 (SE = .005, 95% CI = -.007, .013). Figure
8(a) compares the estimated trajectories at low ability across both low and high
motivation. At low ability, trajectories at low motivation reach an inflection in their
trajectory at around Year 3, after which performance begins to improve. Conversely, at
high motivation, the decrease in performance appears to be sustained over time. Although
the 95% confidence bands suggest that the trajectories do not overlap in initial
performance, substantial overlap is observed beginning slightly prior to Year 2,
suggesting that, among low-ability students, performance trajectories cannot be
distinguished on the basis of motivation.

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At high ability, the estimates for the simple intercepts and slopes are as follows:
low-motivation: intercept = 3.686 (SE = .029, 95% CI = 3.629, 3.743), slope = .003 (SE =
.017, 95% CI = -.030, .036), quadratic = -.009 (SE = .005, 95% CI = -.019, .001); highmotivation: intercept = 3.839 (SE = .026, 95% CI = 3.788, 3.890), slope = -.016 (SE =
.015, 95% CI = -.045, .013), quadratic = -.008 (SE = .004, 95% CI = -.016, .000). Figure
8(b) shows the estimated trajectories at high ability across both low and high
achievement motivation. As was the case at low ability, the two trajectories shown in
Figure 8(b) do not overlap at Year 1; high motivation is associated with significantly
higher initial performance compared to low standing on motivation. However, overlap is
observed in the 95% confidence bands starting at about halfway between the Year 1 and
Year 2 mark and convergence in the two estimated trajectories increases over the four
years. Therefore, similar to what was described above at low ability, the trajectories
associated with low and high standing on achievement motivation are not well
distinguished at high ability. Therefore, even had the interaction been significant, the
form of the interaction was not as hypothesized; thus, Hypothesis 4 is not supported.
Finally, Hypothesis 5 suggested that the structural path between ability and initial
performance would be significantly stronger in magnitude compared to the structural path
between ability and linear change. The 95% confidence interval about the unstandardized
path coefficients were as follows: γAbility→Intercept = .393 (95% CI = .360, .426);
γAbility→Slope = .019 (95% CI = -.001, .039). These results suggest that, in the MultiInstitution sample, ability was more strongly related to initial performance than linear
change overtime; thus, Hypothesis 5 is supported.
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DISCUSSION
The final section concludes by recapitulating and integrating findings from the
two studies as they relate to the theory and hypotheses proposed above. Strengths and
limitations of the present study are then discussed, and the paper concludes by addressing
several potential avenues for future research.
Study Findings
In both studies reported above, ability and achievement motivation had a
significant and positive relationship with initial academic performance. Thus, students
who were higher in either ability or achievement motivation generally obtained higher
initial performance compared to students low in ability or achievement motivation.
Although both predictors were significantly related to initial performance, there was
some evidence that ability was a stronger predictor of true initial performance compared
to achievement motivation, primarily in the Multi-Institution sample. In the MSU-Only
sample, the standardized path estimate for ability and initial performance was .363, while
the standardized path estimate for motivation and initial performance was .347. In the
Multi-Institution sample, the standardized path estimate for ability and initial
performance was .549, while the standardized path estimate for motivation and initial
performance was .133. Somewhat discrepant among these results is the relatively weak
relationship observed between motivation and initial performance in the Multi-Institution
sample. Two possible explanations for the difference in results with regard to the effect
of motivation on initial performance are immediately evident.

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First, the measures of achievement motivation differed between the two studies.
In the MSU-Only sample, the 10-item composite derived from the Steers and Braunstein
(1976) and Fineman (1975) scales was used to operationalize achievement motivation,
while the 15-item biodata measure was used in the Multi-Institution sample. The
relatively weak effect of motivation on initial performance in the Multi-Institution sample
may have been attributable to some aspect related to the measurement of achievement
motivation in this sample. Given the relatively high degree of convergence observed in
the pilot study between the Steers & Braunstein/Fineman scale and the achievement
motivation biodata scale, however, it is not clear how differences in measurement
between the two studies may have produced the pattern of results observed.
A second potential explanation for the discrepant results observed with regard to
the effect of achievement motivation on initial performance pertains to the varying time
frames over which performance was measured in the two studies (GPA measured at the
semester level in the MSU-Only sample, GPA measured yearly in the Multi-Institution
sample, aggregated over semesters within a given year). It is possible that the differential
magnitude of the relationships observed between motivation and initial performance is
related to the temporal specificity of the criterion used. Because GPA was measured at
the yearly level in the Multi-Institution sample, the relationship between achievement
motivation and initial performance may have been attenuated if there exists some factor
specific to first-semester GPA (e.g., being temporally closer to the transition between
high school and college) that is obscured when GPA data is aggregated over semesters to
derive a yearly composite.

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In neither sample was achievement motivation found to be positively related to
linear change in performance over time, although a significant negative relationship was
observed in the MSU-Only sample. Zyphur and colleagues (2008) suggested that
negative relationships between predictors and change parameters may occur if the
predictor is related to initial performance and if initial performance is strongly and
negatively related to performance change. The substantive explanation for this state of
affairs is a ceiling effect inherent in GPA as a criterion: if highly-motivated students
perform very well initially (e.g., 3.8 on a 4.0 scale), those students have less room on the
scale to increase over time compared to individuals who may have obtained a lower GPA
during the initial time period (e.g., a 3.3). In this case, a negative relationship between
motivation and linear change would be expected because low-motivation students, on
average, have more room to increase, while it is more likely that highly motivated
students would either maintain a high GPA or exhibit some degree of decline.
However, evidence provided in the MSU-Only sample does not support a ceilingeffect argument. First, the relationship between initial performance and linear change in
the MSU-Only sample was weak in magnitude (standardized γ = -.132), suggesting only a
slight tendency for those who performed well initially to hit a ceiling on performance.
Second, although motivation was positively related to initial performance in the MSUOnly sample, the relationship was not so strong as to preclude further increases in
performance for highly-motivated students after the first semester. For instance, among
high-motivation students (+1 SD), the estimated intercept was 3.28, which is quite far
from the 4.0 ceiling. Based on these arguments, the negative relationship between
motivation and linear change appears not to be an artifact caused by ceiling effects. An

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alternative explanation is touched upon later when study strengths and limitations are
addressed.
Although no obvious explanation exists for the negative relationship between
achievement motivation and the linear slope trajectory parameter in the MSU-Only
sample, negative relationships have been reported in the past between nonability
characteristics and linear change over time (e.g., conscientiousness and performance
orientation, Yeo & Neal, 2004; emotional stability, Thoresen et al., 2004; motivation to
learn, adaptability, Shivpuri et al., 2006). Whether these findings lend themselves to a
substantive explanation or are simply attributable to methodological artifacts (e.g.,
sampling error, ill-fitted measurement models resulting in latent trajectory parameters
that do not adequately represent change) remains unresolved.
One of the primary purposes of the present research was to test for interactive
effects between ability and achievement motivation, particularly with regard to linear
change in performance over time. The magnitude of the path coefficient between the
interaction term and the latent slope parameter in the Multi-Institutuion sample failed to
reach significance. A significant interaction term was observed in the MSU-Only sample;
however, the form of the interaction was not as predicted. Estimated simple slopes for
low- and high-motivation students at both low and high levels of ability suggested a
tendency for the linear slope to become more negative as motivation increased among
low-ability subjects. Among high-ability subjects, slopes did not appear to differ
significantly between low- and high-motivation students. These findings contradict the
hypothesized form of the interaction, which suggested that achievement motivation
would be more strongly and positively related to linear change in performance among

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high-ability students. A potential explanation for this effect is discussed under study
strengths and limitations below.
Finally, in both samples, support was found for the hypothesis that the
relationship between ability and initial performance would be stronger in magnitude than
the relationship between ability and linear change in performance, evidence was found
for this hypothesis. This hypothesis was predicated on the argument that, due to the
nature of the criterion measure from which trajectories were modeled in the present
research, the primary influence of ability would be to differentiate students in a relatively
constant manner throughout the duration of college, as opposed to influencing how
students‟ performance may change over time. In both samples, it was further found that
performance trajectories for low- and high-ability students never approached
convergence, further supporting the idea that the advantage conveyed by ability is
retained over the course of a student‟s undergraduate career.
Strengths and Limitations
The research reported herein contains a number of strengths in light of the
questions addressed. First and foremost, the repeated measures of performance allowed
for a test of the interaction hypothesis in a manner that has yet to be conducted in an
applied setting. Given the field‟s acknowledgment that performance is not stable over
time and the longstanding nature of the debate on the interaction hypothesis, this design
allows a relatively novel means by which to address the independent and joint effects of
ability and motivation on performance.
Similarly, the present study also represents, to the author‟s knowledge, the first
test of trait achievement motivation as a predictor of performance trajectories. Given the

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recent resurgence of interest in trait-based perspectives on achievement motivation (e.g.,
Cassidy & Lynn, 1989; Kanfer & Heggestad, 2000), as well as arguments highlighting
approach and avoidance temperament as a basic approach to the structure of human
personality (e.g., Elliot & Thrash, 2010; Read, Monroe, Brownstein, Yang, Chopra, &
Miller, 2010), it would appear that research on trait achievement motivation as a
predictor of performance trajectories in applied settings is relatively timely. Second, the
two-study design permitted replication of findings across the two studies. In addition to
providing evidence for generalizability, attempts at replication also highlight potential
boundary conditions (e.g., predictor operationalization, temporal specificity of the
criterion) that may otherwise go unnoticed if a single-study design were to be employed.
Third, the relatively large sample sizes in both studies (599 in the MSU-Only sample,
1,279 in the Multi-Institution sample) allowed for relatively precise parameter estimation.
In addition to the strengths noted above, the present research also contains several
important limitations that should be mentioned. First, the two studies reported herein
focused on predictors of performance trajectories within a relatively broad population
(i.e., college undergraduates). It is quite possible that closer examination would reveal
factors that may systematically alter either the form of performance trajectories or the
relationships observed between trajectory parameters and the individual-difference
constructs examined. One such factor may be college major. To date, no research that the
author is aware of has examined systematic differences in academic performance
trajectories across college majors. Given the large number of majors offered by postsecondary institutions, such an investigation would be challenging from both a logistical
and methodological standpoint. One potential idea may be to explore systematic variation

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in trajectories across major clusters (e.g., natural sciences, social sciences, business, etc.).
However, even within such clusters, majors are often quite different (e.g., within the
social sciences, the course content for economics, psychology, and political science likely
vary with regard to a number of characteristics). Although this issue is important and
substantively interesting, the present study, and the results reported herein, cannot speak
to it.
A second limitation of the present study pertained to the lack of information
regarding choice behavior underlying course selection on the part of the participants.
Beyond general common beliefs regarding course choice behavior for undergraduate
students (e.g., enrollment in introductory classes tends to occur more frequently early in
one‟s collegiate career), no information was available to aid the in the interpretation of
trajectories or to employ as controls for factors such as course difficulty or other course
characteristics. A recent study by Durik and colleagues (2009) found a negative
relationship between the work-mastery facet measured in the Cassidy and Lynn (1989)
achievement motivation scale and diversity in course selection within a sample of
undergraduate students. If these results generalize beyond the sample examined by Durik
et al. (2009), they suggest that students higher in achievement motivation tend to focus
their efforts in a relatively narrow set of courses geared toward their academic interests.
If highly-motivated students exhibit a tendency to enroll in and complete a larger
number of courses within their academic major compared to low-motivation students,
they are also likely to progress more quickly through their major requirements and,
hence, to enroll in a larger number of upper-level courses that are more challenging and
demanding, relative to the courses taught at lower levels. If true, this state of affairs may

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be reflected in a greater tendency for highly-motivated students‟ GPAs to level off, or
even decrease, over time due to the heightened demand and difficulty associated with the
course material they are exposed to. In other words, over their undergraduate careers, the
trajectories for students high in achievement motivation maybe more susceptible to some
decrease over time because such students tend to enroll in more difficult courses
compared to their low-motivation counterparts. This may provide a partial explanation
for the negative relationship observed in the MSU-Only sample between achievement
motivation and linear change in performance over time.
Furthermore, if highly-motivated students exhibit a tendency to focus on classes
within their own major and, hence, enroll in more difficult upper-level courses, they may
be at greater risk for failure if they do not have levels of academic ability commensurate
to the difficulty associated with the course material they are exposed to. If so, then
highly-motivated, low-ability students may exhibit a greater tendency toward a negative
linear change in performance over time, relative to either low-ability, low-motivation or
high-ability, low-motivation students (who presumably enroll in courses that are less
demanding) or high-ability, high-motivation students (who presumably have the
necessary levels of ability needed to excel when presented with challenging course
content). This provides a potential explanation for the form of the significant abilitymotivation interaction observed in the MSU-Only sample, wherein low-ability, highmotivation students exhibited the greatest tendency to decrease in performance over time
(refer to Figure 5[a] and 5[b]).
A third limitation is the inability to explain several discrepant effects observed
between the MSU-Only and Multi-Institution samples. Although the MSU-Only sample

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had lower power to detect significant effects due to the smaller sample size compared to
the Multi-Institution sample, several significant relationships were found in this sample
that were not found in the Multi-Institution sample (e.g., the significant negative
relationship between achievement motivation and linear change and the significant
interaction, as discussed above). Due to the nature of the differences between the samples
(e.g., varying temporal specificity of the criterion measure, the inclusion of one
institution in the MSU-Only sample versus five institutions in the Multi-Institution
sample, differences in the operationalization of motivation between the two samples, the
examination of performance over two years in one sample versus four years in the
second), it is not possible to isolate the cause of the differences in results. That said,
knowledge of these differences provides a potential avenue for future research in an
attempt to systematically delineate potential boundary effects with respect to the effect of
ability and achievement motivation on performance trajectories in academic settings.
A final limitation pertains to the differences observed between the subset of cases
retained for analysis and those cases that were excluded. There was relatively little
evidence for meaningful differences between those cases retained for analysis and cases
that were excluded in the MSU-Only sample. However, the same could not be said for
the Multi-Institution sample, where rather large differences were observed on
demographic, background, and study variables. Although it is difficult to ascertain the
specific implications associated with the attrition effects apparent in the Multi-Institution
sample, it is possible that such effects may have contributed to differences in results
observed compared to the MSU-Only sample. Furthermore, effects due to attrition in the

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MSU-Only and Multi-Institution samples may also reduce the extent to which results
obtained in the present research can be expected to generalize to other samples.
Future Research
With changing views on the dynamic nature of performance as well as increased
understanding of methods for examining change in applied psychology, research on
predictors of performance trajectories has increased greatly over the past twenty years.
However, many topics remain to be examined. In the educational context, only two other
studies known to the author have examined performance trajectories within
undergraduate samples (i.e., Shivpuri et al., 2006; Zyphur et al., 2008). Results from
three studies do not provide sufficient basis to make definitive, generalizable conclusions
regarding individual difference correlates of trajectories. Thus, although the knowledge
base on predictors of trajectories appears to be increasing, additional research is clearly
needed.
Furthermore, no research on performance trajectories in educational settings has
examined the effects of contextual or environmental influences. At a relatively proximal
level, one concept that has been examined with regard to static measures of performance
pertains to the idea of situational constraints introduced Peters and O‟Connor (e.g.,
Peters, Chassie, Lindholm, O‟Connor, & Kline, 1982; Peters, Fisher, & O‟Connor, 1982;
Peters & O‟Connor, 1980) and extended to the academic context (Villanova, 1996). From
a macro perspective, research has also provided support for the influence of various
classes of institutional characteristics found to impact upon academic growth,
achievement, and degree completion in college (e.g., Kim, 2002; Kim & Conrad, 2006).
Again, however, research on institutional characteristics has tended to focus on static

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outcomes, as opposed to development or change in student achievement over time.
Therefore, additional research on proximal and global influences on performance
trajectories originating in the academic context and environment is greatly needed.
A second area for further research pertains to mediators between trait-like
characteristics and performance trajectories. Pitariu and Ployhart (2010) discuss the value
of examining dynamic mediated relationships, wherein both mediating and performance
measures vary over time within subjects. The introduction of theoretically-relevant timevarying mediators into models of predictors of performance trajectories offers the
opportunity to explore how stable characteristics may influence the form of performance
trajectories via state-like or malleable characteristics. For instance, with regard to
achievement motivation in an academic context, examples of potential mediating
constructs of interest might include academic self-efficacy, choice behavior and the
exertion of effort toward task-relevant endeavors, or study habits and learning strategies
employed both in classroom and non-classroom settings.
A similar idea to the situational constraints notion mentioned above would be to
measure students‟ perceptions of events that occur throughout the duration of their
undergraduate careers (e.g., challenges, obstacles, or difficulties of life) that may have a
proximal effect on academic performance. One hypothesis would be that students higher
in approach-oriented forms of motivation and lower in avoidance-oriented forms of
motivation would be better prepared to rebound from challenging circumstances, perhaps
because such individuals employ more adaptive problem-focused coping strategies
(Halamandaris & Power, 1999) compared to individuals higher in avoidance motivation.
Thus, the deleterious effects of difficult events in one‟s life on academic performance at

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various points in time might in part be affected by one‟s standing on characteristics
related to approach- or avoidance-oriented constructs.
Finally, a number of additional approaches could be taken to further the field‟s
understanding of how constructs in the domains of ability and motivation contribute to
trajectories of academic performance. The present study focused on a trait-based
perspective of achievement motivation; therefore, the interaction occurred between two
invariant, between-subjects characteristics. As noted above with regard to dynamic
mediated relationships, a number of more proximal and situationally-responsive
characteristics could also be examined (e.g., self-efficacy, achievement goals, constructs
tied to task-relevant effort, etc.). Cross-level interactions between ability, conceptualized
as a stable trait-like characteristic, and motivational characteristics, conceptualized as
time-varying attributes, could then be examined. Skill acquisition research conducted in
laboratory-based settings has provided evidence supporting the existence of cross-level
ability-motivation interactions of this sort (e.g., Kanfer & Ackerman, 1989; Yeo & Neal,
2004). However, it remains to be seen whether such results generalize to field settings
where principles from skill acquisition may not be expected to function as observed in
controlled lab settings.
Conclusion
The present study extended ideas concerning the interaction hypothesis
suggesting that ability and motivation interact with one another in determining
performance, with more recent perspectives on performance trajectories. Based on the
results reported herein, definitive conclusions cannot yet be reached with regard to the
potential existence or substantive meaningfulness of ability-motivation interactions in the

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prediction of performance trajectories. However, given that research addressing the joint
effect of ability and achievement motivation on performance trajectories has yet to be
conducted in an applied setting, the present study provides an initial start in this direction.
More broadly, it is suggested that researchers continue to examine correlates of
performance trajectories, including characteristics of persons, as well as situations,
contexts, or environments.

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Table 1.
Listing of Achievement Motivation Items employed in MSU-Only Sample.

Items adapted from Steers and Braunstein (1976)
1. I do my best work when my tasks or homework is fairly difficult.
2. I try very hard to improve on my past performance in school work.
3. I sometimes take moderate risks and stick my neck out in volunteering for class
projects to get better grades or learn more.
4. I try to avoid any added responsibilities or projects in my classwork.
5. I try to perform better than my classmates.
Items adapted from Fineman (1975)
6. I often put in more hours than required to get good grades in the courses I take.
7. I appreciate an instructor who gives me difficult homework assignments that lead
to better understanding the material being taught.
8. I don‟t mind working extra hard if it means that I master an interesting subject.
9. I will often work hard to master course material even when my extra work will
have no impact on my grades.
10. I think it is extremely important to do the best I can in all my courses.

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Table 2.
Achievement Motivation Biodata Inventory (AM BIO-15) items.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15

How often have you accomplished something you initially thought was very difficult or
almost impossible?
To what extent has it been important to you to do your very best whenever you take on a
project?
How often have you finished a project when faced with difficult circumstances?
How often do others tend to compliment you on your determination to continue with a
project under difficult circumstances?
How often do you tend to give up on a task after being told that you were not doing
well?
Generally, whenever you lean about a topic or how to perform a task, how often do you
learn all the details as well as the general principles?
How often have you studied for tests by trying to memorize just the basic factors and not
much more?
How do you compare your standards for learning to those of your high school teachers?
In general, what is the lowest grade that you find acceptable for yourself?
In your last year of high school, on how many tests did you "settle" for a passing grade,
rather than spend significant amounts of time learning material well?
How often do you ask a teacher or classmate questions that go beyond the material but
are still relevant to the topic (either in or out of class)?
In the past month, how many times have you looked for more information about
something that you found interesting?
How often do you spend extra time on school assignments, even after they are turned in,
so that you can gain a better understanding of the material or principles?
When a textbook or instructor mentions another source of information on a topic, how
likely are you to find it and learn more on your own?
How important is it to you to succeed in whatever task you are engaged in?

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Table 3.
Listing of Achievement Motivation Biodata Inventory (AM BIO-15) items, College Board
biodata dimensions, and convergent validities with achievement motivation scales in pilot
sample.

AM
AM
CL
CL
SBFCL WE
CL-21
EXC
MAS
10
1
Perseverance
.365
.172
.088
.165
.199
2
Perseverance
.559
.554
.444
.371
.609
3
Perseverance
.398
.220
.076
.173
.285
4
Perseverance
.322
.310
.109
.339
.335
5
Perseverance
.165
.470
.352
.406
.418
6
Knowledge
.458
.417
.322
.299
.379
7
Knowledge
.344
.320
.271
.150
.385
8
Knowledge
.240
.171
.115
.075
.220
9
Knowledge
.146
.261
.168
.193
.302
10
Knowledge
.424
.256
.158
.148
.324
11
Learning
.085
.128
.055
.077
.190
12
Learning
.118
.096
-.002
-.002
.235
13
Knowledge
.302
.172
.118
.072
.267
14
Learning
.255
.183
.028
.184
.185
15
Perseverance
.495
.588
.385
.563
.559
Note. AM SBF-10 = 10-item composite of Steers & Braunstein (1976) 5-item
and Fineman (1975) 5-item scales. AM CL-21 = Cassidy & Lynn (1989) 21-item
scale. CL WE = Cassidy & Lynn (1989): Work Ethic (7-item). CL EXC =
Cassidy & Lynn (1989): Pursuit of Excellence (7-item). CL MAS = Cassidy &
Lynn (1989): Mastery (7-item). CB Dimension = construct assessed in College
Board biodata inventory. All correlations disattenuated for unreliability. N ranges
from 107 to 110.
CB
Dimension

134

Table 4.
Descriptive statistics and intercorrelations for achievement motivation measures.

1
2
3
N
Mean SD Skew Kurt
1. AM BIO-15 110 3.39
.38
.354 .836 .680 .835 .758
2. AM SBF-10 109 3.55
.47
.115 .115 .570 .684 .847
3. AM CL-21
110 3.60
.43 -.224 -.084 .568 .637 .826
Note. AMBIO-15 = Achievement Motivation Biodata Inventory (15-item),
SBF = 10-item composite of Steers & Braunstein (1976) 5-item and
Fineman (1975) 5-item scales, CL = Cassidy & Lynn (1989) 21-item scale.
Internal-consistency estimates shown along the diagonal in italicized
typeface. Correlations below the diagonal are uncorrected; correlations
above the diagonal corrected for unreliability.

135

Table 5.
Differences between analysis sample and excluded subjects on demographic and
background categorical variables (MSU-Only Sample).

²

χ (1) =
.019,
p = .890

²

χ (7) =
13.152, p =
.068

²

χ (2) =
.740,
p = .691

²

χ (1) =
2.481,
p < .115

²

χ (5) =
9.447,
p = .093

Male

Analysis
27.8% (155)

Excluded
27.1% (23)

Female

72.2% (403)

72.9% (62)

0.0% (0)
1.3% (7)
0.0% (0)
0.5% (3)

0.0% (0)
5.9% (5)
0.0% (0)
0.0% (0)

0.2% (1)

0.0% (0)

4.9% (27)
9.2% (51)
80.2% (446)

8.2% (7)
11.8% (10)
69.4% (59)

0.5% (3)

0.0% (0)

3.2% (18)
97.3% (544)
0.4% (2)
2.3% (13)
98.0% (546)

4.7% (4)
96.5% (82)
0.0% (0)
3.5% (3)
95.2% (80)

2.0% (11)

4.8% (4)

0.0% (0)
20.7% (110)
6.4% (34)
6.6% (35)
20.5% (109)
34.6% (184)
11.3% (60)

0.0% (0)
21.0% (17)
8.6% (7)
4.9% (4)
33.3% (27)
22.2% (18)
9.9% (8)

Other
Mexican / Latino
Puerto Rican
Other Hispanic
American Indian or Alaskan
Native
Asian
Black/African American
White/Caucasian
Native Hawaiian or other Pacific
Islander
Two or More Races
U.S. Citizen
Non-U.S. Citizen - Canada
Non-U.S. Citizen - Other
English as Primary Language
English as Secondary Language
Undeclared
Business
Engineering
Fine Arts/ Humanities
Social Science
Natural or Physical Science
Other

Note. Values reported are cell proportions (counts in parentheses). Total sample
size is 644 (analysis n = 559; excluded n = 85).

136

Table 6.
Differences between analysis sample and excluded subjects on demographic and
background categorical variables (Multi-Institution Sample).

²

χ (1) =
4.864,
p = .027

²

χ (9) =
564.985,
p < .001

²

χ (2) =
6.853,
p = .032

²

χ (1) =
17.980,
p < .001

²

χ (6) =
43.019,
p < .001

Male

Analysis
38.2% (488)

Excluded
34.1% (487)

Female

61.8% (791)

65.9% (942)

Other
Mexican / Latino
Puerto Rican
Other Hispanic
American Indian or Alaska Native
Asian
Black/African American
White/Caucasian
Native Hawaiian or other Pacific
Islander
Two or More Races

1.3% (17)
1.3% (16)
0.2% (3)
0.9% (11)
0.1% (1)
5.7% (73)
8.4% (107)
78.8% (1,005)

2.0% (28)
5.8% (82)
0.7% (10)
2.7% (39)
0.2% (3)
8.0% (114)
40.2% (571)
35.3% (501)

0.5% (6)

0.8% (12)

2.8% (36)

U.S. Citizen

97.5% (1,246)

4.3% (61)
95.7%
(1,365)
0.4% (5)
4.0% (57)
93.2%
(1,330)

Non-U.S. Citizen - Canada
Non-U.S. Citizen - Other
English as Primary Language
English as Secondary Language
Undeclared
Business
Engineering
Fine Arts/ Humanities
Social Science
Natural or Physical Science
Other

0.2% (3)
2.3% (29)
96.8% (1,238)
3.2% (41)

6.8% (97)

14.3% (183)
16.3% (208)
11.3% (145)
9.0% (115)
14.3% (183)
20.2% (258)
14.6% (187)

10.2% (146)
13.9% (198)
12.4% (177)
9.8% (140)
18.9% (269)
14.9% (212)
19.9% (284)

Note. Values reported are cell proportions (counts in parentheses). Total sample
size is 2,787 (analysis n = 1,279; excluded n = 1,508).

137

Table 7.
Differences between analysis sample and excluded subjects on continuous variables (MSU-Only Sample).
Analysis
Mean SD
n
18.48 .57
559
.57
.67
559

Excluded
Mean
SD
18.58
.72
.42
.73

n
83
79

Standardized Difference
95% L 95% U
d
-.163
-.394
.067
.220
-.016
.456

3.42

.51

559

3.40

.45

84

.040

-.189

.269

3.08

.65

559

2.59

1.11

66

.685

.426

.942

GPA2

3.11

.65

559

2.55

1.14

63

.787

.522

1.050

GPA3

3.01

.72

554

1.84

1.77

8

1.582

.876

2.284

GPA4

3.04

.74

544

.72

1.36

6

3.113

2.283

3.934

Age
Ability
Achievement
Motivation
GPA1

Note. 95% L = Lower 95% confidence interval. 95% U = Upper 95% confidence interval. Estimates
for analysis sample based on observed values prior to imputation and mean-centering.

138

Table 8.
Differences between analysis sample and excluded subjects on continuous variables (Multi-Institution
Sample).
Analysis
Mean
SD
n
18.12
.39 1,278
.90
.80 1,236

Excluded
Mean
SD
n
18.15
.56
1,421
.32
.94
1,305

Standardized Difference
95% L 95% U
d
-.064
-.140
.012
.659
.578
.738

3.41

.44

1,279

3.37

.43

1,435

.095

.020

.171

3.45

.60

1,273

2.60

.95

217

1.286

1.134

1.436

GPA2

3.43

.61

1,264

2.47

.78

80

1.545

1.310

1.777

GPA3

3.41

.62

1,271

1.43

.78

8

3.202

2.494

3.906

GPA4

3.43

.60

1,180

2.88

.81

5

.926

.046

1.804

Age
Ability
Achievement
Motivation
GPA1

Note. 95% L = Lower 95% confidence interval. 95% U = Upper 95% confidence interval. Estimates for
analysis sample based on observed values prior to imputation and mean-centering.

139

Table 9.
Summary of y-measurement models evaluated in MSU-Only and Multi-Institution
Samples.
1. Random-Intercept Only
2. Fixed-Intercept, Fixed-Slope
3. Random-Intercept, Fixed-Slope
4. Fixed-Intercept, Random-Slope
5. Random-Intercept, Random-Slope
6. Random-Intercept, Random-Slope, Fixed-Quadratic
7. Random-Intercept, Random-Slope, Random-Quadratic
8. Fixed-Intercept, Fixed-Slope (Logarithmic Slope)
9. Random-Intercept, Fixed-Slope (Logarithmic Slope)
10. Random-Intercept, Random-Slope (Logarithmic Slope)
11. Random-Intercept, Fixed-Slope (Loadings Estimated at Times 3 and 4)
12. Random-Intercept, Random-Slope (Loadings Estimated at Times 3 and 4)

140

Table 10.
Descriptive statistics and intercorrelations among study measures.
MSU-Only

1. Ability
2. Achievement
Motivation
3. Interaction
4. GPA1

Mean SD
.00
.67

MultiInstitution
Mean
.00

SD
.81

1

2
.109

3
.008

4
.546

5
.546

.042

.191
.013

.185 .180 .148
-.012 -.010 -.018

.00
-.03

.51
.36

.00
.04

.44
.35

-.084
-.044

.116

3.08

.65

3.45

.60

.290

.235

.005

5. GPA2

3.11

.65

3.42

.61

.261

.264

-.004

.647

6. GPA3

3.01

.72

3.40

.62

.273

.119

.047

.536

7. GPA4

.923

6
.514

7
.461

.781

.959
.650

.863

.878
.919

3.03 .74
3.38
.63
.266 .132 .074 .494 .568 .624
Note. MSU-Only sample n = 559; Multi-Institution sample n = 1,279. Correlations below diagonal
from MSU-Only sample (r > |.083| significant at p < .05); correlations above diagonal from MultiInstitution sample (r > |.055| significant at p < .05).

141

Table 11.
Global model fit statistics for measurement model (MSU-Only Sample).
Model Description
1. Random Intercept
Only
2. Fixed-Intercept,
Fixed-Slope
3. Random-Intercept,
Fixed-Slope
4. Fixed-Intercept,
Random-Slope
5. RandomIntercept, RandomSlope
6. Random-Intercept,
Random-Slope,
Fixed-Quadratic
7. Random-Intercept,
Random-Slope,
Random-Quadratic
8. Fixed-Intercept,
Fixed-Slope
(Logarithmic)
9. Random-Intercept,
Fixed-Slope
(Logarithmic)

Submodel
(df)
1 (11)
2 (8)
3 (7)
1 (11)
2 (8)
3 (7)
1 (10)
2 (7)
3 (6)
1 (10)
2 (7)
3 (6)
1 (8)
2 (5)
3 (4)
1 (7)
2 (4)
3 (3)
1 (4)
2 (1)
1 (11)
2 (8)
3 (7)
1 (10)
2 (7)
3 (6)
1 (8)
2 (5)
3 (4)
1
2

²

²

.117
.102
.071
.398
.463
.310
.117
.101
.069
.327
.354
.287
.077
.071
.062
.083
.080
.073
.101
.135

Lower
90%
.096
.078
.044
.377
.439
.284
.095
.075
.039
.305
.328
.259
.051
.039
.025
.057
.045
.033
.067
.072

Upper
90%
.139
.129
.100
.419
.488
.337
.141
.129
.101
.350
.380
.316
.104
.106
.102
.112
.119
.118
.139
.211

.398
.463
.311
.118
.104
.072
.089
.075
.068

.377
.439
.285
.096
.077
.043
.064
.043
.032

.419
.488
.337
.142
.132
.104
.115
.109
.107

²

χ /df

Δχ

Δdf

Δp

CFI

TLI

RMSEA

94.48
54.83
26.72
983.42
966.43
384.15
84.03
46.93
21.90
608.76
496.34
282.47
34.23
18.98
12.56
34.13
18.33
11.89
26.95
11.15

8.59
6.85
3.82
89.40
120.80
54.88
8.40
6.70
3.65
60.88
70.91
47.08
4.28
3.80
3.14
4.88
4.58
3.96
6.74
11.15

−
39.65
28.11
−
16.98
582.28
−
37.09
25.04
−
112.41
213.88
−
15.24
6.42
−
15.80
6.45
−
15.80

−
3
1
−
3
1
−
3
1
−
3
1
−
3
1
−
3
1
−
3

−
.000
.000
−
.001
.000
−
.000
.000
−
.000
.000
−
.002
.011
−
.001
.011
−
.001

.913
.951
.979
.000
.000
.606
.919
.958
.983
.374
.489
.711
.973
.985
.991
.972
.985
.991
.976
.989

.952
.963
.982
.446
.249
.662
.952
.964
.983
.624
.562
.711
.979
.982
.987
.976
.978
.981
.964
.936

983.89
967.03
384.54
88.15
48.94
23.52
43.09
20.53
14.29

89.44
120.88
54.93
8.81
6.99
3.92
5.39
4.11
3.57

−
16.86
582.49
−
39.21
25.42
−
22.56
6.23

−
3
1
−
3
1
−
3
1

−
.001
.000
−
.000
.000
−
.000
.013

.000
.000
.605
.918
.956
.982
.963
.984
.989

.445
.248
.662
.951
.962
.982
.972
.981
.984

χ

SRMR
.085
.060
.050
.392
.387
.278
.082
.058
.047
.323
.293
.255
.040
.030
.024
.039
.029
.024
.036
.022
.393
.387
.278
.083
.058
.048
.043
.031
.026

10. RandomIntercept, RandomSlope (Logarithmic)
11. RandomIntercept, Fixed
Slope (Loadings
Estimated at Times 3
3
& 4)
12. Random1 (6)
30.81
5.14
−
−
−
.974 .974
.086
.057
.117
.034
Intercept, Random2 (3)
8.79
2.93
22.02
3 .000 .994 .988
.059
.059
.106
.029
Slope (Loadings
Estimated at Times 3
3
& 4)
Note. n = 559. Lower 90% and Upper 90% refer to 90% confidence intervals about the RMSEA estimate. Model highlighted in bold
typeface selected as measurement model. Submodel 1: homogeneous, uncorrelated error variances for GPA indicators. Submodel 2:
heterogeneous, uncorrelated error variances for GPA indicators. Submodel 3: heterogeneous error variances for GPA indicators with
correlations permitted between time-adjacent indicators constrained to equality over indicator pairs. Rows highlighted in dark grey
indicate models that failed to converge during estimation.

142

Table 12.
Unstandardized model parameters for unconditional measurement model (MSU-Only
Sample).
Submodel
1
2
3
Est.
Est.
Est.

Parameter
ψIntercept↔Slope

-.014

-.001

ψIntercept↔Intercept

.272

.286

.248

ψSlope↔Slope

.019

.019

.010

μIntercept

3.090 3.092 3.090

μSlope

-.023

-.023

-.021

θε GPA1
5. RandomIntercept,
RandomSlope

-.010

.168

.146

.179

θε GPA2

.168

.137

.161

θε GPA3

.168

.198

.224

θε GPA4

.168

.195

.223

−

−

.027

.618

.662

.581

.618

.669

.615

.649

.607

.561

θε GPA(t)↔GPA(t+1)

²
R² GPA2
R² GPA3
R² GPA4
R GPA1

.698 .657 .603
Note. n = 559. Est. = parameter estimate. Entries in bold, italicized
typeface significant at p < .05. Submodel 1: homogeneous,
uncorrelated error variances for GPA indicators. Submodel 2:
heterogeneous, uncorrelated error variances for GPA indicators.
Submodel 3: heterogeneous error variances for GPA indicators
with correlations permitted between time-adjacent indicators
constrained to equality over indicator pairs. Columns highlighted
in dark grey indicate models that failed to converge during
estimation. Columns highlighted in black indicate submodels not
considered for a given model.

143

Table 13.
Global model fit statistics for structural model (MSU-Only Sample).
Model
Submodel
Lower Upper
CFI TLI RMSEA
SRMR
Δdf
Δp
χ
χ /df Δχ
Description
(df)
90%
90%
5. Random2 (11)
30.93 2.81 15.98
3
.001 .982 .970
.057
.034
.081
.023
Intercept,
Random-Slope
Note. n = 559. Lower 90% and Upper 90% refer to 90% confidence intervals about the RMSEA estimate. Submodel 2:
heterogeneous, uncorrelated error variances for GPA indicators.

²

²

²

144

Table 14.
Local model fit statistics for structural model (MSU-Only Sample).

Parameter

Submodel
2
Est.

ψIntercept↔Slope
ψIntercept↔Intercept

.220

ψSlope↔Slope

.018

γAbility→Intercept

.291

γAbility→Slope

.006

γMotivation→Intercept

.363

γMotivation→Slope

-.053

γInteraction→Intercept

-.055

γInteraction→Slope

.062

αIntercept

3.091

αSlope

-.021

θε GPA1

.149

θε GPA2

.135

θε GPA3

.199

θε GPA4

5. RandomIntercept,
RandomSlope

-.010

.195

θε GPA(t)↔GPA(t+1)

²
R² GPA2
R² GPA3
R² GPA4
R² Intercept
R² Slope
R GPA1

−
.657
.672
.606
.657
.230

.059
Note. n = 559. Est. = parameter estimate. Entries in
bold, italicized typeface significant at p < .05.
Submodel 2: heterogeneous, uncorrelated error
variances for GPA indicators.

145

Table 15.
Global model fit statistics for measurement model (Multi-Institution Sample).
Submodel
Lower Upper
CFI
TLI RMSEA
SRMR
Δdf Δp
χ
χ /df
Δχ
(df)
90%
90%
1 (11)
1482.30 134.75
−
−
−
.818 .901
.323
.310
.337
.052
1. Random Intercept
2 (8)
661.13
82.64
821.17
3 .000 .919 .940
.253
.237
.269
.077
Only
3 (7)
197.74
28.25
463.39
1 .000 .976 .980
.146
.129
.164
.055
1 (11)
8116.46 737.86
−
−
−
.000 .455
.759
.745
.773
.583
2. Fixed-Intercept,
2 (8)
8111.44 1013.93
5.03
3 .170 .000 .250
.890
.874
.906
.582
Fixed-Slope
3 (7)
3560.33 508.62 4551.10 1 .000 .562 .624
.630
.613
.647
.484
1 (10)
1415.39 141.54
−
−
−
.827 .896
.331
.317
.346
.048
3. Random-Intercept,
2 (7)
608.34
86.91
807.06
3 .000 .926 .936
.259
.242
.277
.073
Fixed-Slope
3 (6)
158.01
26.33
450.33
1 .000 .981 .981
.141
.122
.160
.051
1 (10)
6592.82 659.28
−
−
−
.188 .513
.717
.703
.732
.515
4. Fixed-Intercept,
2 (7)
5063.44 723.35 1529.37 3 .000 .376 .465
.752
.734
.769
.478
Random-Slope
3 (6)
2446.87 407.81 2616.58 1 .000 .699 .699
.564
.545
.583
.568
1 (8)
425.78
53.22
−
−
−
.948 .961
.202
.186
.219
.031
5. Random-Intercept,
2 (5)
144.55
28.91
281.23
3 .000 .983 .979
.148
.128
.169
.062
Random-Slope
3 (4)
68.13
17.03
76.42
1 .000 .992 .988
.112
.090
.136
.042
1 (7)
425.97
60.85
−
−
−
.948 .956
.216
.199
.234
.031
6. Random-Intercept,
2 (4)
144.43
36.11
281.54
3 .000 .983 .974
.166
.143
.189
.062
Random-Slope,
Fixed-Quadratic
3 (3)
68.01
22.67
76.42
1 .000 .992 .984
.130
.104
.158
.042
1 (4)
64.27
16.07
−
−
−
.993 .989
.109
.086
.133
.005
7. RandomIntercept, Random2 (1)
.57
.57
63.71
3 .000 1.000 1.000
.000
.000
.067
.001
Slope, Random3
Quadratic
1 (11)
8116.67 737.88
−
−
−
.000 .455
.759
.745
.773
.583
8. Fixed-Intercept,
2 (8)
8111.64 1013.95
5.03
3 .169 .000 .250
.890
.874
.906
.582
Fixed-Slope
(Logarithmic)
3 (7)
3560.27 508.61 4551.36 1 .000 .562 .624
.630
.613
.647
.484
1 (10)
1417.21 141.72
−
−
−
.826 .896
.332
.317
.346
.048
9. Random-Intercept,
2 (7)
609.99
87.14
807.22
3 .000 .926 .936
.260
.242
.277
.073
Fixed-Slope
(Logarithmic)
3 (6)
159.37
26.56
450.62
1 .000 .981 .981
.141
.123
.161
.051
1 (8)
498.17
62.27
−
−
−
.940 .955
.219
.203
.235
.026
10. Random2 (5)
111.11
22.22
387.06
3 .000 .987 .984
.129
.109
.150
.055
Intercept, RandomSlope (Logarithmic)
3 (4)
46.43
11.61
64.68
1 .000 .995 .992
.091
.069
.115
.036
11. Random1 (8)
1415.21 176.90
−
−
−
.826 .870
.371
.355
.387
.048
Intercept, Fixed
2 (5)
607.92
121.58 807.30
3 .000 .926 .911
.307
.287
.328
.073
Slope (Loadings
Estimated at Times 3
3 (4)
157.32
39.33
450.60
1 .000 .981 .972
.173
.151
.197
.051
& 4)
12. Random1 (6)
409.62
68.27
−
−
−
.950 .950
.229
.211
.248
.031
Intercept, Random2 (3)
54.61
18.20
355.00
3 .000 .994 .987
.116
.090
.144
.050
Slope (Loadings
Estimated at Times 3
3 (2)
23.70
11.85
30.91
1 .000 .997 .992
.092
.061
.127
.016
& 4)
Note. n = 1,279. Lower 90% and Upper 90% refer to 90% confidence intervals about the RMSEA estimate. Model highlighted in
bold typeface selected as measurement model. Submodel 1: homogeneous, uncorrelated error variances for GPA indicators.
Submodel 2: heterogeneous, uncorrelated error variances for GPA indicators. Submodel 3: heterogeneous error variances for GPA
indicators with correlations permitted between time-adjacent indicators constrained to equality over indicator pairs. Rows
highlighted in dark grey indicate models that failed to converge during estimation.
Model Description

²

²

²

146

Table 16.
Local model fit statistics for unconditional measurement model (Multi-Institution
Sample).

Parameter

Submodel
1
2
3
Est.
Est.
Est.

ψIntercept↔Slope

.010

ψIntercept↔Quadratic

-.004

-.008

ψSlope↔Quadratic

-.015

-.010

ψIntercept↔Intercept

.342

.330

ψSlope↔Slope

.060

.043

ψQuadratic↔Quadratic

.005

.003

μIntercept

3.447 3.446

μSlope

-.023

-.023

μQuadratic

.001

.001

θε GPA1

.011

.024

θε GPA2

.011

.006

θε GPA3

.011

.013

θε GPA4

7. RandomIntercept,
RandomSlope,
Random
Quadratic

-.004

.011

.027

−

−

.970

.932

.971

.985

.972

.967

θε GPA(t)↔GPA(t+1)

²
R² GPA2
R² GPA3
R² GPA4
R GPA1

.973 .933
Note. n = 1,279. Est. = parameter estimate. Entries in bold,
italicized typeface significant at p < .05. Submodel 1:
homogeneous, uncorrelated error variances for GPA indicators.
Submodel 2: heterogeneous, uncorrelated error variances for
GPA indicators. Submodel 3: heterogeneous error variances for
GPA indicators with correlations permitted between timeadjacent indicators constrained to equality over indicator pairs.
Columns highlighted in dark grey indicate models that failed to
converge during estimation.

147

Table 17.
Global model fit statistics for structural model (Multi-Institution Sample).
Model Description

Submodel
(df)

²

χ

²

χ /df

Δχ

²

Δdf

Δp

CFI

TLI

RMSEA

Lower Upper
SRMR
90%
90%

7. Random-Intercept,
2 (4)
5.65 1.41 61.82 3 .000 1.000 .999
.018
.000
.049
.002
Random-Slope,
Random-Quadratic
Note. n = 1,279. Lower 90% and Upper 90% refer to confidence intervals about the RMSEA estimate. Submodel 2:
heterogeneous, uncorrelated error variances for GPA indicators.

148

Table 18.
Local model fit statistics for structural model (Multi-Institution Sample).

Parameter

Submodel
1
2
3
Est.
Est.
Est.

ψIntercept↔Slope

.002

ψIntercept↔Quadratic

-.001

-.004

ψSlope↔Quadratic

-.014

-.010

ψIntercept↔Intercept

.230

.221

ψSlope↔Slope

.059

.045

ψQuadratic↔Quadratic

.005

.003

γAbility→Intercept

.393

.393

γAbility→Slope

.019

.019

γAbility→Quadratic

-.011

-.011

γMotivation→Intercept

.179

.176

γMotivation→Slope

.013

.012

γMotivation→Quadratic
7. RandomIntercept,
Random-Slope,
RandomQuadratic

-.010

-.008

-.007

γInteraction→Intercept

.003

.000

γInteraction→Slope

-.039

-.042

γInteraction→Quadratic

.008

.010

αIntercept

3.447

3.446

αSlope

-.021

-.022

αQuadratic

.000

.000

θε GPA1

.011

.022

θε GPA2

.011

.006

θε GPA3

.011

.012

θε GPA4

.011

.028

−

−

.970

.939

.971

.983

.972

.969

.973

.928

θε GPA(t)↔GPA(t+1)

²
R² GPA2
R² GPA3
R² GPA4
R GPA1

149

Table 18 (cont‟d).

Parameter
7. RandomIntercept,
Random-Slope,
RandomQuadratic

²

Submodel
1
2
3
Est.
Est.
Est.

R Intercept

.326

.335

R² Slope

.008

.011

R² Quadratic
.022
.032
Note. n = 1,279. Est. = parameter estimate. Entries in bold, italicized
typeface significant at p < .05. Submodel 1: homogeneous,
uncorrelated error variances for GPA indicators. Submodel 2:
heterogeneous, uncorrelated error variances for GPA indicators.
Submodel 3: heterogeneous error variances for GPA indicators with
correlations permitted between time-adjacent indicators constrained
to equality over indicator pairs. Columns highlighted in dark grey
indicate models that failed to converge during estimation.

150

Figure 1. Equations describing relationship between performance and time (withinsubjects) and person-specific change parameters to subject characteristics (betweensubjects).

(1)

(2)

(3)

(4)

(5)

(6)

151

Figure 1(cont‟d).

(7)

(8)

(9)

(10)

(11.a)
(11.b)

(12)

152

Figure 1(cont‟d).

(13)

153

Figure 2. Conceptual path diagram of predictors of latent trajectory parameters (intercept, slope).

154

Figure 3. Plot of unconditional performance trajectory for MSU-Only Sample.

Performance (Semester GPA)

3.40
3.30
3.20
3.10
3.00
2.90
2.80
1

2

3

Time (Semester)

155

4

Figure 4. Plots of ability main effects (low: -1 SD, high: +1 SD) on latent performance
trajectories (MSU-Only Sample).

3.50
Performance (Semester GPA)

3.40
3.30
3.20
3.10
3.00
AbilityLow
AbilityHigh

2.90
2.80
2.70
2.60
2.50
1

2

3

Time (Semester)

156

4

Figure 5. Plots of motivation main effects (low: -1 SD, high: +1 SD) on latent
performance trajectories (MSU-Only Sample).

3.50
Performance (Semester GPA)

3.40
3.30
3.20
3.10
3.00
Motivation-Low

2.90

Motivation-High

2.80
2.70
2.60
2.50
1

2

3

Time (Semester)

157

4

Figure 6. Plots of motivation conditional effects on latent performance trajectories at low

Performance (Semester GPA)

ability (MSU-Only Sample).

3.70
3.60
3.50
3.40
3.30
3.20
3.10
3.00
2.90
2.80
2.70
2.60
2.50

Ability-Low,
MotivationLow
Ability-Low,
Motivation
High

1

2
3
Time (Semester)

158

4

Figure 7. Plots of motivation conditional effects on latent performance trajectories at
high ability (MSU-Only Sample).

3.70
Performance (Semester GPA)

3.60
3.50
3.40
3.30

Ability-High,
MotivationLow

3.20
3.10

Ability-High,
MotivationHigh

3.00
2.90
2.80
2.70
2.60
2.50
1

2

3

Time (Semester)

159

4

Figure 8. Plot of unconditional performance trajectory for Multi-Institution sample.

Performance (Yearly GPA)

3.70
3.60
3.50
3.40
3.30
3.20
3.10
1

2

3
Time (Year)

160

4

Figure 9. Plots of ability main effects (low: -1 SD, high: +1 SD) on latent performance
trajectories (Multi-Institution Sample).

3.90

Performance (Yearly GPA)

3.80
3.70
3.60
3.50
3.40

AbilityLow

3.30
3.20

AbilityHigh

3.10
3.00
2.90
1

2

3
Time (Year)

161

4

Figure 10. Plots of motivation main effects (low: -1 SD, high: +1 SD) on latent
performance trajectories (Multi-Institution Sample).

3.70

Performance (Yearly GPA)

3.60
3.50
3.40
MotivationLow

3.30
3.20

MotivationHigh

3.10
3.00
1

2

3

Time (Year)

162

4

Figure 11. Plots of motivation conditional effects on latent performance trajectories at

Performance (Yearly GPA)

low ability (Multi-Institution Sample).

4.00
3.90
3.80
3.70
3.60
3.50
3.40
3.30
3.20
3.10
3.00
2.90
2.80
2.70

Ability-Low,
MotivationLow
Ability-Low,
Motivation
High

1

2

3
Time (Year)

163

4

Figure 12. Plots of motivation conditional effects on latent performance trajectories at

Performance (Yearly GPA)

high ability (Multi-Institution Sample).

4.00
3.90
3.80
3.70
3.60
3.50
3.40
3.30
3.20
3.10
3.00
2.90
2.80
2.70

Ability-High,
MotivationLow
Ability-High,
MotivationHigh

1

2

3
Time (Year)

164

4

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