A SOCIAL NETWORK OF STUDENT-ATHLETES AND
EDUCATIONAL OUTCOMES IN HIGH SCHOOL
By
Seunghyun Hwang

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
Kinesiology-Doctor of Philosophy
Measurement and Quantitative Methods-Doctor of Philosophy
2013

ABSTRACT
A SOCIAL NETWORK OF STUDENT-ATHLETES AND EDUCATIONAL OUTCOMES
IN HIGH SCHOOL
By
Seunghyun Hwang
Athletic participation is the most popular school-sponsored extracurricular
activity. Regarding the relationship between athletic participation and educational
consequences, this study is focused on social networks of student athletes in high
school. The purpose of this study was to examine the effect of peer network on
educational outcome variables (Study I), to identify how student athletes construct their
peer networks among student athletes in school (Study II), and to apply a measurement
model in polytomous multilevel item response theory for psychometrical evaluation.
Data were longitudinally collected from approximately 300 student athletes in a local
high school in the beginning and end of Winter season. In Study I, results indicated that
the same team-exposure (interactions with athletes on the same team) had a positive
effect on college expectation and athletic identity, while the different team-exposure
(interactions with athletes on teams other than one’s own) positively influenced
academic efficacy. Also some fixed effects of team-level predictors were found. Results
of Study II indicated that student athletes were more likely to choose friends to interact
with if they were same gender and had a same team membership and similar
orientation for going a college. They also formed peer networks that are different (not
similar) in grade level, academic achievement, and perception toward their coach.
Lastly, multilevel rating scale was an appropriate measurement model for the five items
measuring peer interaction in this study in order to estimate the latent depth of

interaction, which is suggested to be used when modeling the effect of interaction.
Altogether, this study implies that athletic participation is not detrimental to educational
outcomes. Instead athletic participation ameliorates peer relationships in school, which
is a form of social capital for students to achieve their goals for academic, social, and
physical wellbeing in school and future aspirations.
Key words: student-athletes, athletic participation, education, social capital, social
network analysis,

Copyright by
SEUNGHYUN HWANG
2013

ACKNOWLEDGEMENTS
I would like to acknowledge Drs. Deborah L. Feltz and Kenneth A. Frank both for
directing this study and my doctoral program. Their personal and professional supports
motivated me to keep developing my competencies as a scholar. Without their
continued supports, I could not have completed the dual degree program. Also, I would
like to thank Drs. Alan Smith and Mark Reckases for their review and encouragement in
this study. In addition, I give special thanks to Christel Beverly, Mr. Kimball, and his
student athletes for their help in data collection for this study.
Beyond this study, I appreciate Dr. Dan Gould for his services and classes, which
positively influenced my growth as a scholar from master degree. Also I would like to
thank other members, Sue, Verna, JoAnn, and Jan in Kinesiology for their
administrative support. Those services helped me my campus life in MSU from the
beginning of my new life in U.S. I would like to thank all advisees of Dr. Feltz, and
Korean community of the College of Education at MSU, and scholars in Korea for their
friendship and professional networks.
Lastly, I would like to mention sacrifices from my family, Namhyo, Jacob, Katie,
parents, parents in law, and brother’s family. With their continued supports, I could
complete my doctoral program.

v

TABLE OF CONTENTS

LIST OF TABLES …………………………………………………………………………..viii
LIST OF FIGURES ……………………………………………………………………… xiv
CHAPTER I: STATEMENT OF PROBLEM AND OVERVIEW OF
THIS DISSERTATION …………………………………………………………………… 1
REFERENCES …………………………………………………………………… 7
CHAPTER II: PEER INFLUENCE ON EDUCATIONAL OUTCOMES (STUDY I) …. 13
Introduction ………………………………………………………………………... 13
Method ……………………………………………………………………………... 22
Participants and Procedures …………………………………………….. 22
Outcome Measures ………………………………………………………. 23
Academic Achievement ………………………………………….. 23
Academic Efficacy ………………………………………………… 23
College Aspiration/ Expectation …………………………………. 23
Academic and Athletic Identities ………………………………… 24
Self-regard …………………………………………………………. 24
Control Measures …………………………………………………………. 25
Team Characteristic ………………………………………………. 25
Group Cohesion …………………………………………………… 25
Courses and Other Extracurricular Activities ............................ 26
Perceived Educational Expectations of Significant Others……. 26
Coach’s Regard on Academics ………………………………….. 26
Social Network Measure ………………………………………………..... 27
Data Analysis and Statistical Model …………………………………….. 28
Exposure …………………………………………………………… 28
Influence Models…………………………………………………… 29
Multilevel Influence Models……………………………………….. 30
Results ……………………………………………………………………………… 33
Basic Statistics …………………………………………………………….. 33
Basic Influence Models …………………………………………………… 34
Multilevel Influence Models ………………………………………………. 36
Discussion……………………………………………………………..……………. 40
REFERENCES……………………………………………………….…………….. 46
CHAPTER III: PEER SELECTION IN ATHLETIC TEAM (STUDY II) ……………….. 56
Introduction ………………………………………………………………………… 56
Method ……………………………………………………………………………... 63
vi

Participants and Procedures …………………………………………….. 63
Dependent Variable ………………………………………………………. 64
Independent Variables ……………………………………………………. 64
Demographic Information ………………………………………… 64
Prior Network at Time 1…………………………………………… 64
Courses and Other Extracurricular Activities …………………… 64
Similarity in Attributes …………………………………………….. 65
Data Analysis and Statistical Model ……………………………………...65
Basic (Single level) Selection Models …………………………… 65
Multilevel Selection Model ……………………………………….. 67
Results………………………………………………………………………………. 70
Basic Selection Models……………………………………………………. 70
Multilevel Selection Model………………………………………………… 72
Discussion………………………………………………………………………….. 74
REFERENCES …………………………………………………………………….. 78
CHAPTER IV: THE PSYCHOMETRICAL EVALUATION OF STUDENT INTERACTION
(DEPTH OF INTERACTION) MEASURES – APPLICATION OF GRADED RESPONSE
MULTILEVEL ITEM RESPONSE THEORY (STUDY III)……………………………… 84
Introduction………………………………………………………………............... 84
Method………………………………………………………………………………. 92
Participants and Instrument………………………………………………. 92
Analytic Strategy and Measurement Model……………………………... 93
Results………………………………………………………………………………. 97
Preliminary Analysis: Dimensionality and Reliability…………………… 97
Multilevel 2PL-PCM……………………………………………………….. 98
The Application of the Latent Score on the Depth of Interaction……… 101
Discussion………………………………………………………………………….. 103
REFERENCES ……………………………………………………………………. 109
CHAPTER V: CONCLUSION AND IMPLICATION OF THIS DISSERTATION .….... 114
REFERENCES ……………………………………………………………………. 117
APPENDICES…………………………………………………………………………........ 119
APPENDIX A: Tables……………………………………………………………... 120
APPENDIX B: Figures……………………………………………………………. 207
APPENDIX C: Questionnaires……………………………………...…………… 208
APPENDIX D: STATA Codes for This Study……………..……………………. 212

vii

LIST OF TABLES

Table 2.1.

Participants’ distributions on teams …………………………………………. 120

Table 2.2.

Gender and school years of samples in the first and second survey …… 121

Table 2.3.

Teams’ characteristics and norms …………………………………………… 122

Table 2.4.

The descriptive statistics of the network at time1 ……………………….. 123

Table 2.5.

The descriptive statistics of the network at time 2 ………………………

Table 2.6.

Descriptive statistics of outcome variables at Time1 and Time2 ………… 125

Table 2.7.

Paired t-test of outcome variables …………………………………………… 126

Table 2.8.

Descriptive statistics of three exposures, and paired ……………………... 127
t-test between same and different team-exposure

Table 2.9.

Regression models of the outcome variables (y) ………………………….. 128
with overall interactions

124

Table 2.10. Regression models of the outcome variables ……………………………… 129
(y) with a specific type of interaction
Table 2.11. Model 1: Null multilevel (unconstrained) …………………………………. 130
models of the outcome variables
Table 2.12a. Model 2 and 3 for academic achievement …………………………………. 131
with team size for the team level
Table 2.12b. Model 2 and 3 for academic achievement …………………………………. 132
with popularity for the team level
Table 2.12c. Model 2 and 3 for academic achievement …………………………………. 133
with winter season for the team level
Table 2.12d. Model 2 and 3 for academic achievement …………………………………. 134
with revenue for the team level
Table 2.12e. Model 2 and 3 for academic achievement …………………………………. 135
with tradition for the team level
Table 2.12f. Model 2 and 3 for academic achievement with …………………………... 136
coach’s regard for academics for the team level
viii

Table 2.12g. Model 2 and 3 for academic achievement …………………………………. 137
with task cohesion for the team level
Table 2.12h. Model 2 and 3 for academic achievement …………………………………. 138
with social cohesion for the team level
Table 2.13a. Model 2 and 3 for academic efficacy ………………………………………. 139
with team size at both levels
Table 2.13b. Model 2 and 3 for academic efficacy ………………………………………. 140
with popularity at both levels
Table 2.13c. Model 2 and 3 for academic efficacy ………………………………………. 141
with winter season at both levels
Table 2.13d. Model 2 and 3 for academic efficacy ………………………………………. 142
with revenue at both levels
Table 2.13e. Model 2 and 3 for academic efficacy ………………………………………. 143
with tradition at both levels
Table 2.13f. Model 2 and 3 for academic efficacy with
………………………………. 144
coach’s regard for academics at both levels
Table 2.13g. Model 2 and 3 for academic efficacy ………………………………………. 145
with task cohesion at both levels
Table 2.13h. Model 2 and 3 for academic efficacy ………………………………………. 146
with social cohesion at both levels
Table 2.14a. Model 2 and 3 for college aspiration
with team size at both levels

………………………………………. 147

Table 2.14b. Model 2 and 3 for college aspiration
with popularity at both levels

………………………………………. 148

Table 2.14c. Model 2 and 3 for college aspiration
with winter season at both levels

………………………………………. 149

Table 2.14d. Model 2 and 3 for college aspiration
with revenue at both levels

………………………………………. 150

Table 2.14e. Model 2 and 3 for college aspiration
with tradition at both levels

………………………………………. 151

Table 2.14f. Model 2 and 3 for college aspiration with
……………………………….. 152
coach’s regard for academics at both levels .
ix

Table 2.14g. Model 2 and 3 for college aspiration
with task cohesion at both levels

………………………………………. 153

Table 2.14h. Model 2 and 3 for college aspiration
with social cohesion at both levels

………………………………………. 154

Table 2.15a. Model 2 and 3 for college expectation ………………………………………. 155
with team size at both levels
Table 2.15b. Model 2 and 3 for college expectation ………………………………………. 156
with popularity at both levels
Table 2.15c. Model 2 and 3 for college expectation ………………………………………. 157
with winter season at both levels
Table 2.15d. Model 2 and 3 for college expectation ………………………………………. 158
with revenue at both levels
Table 2.15e. Model 2 and 3 for college expectation ………………………………………. 159
with tradition at both levels
Table 2.15f. Model 2 and 3 for college expectation with ……………………………….. 160
coach’s regard for academics at both levels
Table 2.15g. Model 2 and 3 for college expectation ………………………………………. 161
with task cohesion at both levels
Table 2.15h. Model 2 and 3 for college expectation ………………………………………. 162
with social cohesion at both levels
Table 2.16a. Model 2 and 3 for student identity with ……………………………………… 163
team size at both levels
Table 2.16b. Model 2 and 3 for student identity with ……………………………………… 164
popularity at both levels
Table 2.16c. Model 2 and 3 for student identity with ……………………………………… 165
winter season at both levels
Table 2.16d. Model 2 and 3 for student identity with ……………………………………… 166
revenue at both levels
Table 2.16e. Model 2 and 3 for student identity with ……………………………………… 167
tradition at both levels
Table 2.16f. Model 2 and 3 for student identity with
………………………………. 168
coach’s regard for academics at both levels
x

Table 2.16g. Model 2 and 3 for student identity with ……………………………………… 169
task cohesion at both levels
Table 2.16h. Model 2 and 3 for student identity with ……………………………………… 170
social cohesion at both levels
Table 2.17a. Model 2 and 3 for athletic identity with ……………………………………… 171
team size at both levels
Table 2.17b. Model 2 and 3 for athletic identity with ……………………………………… 172
popularity at both levels
Table 2.17c. Model 2 and 3 for athletic identity with ……………………………………… 173
winter season at both levels
Table 2.17d. Model 2 and 3 for athletic identity with ……………………………………… 174
revenue at both levels
Table 2.17e. Model 2 and 3 for athletic identity with ……………………………………… 175
tradition at both levels
Table 2.17f. Model 2 and 3 for athletic identity with
……………………………….. 176
coach’s regard for academics at both levels
Table 2.17g. Model 2 and 3 for athletic identity with ……………………………………… 177
task cohesion at both levels
Table 2.17h. Model 2 and 3 for athletic identity with ……………………………………… 178
social cohesion at both levels
Table 2.18a. Model 2 and 3 for physical ability with ……………………………………… 179
team size at both levels
Table 2.18b. Model 2 and 3 for physical ability with ………………………………………. 180
popularity at both levels
Table 2.18c. Model 2 and 3 for physical ability with ………………………………………. 181
winter season at both levels
Table 2.18d. Model 2 and 3 for physical ability with ………………………………………. 182
revenue at both levels
Table 2.18e. Model 2 and 3 for physical ability with ………………………………………. 183
tradition at both levels
Table 2.18f. Model 2 and 3 for physical ability with
……………………………….. 184
coach’s regard for academics at both levels
xi

Table 2.18g. Model 2 and 3 for physical ability with ………………………………………. 185
task cohesion at both levels
Table 2.18h. Model 2 and 3 for physical ability with ………………………………………. 186
social cohesion at both levels
Table 2.19a. Model 2 and 3 for physical appearance ……………………………………… 187
with team size at both levels
Table 2.19b. Model 2 and 3 for physical appearance …………………………………… 188
with popularity at both levels
Table 2.19c. Model 2 and 3 for physical appearance …………………………………… 189
with winter season at both levels
Table 2.19d. Model 2 and 3 for physical appearance …………………………………… 190
with revenue at both levels
Table 2.19e. Model 2 and 3 for physical appearance …………………………………… 191
with tradition at both levels
Table 2.19f. Model 2 and 3 for physical appearance with ……………………………….. 192
coach’s regard for academics at both levels
Table 2.19g. Model 2 and 3 for physical appearance …………………………………….. 193
with task cohesion at both levels
Table 2.19h. Model 2 and 3 for physical appearance …………………………………….. 194
with social cohesion at both levels
Table 3.1.

Descriptive statistics of independent ………………………………………. 195
variables of selection models

Table 3.2.

Selection model for friendship
network at Time2 (n=18505)

Table 3.3.

Selection model for forming new …………………………………………… 197
friendships (Time1->Time2)

Table 3.4.

Multilevel analysis of selection model ………………………………………. 198
with network data at Time2

Table 4.1.

Descriptive statistics of the five items ……………………………………….. 199

Table 4.2.

The coefficient of one factor model …………………………………………... 200

Table 4.3.

Bivariate correlations between the items …………………………………… 201

…………………………………………… 196

xii

Table 4.4.

Item-test correlation and reliability (Cronbach’s alpha) …………………… 202

Table 4.5.

Comparison of single-level IRT models ……………………………………… 203

Table 4.6.

The results of Multilevel 2PL-PCM …………………………………………... 204

Table 4.7.

Comparison of the two influence models with …………………………….. 205
the raw frequency and the depth of interaction

xiii

LIST OF FIGURES

Figure 4.1. The distribution of the depth of interaction …………………………………. 206
Figure 4.2. The distribution of the mean of frequency of interactions ………………… 207

xiv

Chapter I. STATEMENT OF PROBLEM AND OVERVIEW OF THIS DISSERTATION

Athletic participation in the U.S. is the most popular school-sponsored
extracurricular activity (Eccles & Barber, 1999; Edie & Ronan, 2001). According to the
annual high school athletics participation survey conducted by the National Federation
of State High School Association, 55.5% of students enrolled in high schools participate
in athletic programs, and this participation rate increased for the 22

nd

consecutive

school year in 2010-11 (Howard, 2011). Due to the popularity of athletic programs in
high school, educators, researchers, and policy-makers have extensively investigated
the role of athletic programs in students’ educational pursuits.
However, the relationship between athletic involvement and educational
consequences has been controversial and complex (Eitle & Eitle, 2002). The theoretical
debates have yielded both positive and negative effects of athletic participation. The
positive effects include increasing academic motivation, school engagement,
educational attainment, and psychological well-being (i.e., self-esteem), while the
negative effects, some argue, include reduced times and focus for studying as
distracters and induced likelihood to exposure to delinquent behaviors, such as drug
use, smoke, and skipping school (Sokol-Katz, Kelley, Basinger-Fleischman, &
Braddock, 2006). Along with the theoretical debates, empirical investigations have also
produced inconsistent results. In an economical analysis, high school sports
participation resulted in a 2% increase in standardized math and science test scores,
and students-athletes were 5% more likely to aspire to college attendance on a national
survey sample, controlling for other background factors, such as socio-economic status
1

(SES; Lipscomb, 2006). These positive effects of athletic involvement were replicated in
several large-scale longitudinal studies (e.g., Barber, Eccles, & Stone, 2001; Eccles &
Barber, 1999; Marsh & Kleitman, 2003; McNeal, 1995; Rees & Sabia, 2010; Snyder &
Spreitzer, 1990). Despite positively oriented myths and empirical results, there are
skepticisms surrounding this claim that such findings are an artifact of preexisting
differences (Eitle & Eitle, 2002; Marsh, 1993; Otto, 1982). Eitle and Eitle (2002)
asserted that the relationship between athletic participation in school and academic
achievement depends on different social groups, such as type of sport and participants’
ethnicity. Eide and Ronan (2001) found evidence that sports participation has a
negative effect on the educational attainment of white male student athletes. And,
participation in football and basketball was negatively associated with academic
achievement (Eitle & Eitle 2002; Goldsmith, 2003, 2004). Those differences are due to
social group, cultural capital, household educational resources, and perceived
importance of playing high profile sports, such as football and basketball (Eitle & Eitle,
2002).
As such, studies on this controversial issue of athletic participation and
educational outcomes have suggested that mediating or moderating variables, such as
social factors (i.e., interpersonal relationships with peers, coaches, teachers, coaches
and parents) may explain more about the relationship (Eitle & Eitle, 2002). There are
many aspects of interpersonal relationship that positively influence educational
outcomes. Perceived social and emotional support from peers has been related with
motivational outcomes, such as the academic pursuit, pro-social goals, intrinsic value,
and self-concept (Dubois, Felner, Brand, Adan, & Evans, 1992; Harter, 1996; Wentzel,
2

1994, 1998). Also, Cause, Connell, Spencer, & Aber (1994) and Wentzel (1998) found a
positive association of parental support with perceived competence, academic effort,
and interest in school. Perceived support from teachers has been related to pro-social
behaviors, educational aspirations and values, intrinsic values, and self-concept
(Goodenow, 1993; Hatter, 1996; Marjoribanks, 1985; Midgley, Feldlaufer, & Eccles,
1989; Wentzel, 1994, 1998). Hwang, Feltz, Kietzmann, and Diemer (in press) found that
high school students’ perceptions of the educational expectation of significant others
such as parents, teachers, peers, and coaches predicted their educational expectations,
which in turn, were predictive of later educational attainment.
Although the roles of parents and teachers in the social context of school have
been widely emphasized in education (e.g., Berger & Riojas-Cortez 2011; Pellicer &
Anderson, 1995; Pomerantz, Grolnick, & Price, 2005; Snook, Nohria, & Khurana, 2011),
peer influence in education has received relatively less attention (Buckley, 2009; Ryan,
2000), the recognition of peer influence during adolescence has been increasing in the
socialization process for their education. This may be due to the following reasons: (a)
adolescents spend twice as much time with peers as with their family (Larson &
Richards, 1991), (b) peers fulfill a developmental need that cannot be met by parents or
other adults (Hartup, 1993), and (c) peers provide a source of companionship and help
in school work (Wentzel, 2005).
To empirically support these claims, Hwang et al. (in press) found that peer
support for academics led to higher academic identity, which, in turn, positively
influenced educational expectation and attainment. Also, Buchmann and Dalton (2002)
found the positive link between peers’ influences and college aspiration. Likewise,
3

longitudinal studies have shown the positive impact of peers on school adjustment,
social competence, and academic achievement (Heaven, Ciarrochi, & Vialle, 2008;
Wentzel & Caldwell, 1997). On the other hand, Scheider and Stevenson (1999) found
that peers hold little influence on students’ outcomes, such as educational aspiration.
On the negative side, negative influences of peers have been reported for dropouts
(Pittman, 1991) and anti-social behaviors, such as aggression, skipping class, being
disruptive, and delinquency (Finn, 1989).
Previous research using the general high school student population has been
explored based on data from nationally representative samples (i.e., National Education
Longitudinal Study and National Center for Education Statistics). These have yielded
more acceptable conclusions by longitudinal, multi-wave designs that relate effect of
athletic participation and other social factors to a set of educational outcomes controlling
for preexisting differences, such as background variables and previous status (e.g.,
Barber, Eccles, & Stone, 2001; Marsh & Kleitman, 2003; Snyder & Spreitzer, 1990),
However, these studies were based on self-reported data and, specially for the effect of
social relations with others, have used data based on students’ perceptions of support
from others (e.g., Wentzel, 1998).
The perceived reports may be subjective, and the studies may generate inflated
correlations between respondents’ and actual others’ behavior (Ryan, 2001). To
increase the validity of studies in a social context using actual report (i.e., indicating with
whom I am interacting, and how often I am interacting with them) on their relations, a
social network analysis can be used as a statistical model to quantify and evaluate the
social relations. This sociometric data contains participants’ reports on their interactions,
4

such as specific names and amount of interaction, which is modeled to identify how to
construct peer groups (i.e., peer selection), and examines the effect of their interaction
(i.e., peer influence).
Few studies have been conducted using this frame of data analysis. For
instance, Ryan (2001) used social network analysis to identify peer groups of
adolescents in middle school and found changes of intrinsic motivation (i.e., enjoyment
of school) in school. However, the nature and extent of peer relationships within an high
school athletic teams may be different than described above because they form their
own subcultures that are particularly defined by a team’s norm and rule. Thus, it is
probable to anticipate that peer interactions with team members can have different
forms and effects on their academics, and that more adaptive interpersonal
relationships with peers in an athletic team promotes better experience in academics as
well as athletics in school.
In sum, this dissertation addresses the issues of social relation in the exploration
of the role of peers for high school student athletes’ academic outcomes through use of
social network analysis. Applying a social network analysis helps enabling description
and quantification of antecedents and consequences from peer networks. This peer
group process has two phases, peer influence and peer selection (Frank, 1998; Kiuru,
Aunola, Nurmi, Leskinen, & Salmela-Aro, 2008; Ryan, 2000, 2001). Students choose
peers to interact with, which create a social context (i.e., athletic team) that exposes
them to a set of their peers’ thoughts, attitudes, and behavior. Within the group, they
influence each other. Also, Moran and Weiss (2006) suggest these two dimensions of
peer relationship should be examined together in sport.
5

Thus, Study I examined the effect of peers in athletic teams on outcome
variables such as academic motivation, achievement, college aspiration, and identity.
Study II identified how peers construct their patterns of relations based on variables
such as academic/athletic ability and identities and demographics. Lastly, Study III
tested if a network measure adapted in this dissertation is psychometrically sound,
using Graded Responses Multi-Level Item Response Theory Model.
Considering various forms of peer interaction in school during adolescence, the
following delimitations were applied to answer the above mentioned research questions:
1) This study focused only on peers in athletic teams (same and different teams),
so other friendships formed with friends who were not enrolled in any athletic program
was not included. Thus, the social context was the groups of student athletes in a high
school.
2) An athletic team was defined as a sport team offered by a high school as an
extracurricular activity, regardless level (i.e., varsity, Jr. varsity, and freshmen).
3) For peer network, only ego-centric data were utilized to model, in which egos
were independent. Thus, dyadic relationships were not modeled.
4) Social interaction was delimited to the interaction regarding academics,
athletics, social topics, and emotional supports within the group of student athletes.

6

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Chapter II: PEER INFLUENCE ON EDUCATIONAL OUTCOMES (STUDY I)
Introduction
Peer influence during adolescence is the more potent than the influence of
parents and schools (Harris, 1995; Ryan, 2001; Schunk, 1987). Possible explanations
offered are increased peer involvement (Brown, 1990; Brown & Theobald, 1999) and
strong social identity to spend more time with their friends (Csikszentmihalyi, Larson, &
Prescott, 1977). In this regard, peers are important as a socializing context. This
dissertation proposes that an athletic team is a social context, in which team members
are interacting with teammates not only for athletic development but also for educational
development.
Peer influences, in general, can be negative during adolescence. Empirical
research has demonstrated negative influences of peers on such anti-social behaviors
as breaking rules (Aseltine, 1995; Haynie, 2001; Sieving, Perry, & Williams, 2000);
delinquent behavior, such as drinking alcohol, smoking, and using illegal substances
(Kobus, 2003; Urberg, Degirmencioglu, & Colleen, 1997; Urberg, Luo, Pilgrim, &
Degirmencioglu, 2003); and development of psychopathology (Deater-Deckard, 2001).
Of course, the positive role of peers has been emphasized in terms of positive
development, particularly in school (Brown, 1990; Brown, Eicher, & Petrie, 1986;
Wentzel, 1989, 1997). Likewise, the literature on adolescence has established that peer
relations appear to play a significant role for educational experience among high school
students, such as achievement, motivation, expectation, and aspiration (e.g., Cook,
Deng, & Morgano, 2007; Gilman & Anderman, 2006; Liem & Martin, 2011; Ryan, 2001;
Wentzel & Asher, 1995).
13

In the light of positive influence, close friendship has been shown to be positively
related to academic motivation and performance (e.g., Altermatt & Pomerantz, 2003;
Berndt, Hawkins, & Jiao, 1999; Crosnoe, Cavanagh, & Elder, 2003; Wentzel & Caldwell,
1997). Also, early work has shown that high school friends influence one’s aspiration to
attend college (e.g., Campbell & Alexander, 1965; Cohen, 1983; Hauser, 1972).
However, Cohen (1983) argued that the effect of peer influence on college aspiration is
smaller than these findings suggest because estimates have been inflated by the
omission of a control (i.e., initial aspiration before building friendship), and then found a
weak effect with a path coefficient less than .15, controlling for their initial status. More
recently, Nurmi (2001, 2004) found that peer groups form a social context wherein they
discuss their thoughts and plans about the future. For example, adolescents often
discuss their future-related decisions with their peers. Peers are also an important
source of future-related information among adolescents (Malmberg, 1996). Moreover,
young people may model their peers’ decisions concerning future education, particularly
when they are uncertain of their own plans (Kiuru, Aunola, Vuori, & Nurmi, 2007).
In criticism of such correlational studies, Cook et al. (2007) emphasized the
methodological problems of research on peer influences (i.e., sampling issues, causal
claims, biased standard errors, and construct validity of peer groups). Using the cluster
algorithm, a longitudinally collected data set, and controlled confounding variables,
Cook et al. found peers’ attributes, such as grade point average (GPA), affected
individual school performance outcomes.
This effect of peer relationship on the optimal educational outcomes in a social
context is well explained by social capital theory. Social capital is defined as ‘resources’
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that actors may access through social ties (Bourdieu, 1986; Coleman 1988, 1990; Frank
& Yasumoto, 1998). In school settings, it includes resources obtained through
interaction with friends, parents, and teachers. For example, with a basis of social
capital theory, social capital of well-educated parents (i.e., parent-child discussion and
parental involvement in school) has shown a positive association with educational
outcomes, such as GPA, achievement test scores, educational attainment, high school
completion, and college enrollment (e.g., Carbonaro, 1998; Hao & Bonstead-Bruns,
1998; Sun 1998). Also, positive help has been found from social capital of peers (i.e.,
number of close friends) attending a same school and ties with peers on achievement
score (e.g., Morgan & Sørensen, 1999; Sun, 1999).
Social capital theory highlights the importance of social networks, and illuminates
specific mechanisms through which the social ties (i.e., friendship) developed in school
may benefit educational outcomes. Recently, research on peer effect as a form of social
capital in educational settings has been conducted at different levels of social context,
such as community (Levine & Painter, 2008), school (Angrist & Lang, 2004), cohort
(Carrell, Fullerton, & West, 2009), and the classroom (Burke & Sass, 2008; Lavy, Silva,
& Weinhardt, 2009). However, none of research has been conducted in a group of
student athletes in schools. In this respect, this study focuses on athletic teams, where
students are nested in high schools, which may serve to create more social capital for
students’ educational outcomes by providing more time and opportunities for increased
social ties among team members within their teams or other friends in different teams
with same interest in participating in an athletic program.

15

Early research on peer relationships within the culture of high school sport,
however, focused primarily on peer acceptance. That is, students who were good at
sports were more likely to be accepted as friends (Smith, 2003; Weiss & Stuntz, 2004).
In observational studies, perceived sport competence is important to peer relationships
(e.g., Adler, Kless, & Adler, 1992; Buchanan, Blankenbaker, & Cotton, 1976; Holland &
Andre, 1994; Kane, 1988. For example, Buchanan et al. asked 4

th

grade through 6

th

grade students to nominate who were the best students, the best athletes, and the most
popular. For boys, being good at sports was most important for popularity, while girls
reported good grades were more important for popularity than just being good at sports,
but only by a small margin. Similar to the result of Buchanan et al.’s study, Chase and
Dummer (1992) found that being good at sport was the most important, followed by
physical appearance for boys, while girls indicated being pretty was the most important,
and good grades were the second, followed by being good at sport. To reflect changes
of these factors for popularity more recently, Chase and Machida (2011) replicated and
compared their findings to the previous studies (i.e., Buchanan et al., 1976; Chase &
Dummer, 1992). Chase and Machida found gender differences for popularity. The
importance of sport for girls’ popularity has not changed in 30 years, but has decreased
for boys. In addition, the positive association of peer acceptance to physical skill was
found with observational studies (Evans & Roberts, 1987; Farmer, Estell, Bishop,
O’Neal, & Cairns, 2003), whereas, Hymel, Bowker, and Woody (1993) found that
students who had low athletic skills were perceived by peers as unpopular and socially
isolated.
In contrast, friendship in sport settings has been examined to see the impact
16

within its social context. Weiss & Smith (1999) developed a self-report assessment of
sport friendship quality in an attempt to account for the context-specific nature of
friendship perceptions in sport settings. The six sub-scales of the Sport Friendship
Quality Scale (SFOQ), validated by Weiss and Smith (2002), are self-esteem
enhancement and supportiveness, loyalty and intimacy, things in common,
companionship and pleasant play, conflict resolution, and conflict elements of sport
friendships. These sub-scales distinguished youth perceptions of a best friend versus a
third-best friend, suggesting that the measure is relatively sensitive to the quality of
particular relationships. Using this scale, research on friendship has been examined in
conjunction with motivation–related variables in youth sports. Higher friendship quality
has been demonstrated to associate with more adaptive achievement goal orientations
(Ommundsen, Roberts, Lemyre, & Miller, 2005; Smith, Balaguer, & Duda, 2006),
greater perceived physical competence, lower sport stress, greater sport enjoyment,
more self-determined motivation (Ullrich-French & Smith, 2006), and greater self-worth
and stronger sport commitment (McDonough & Crocker, 2005).
However, due to the limitation of self-report that can only be interpreted as
individual perception for friendship quality with a single best friend, a social network
analysis has been suggested to study peer relationships in sport (Smith, 2003) by which
we can quantitatively model the effect of multiple peer relationships (see exposure in
Method). For instance, Smith et al. (2006) showed a positive correlation with task-goal
orientation, and a negative correlation with ego-goal orientation based upon youth
athletes’ perceptions of friendship with a single best friend, which does not cover
modeling the actual effect of friends in changing the goal orientation. Very few studies
17

have adopted a social network analysis in sport settings. For example, Hwang,
Machida, Feltz, and Frank (in press) studied the influence of peer interaction on sportconfidence and goal orientation in a youth soccer club. Hwang, Machida et al.
concluded that peer interaction influenced changes in sport-confidence and
achievement goal orientation. More specifically, the interaction among peers in the
same age groups positively influenced the change in sport-confidence about cognitive
efficiency and resiliency, and in task goal orientation, while ego goal orientation was
positively affected by the interaction among peers in the different age groups.
For educational outcomes, however, no studies have been systematically
conducted regarding the effect of social interaction among student athletes. However,
the study of social ties within athletic teams has great potential to help understand the
link between sport participation and educational pursuits because an athletic team is a
type of social context, just like a school and classroom, in which student athletes build
their social relationships. Although not directly relevant to the reciprocal relationship in a
team, research has found that high school student athletes have identifications as a
student and an athlete, but they develop their educational expectations through their
student identity (Hwang, Feltz et al., in press). Also, there is a general argument that
athletic identity leads to a stronger identity with one’s school and academic achievement
objectives (Barber, Eccles, & Stone, 2001; Guest & Schneider, 2003).
In addition, peers in athletic teams have been found to develop tight bonds and
sub-culture (Philips & Schafer, 1971; Schneider & Stevenson, 1999), which may lead to
more social interaction for both athletic and educational aspirations. Also, peer
influences among athletic team members may be greater than other friends in school
18

because peers in a same athletic team have similar interests and goals (i.e., skill
improvement), and participation in school athletic teams requires time commitment
beyond a regular school curriculum, which may facilitate more frequent interaction with
team members (Broh, 2002; McNeal, 1995). Due to the nature of athletic teams in high
school, there is reason to investigate how effective the social interaction with team
members is on their educational goals. The effect is hypothesized to be positive
because of the followings set of possibilities: increased interest in school, the need to
maintain good grades to stay eligible, increased attention from teachers and coaches,
and interaction with educationally oriented peers (Snyder & Spreitzer, 1990).
In the studies of peer relationships in school, several methodological issues are
involved. Social network analysis has been recently suggested in order to resolve the
following issues (see Frank, 1998; Ryan, 2000, 2001 for a review). Firstly, many studies
have relied on respondents’ perceptions of their peers’ characteristics rather than
asking for peers’ names and collecting the characteristics from the referred peers. Data
based on students’ perceptions may not be accurate and involves students’ own
projection onto peers although the use of the data is often justified by reasoning that
what students think of peers is more influential than who peers actually are (Ryan,
2000). A social network analysis requires a network metrics that contains the referred
peers’ names and responses in order to quantify the relational information among
peers, such as referred friends and their characteristics).
For socialization of peers (i.e., peers tend to become similar), early studies
employed correlational techniques to assess similarity of peer groups for academic
characteristics, such as GPA (Epstein, 1983), college aspirations (Cohen, 1983;
19

Epstein, 1983; Hallinan & Williams, 1990), time spent on homework (Cohen, 1977), and
general engagement in schoolwork (Kindermann, 1993). However this correlational
evidence does not warrant the conclusion that peers influence academic outcomes.
Instead, it could be that the students select peers who are similar to them to begin with.
A social network analysis examines data longitudinally. Longitudinal data have a
benefit over a single data collection. Longitudinal data can specify and estimate
changes in individuals’ beliefs as a function of the beliefs of others with whom they are
interacting with in previous time periods (Frank, 1998; Friedkin & Marsden, 1994). Also,
the individual’s previous belief can be used as a covariate to control for the effect of his
or her own previous belief (Time 1) on current belief (Time 2).
Regarding the issue of nested structure of data, Frank (1998) suggests a
potential to integrate multilevel models and models of social network processes.
Multilevel models enable partitioning of the variance of an outcome variable into
individual level (i.e., athletes) and group level (i.e., team) components. By the multilevel
models of network analysis, the researcher can characterize the extent of variation of an
outcome variable within- and between- athletic teams, and specify and estimate effects
of individual- and team-level characteristics, as well as the interaction of individual and
team characteristics. In the light of methodological advancement, Ryan (2001) used a
social network analysis in a multilevel model and found peer groups socialized some
academic characteristics. That is, changes in achievement and intrinsic motivation (i.e.,
enjoyment of school) were predicted by peer group socialization over the school year.
The review of the methodological issues and characteristics of student athletes’
groups suggest a statistical model, which includes the network metrics, longitudinal type
20

of data, and two-level multilevel modeling (i.e., student and team levels). At the team
level, coaches’ attitude on academics as a predictor is added, along with the unique
effect of the team, because team members share the team norm and culture, which
affect team members differently across teams. A coach’s regard on academics
influences team culture and student athletes’ identity as students (Feltz et al., 2013). At
the student level, other external influences are specified and controlled beside the effect
of peer interaction in teams. They include the perceived educational expectation of
significant others, such as father, mother, and teacher as well as their previous status
by a longitudinal data. Therefore, the purpose of Study I was to examine the effect of
peers in athletic teams on educational and identity outcome variables, controlling for
individual effects, group effects and coaches’ direct effect on groups, using an
integrated model of social network (influence model) in multilevel model.

21

Method
Participants and Procedures
Data were collected from a local high school in which approximately 500 students
are enrolled, and 350 students play at least one sport for the school. The school has a
total of 22 athletic teams regardless season. After getting approvals from the athletic
director of the school and the University Committee on Research Involving Human
Subjects (UCRIHS), a meeting with all student athletes was made in an auditorium for
data collection. The data were collected longitudinally to examine the social interaction
during a certain period and control the initial status on the outcome variables. The first
data set was collected in the beginning of 12-13 Winter season (i.e., the first week of
November), and the second data set was collected in the end of 12-13 Winter season
(i.e., the fourth week of February). Participants were told that they would receive $5 by
completing the two surveys. Two-hundred and ninety-one and 242 student athletes
completed the first and second survey respectively. Table 2.1 shows participants’
distribution on each team. This distribution is based only on the primary sports team
reported by them regardless season (i.e., one belongs to one sport team). There were
students who reported multiple sports in the two surveys (137 and 91 respectively).
Two-hundred and thirteen student athletes completed the both surveys, 79 and
29 completed only the first survey and second survey respectively. Three-hundred and
twenty-one student athletes participated in at least one survey, among which 82.5% are
White. The distributions of gender and school years are in Table 2.2.

22

Outcome Measures
The outcome measures included academic-related variables, such as academic
achievement, academic efficacy, college aspiration, academic and athletic identities,
and self-regard. These measures were chosen based on the literature review of the
relationship among peers, sport participation and educational outcomes.
Academic Achievement: Grade point average (GPA) was derived from selfreports of the most recently earned overall grade. Cassady (2001) supported the use of
self-reported GPA by showing a high correlation with official records, r = .88.
Academic Efficacy: Academic efficacy refers to students' judgments of their
capability to complete their work successfully, and was measured using the Pattern of
Adaptive Learning Scale (PALS: Midgley et al., 2000). Midgley et al. reported the
internal consistency (α) was .78. Also, Bong (2001) tested the construct validity across
subjects (i.e., English, math, science, and social studies) of this measure and yielded
CFI=.96 and NNFI=.94 for high school students. The PALS consists of the five items
with a five-point Likert scale (1 = Not at all true, 3 = Somewhat true, and 5 = Very true).
Items are in Appendix.
College Aspiration/ Expectation: Two items from the National Longitudinal Study
of Adolescent Health (Add Health) were used to measure college aspiration (‘how much
do you want to go to college?’) and expectation (‘how likely is it that you will go to
college?’) on a five-point Likert scale (1=low through 5=high). Aspiration reflects the
degree to which students want to attend college while expectation reflects the degree to
which students believe they will attend college. Aspiration is considered to be somewhat
abstract, representing idealistic preferences for the future, whereas expectation is a
23

more realistic self-assessment (Bohon, Johnson, & Gorman, 2006).

Academic and Athletic Identities. Athletic identity was measured by Athlete
Identity Measurement Scale (AIM) (Brewer, Van Raalte, & Linder, 1993), which
assesses the importance of the athlete role to the individual with two dimensions,
strength and exclusiveness. AIM consists of 10 items with a 7-point Likert scale, raning
from 1 (strongly disagree) to 7 (strongly agree). Brewer et al. (1993) reported an internal
reliability for the AIMS of α = .83. And, for academic identity, AIM was revised by
changing athlete for student and academics for sport for one’s academic identity. Items
are in Appendix.
Self-regard. The sub-set of Self-Rating Scale (Fleming & Courtney, 1984) was
adapted to measure their perception on physical appearance and ability because they
were found to be factors in forming a higher level of social identity with a group (Tarrant,
MacKenzie, & Hewitt, 2006). The Self-Rating scale originally consists of five
dimensions: general self-regard, school abilities, social confidence, physical
appearance, and physical abilities with 30 items. For this study, only 10 items for
physical appearance and abilities were used with a 7-point Likert scale, ranging from
1(almost never) to 7 (very often). Fleming and Courney (1984) reported internal
consistency (α=.92) and test-retest reliability (r=.84). Also, using principal component
analysis, they confirmed the five factor solutions and selected 30 items, which factor
loadings were above .40 to each dimensions. Bushman and Baumeister (1998) also
reported .93 of internal consistency. Items are in Appendix.

24

Control Measures
Team Characteristic. Team characteristics were considered as predictors at
Level 2 (Team-level) because it was hypothesized that peer interaction is formed based
on team characteristics, which includes size, popularity, season, revenue generating,
and traditions (state championship banner). For instance, interaction on a popular team
is hypothesized to be more effective. These data were obtained from the athletic
director of the school. Table 2.3 shows the team characteristics.
Group cohesion. Individual perception of group cohesion was measured to use
and control group norms on team (i.e., highly cohesive vs less cohesive teams), using
the Youth Sport Environment Questionnaire (YSEQ; Eys, Loughead, Bray, & Carron,
2009). The YSEQ is an 18-item questionnaire on a 9-point Likert scale ranging from 1
(strongly disagree) to 9 (strongly agree) that assesses task and social cohesion.
However, two spurious negative items were not included in the survey. According to Eys
et al. (2009), Task cohesion (8 items) is defined as an individual’s perception about the
closeness, bonding, and similarity around team’s goal and task, while social cohesion (8
items) is around team as a social unit. In addition, task cohesion includes personal
involvement with team’s goal and task, while personal acceptance and social interaction
with team are part of social cohesion. Eys et al. (2009) demonstrated content validity by
focus group, open-ended questionnaires, and a literature review, and construct validity
by principal component analysis and confirmatory factor analysis. Also, Bosselut,
McLaren, Eys, and Heuze (2012) showed high internal consistency for both task (.94)
and social (.95) cohesion. The task- and social-norm (i.e., average of each team both at
Time 1 and Time 2) on each team are in Table 2.3.
25

Courses and Other Extracurricular Activities. Beside friends on an athletic team,
friendship can be formed in various school activities, such as taking the same course,
participating in the same club (e.g., art club), and belonging to the same academic
organizations (e.g., Model UN) (Frank, Muller, & Muller, 2013), which need to be taken
into account. Participants were asked to list courses that they were taking, and choose
extracurricular activities in the list of extracurricular activities obtained from the National
Longitudinal Study of Adolescent Health (Add Health): French Club, German Club, Latin
Club, Spanish Club, Book Club, Computer Club, Debate team, Newspaper, Honor
Society, Student Council, Yearbook, Drama club, band, Chorus or Choir, Orchestra.
Beside sport participation, the numbers of shared activities, including extracurricular
activities and courses between nominators and nominees at Time 1 ranged from 0 to 8
with a mean of 1.36 and a standard deviation of 1.72. The shared activities at Time 2
ranged from 0 to 6 with a mean of 1.19 and a standard deviation of 1.54.
Perceived Educational Expectations of Significant Others. In order to control the
effect of significant others (i.e., parents, teachers and coaches) on educational
outcomes, perceived educational expectations of significant others were measured by
items from NELS-88: How far in school do your father, mother, teacher, and coach want
you to go after high school? Response anchor follows as 1 = get a job after high school,
2= enter a trade school, 3 = go to community college, 4 = go to four years college, 5 =
go to graduate school. The range of the means was from 4.12 to 4.37 with the range of
standard deviation from .53 to .75 both at Time 1 and Time 2.
Coach’s Regard on Academics. I measured the subjects’ perception on their
coaches’ opinions of academic ability because coaches’ attitude toward academics is
26

pertinent to the norm and circumstance about academics in athletic teams of high
school. In the team, the coach has a role to guide student-athletes for both academics
and athletics (Gould, Chung, Smith, & White, 2006; Jackson & Beauchamp, 2010). Feltz
et al. (2013) found that coach’s attitude toward academics predicted perceived
stereotype threat, and academic/ athletic identities of student athletes. An item from
Feltz et al. (2013) was revised and used with a seven-point scale (1=strongly disagree
through 7=strongly agree) as follows: My coach has a high opinion of my academic
ability. For this study, the means were 5.58 (SD=1.35) and 5.11 (SD=1.64) at Time 1
and Time 2 respectively.

Social Network Measure
The network data were collected through a socio-metric instrument at the 1
nd

(i.e., around the beginning of the 2012-2013 Winter season) and 2

st

data collection

(i.e., around the end of 2012-2013 Winter season), and measured as complete
networks with each participant referring to friends on same and other teams when
responding to a network item. Complete network analysis includes all interactions
among actors within the student group who were participating in at least one sport in the
school, which produces an actor-by-actor matrix of relational values. The interaction
network item asks participants to rate how frequently they talk with each of the referred
friends about general, academic, athletic, social, and emotional topics. Participants
were asked to circle the appropriate number next to the five types of interaction on a 5point rating scale, ranging from 1 (Daily) to 5 (Monthly). These values were reversely
recoded in order to interpret higher values as more frequent interactions. Depending on
27

the research questions, each frequency and the mean were used for the extent of
relation between two actors. Table 2.4 and Table 2.5 include the descriptive statistics of
friendship at Time 1 and Time 2, such as total number of ties, and average degree (i.e.,
total ties are divided by the total number of student athletes on each team). The total
number of ties at Time 1 was 1,179, and 855 was the total number of ties at Time 2.

Data Analysis and Statistical Model
The influence model of a social network analysis was employed to examine the
effect of social ties (i.e., network) on changes in the outcome variables over the fixed
time frame. In basic analyses, the descriptive statistics and paired t-test were reported
to see whether the changes of the outcome variables occurred between Time 1 and
Time 2.
Exposure. For the influence model, exposure is defined as the degree of being

(∑ 𝑖 ′ 𝑖′
𝑤 𝑦 ′ )/𝑛 𝑖′ in order to estimate the effect of network on outcome
=1,𝑖≠𝑖′ 𝑖𝑖′ 𝑖 𝑡−1
𝑛

exposed to others and their attributes, which can be quantitatively modeled as

variables.

𝑤 𝑖𝑖′ indicates extent of relation (i.e., frequency of interaction) between i

(nominator) and i’ (nominee), as perceived by i (i.e., a network metrics).

𝑦 𝑖 ′ 𝑡−1

is

nominee’s previous attribute at Time 1. The sum of the relation is divided by 𝑛 𝑖′ , which

is the number of i’ (nominee) of i (nominator) for normative effect (i.e., mean) because

every nominator has different number of nominees. This exposure is a variable of each
nominator for the effect of interaction with friends nominated. This all exposure was
divided into four exposures to separately account for exposures in a same (or different)
28

team and shared activity: 1) exposure of friends in a same team with at least one
shared activity, 2) exposure of friends in a same team with no other shared activities
beside sport participation, 3) exposure of friends in different teams with at least one
shared activity, 4) exposure of friends in different teams with no other shared activities
beside sport participation.
Although the four different exposures were hypothesized to be identified, shared
activity was not accounted for because of higher correlations between the exposures,
which cause multicollinearity in multiple regression. For instance, correlation between
Exposure 1 and Exposure 2 were .91, .73, .70, and .99 for academic achievement,
academic efficacy, student identity, and physical appearance respectively. Correlation
between Exposure 3 and Exposure 4 were .81, .79, .97, and .92 for college aspiration,
college expectation, student identity, and physical ability. Instead only exposure in a
same team and exposure in different team were considered for the analyses,
Influence Models. Two ordinarily least square (OLS) regressions were employed

𝑦 𝑖 = 𝛽0 + 𝛽1 (prior 𝑖 ) + 𝛽2 (all exposure 𝑖 ) + 𝛽3 (others' edu. expec. 𝑖 )

to examine the effect of the exposures with control variables as follows:

+𝛽4 D1𝑖 + ⋯ + 𝛽24 D21𝑖 + 𝑒 𝑖

𝑦 𝑖 = 𝛽0 + 𝛽1 (prior 𝑖 ) + 𝛽2−1 (same team exposure 𝑖 )

+𝛽2−2 (different team exposure 𝑖 ) + 𝛽3 (others' edu. expec. 𝑖 )
+𝛽4 D1𝑖 + ⋯ + 𝛽24 D21𝑖 + 𝑒 𝑖

29

The dependent variable ( 𝑦 𝑖 ) is a measure of an outcome for a person (i) at

Time2. The 𝛽0 is the intercept. 𝛽1 is the effect of prior status of nominators on the
outcome variables, which controls for a student’s original status on the outcome

variables. It allows us to examine a specific effect of exposures on changes over the

𝛽2

fixed time (from Time1 to Time2), not confounded with the prior status of the outcome
This all-exposure was separated into two exposures from ties in same teams ( 𝛽2−1 )

variables.

is the effect of all exposures from all ties regardless of team membership.

and ties from different teams ( 𝛽2−2 ). 𝛽3 was set as a controlling variable (average of
significant others’ educational expectation at Time2). Also, to control team’s variance

(i.e., teams’ different characteristics), 21 dummy variables (D1i-D21i) for specific team
involvement were entered in the model, while the Boys and Girls bowling team set as a
reference group (see Table 2.3 for the specific dummy variables).
Multilevel Influence Models. In order to account for team effect on changes in the
outcome variables, random slope and intercept multilevel modeling was integrated with
the influence model of a social network analysis. The extent of the exposures varies
randomly across team (i.e., only same team exposure) because of the team
characteristics, such as team size, popularity, season, revenue generating, and
traditions (state championship banner), coach’s regard for academics, and team’s norm
for task- and social-cohesion (e.g., this team is a more socially cohesive team). The
teams’ average of coach’s regard and task- and social-cohesion were specified as
predictors at the team level. The three multilevel influence models were as follows:
30

Model 1 (Unconditional models) was specified to examine the proportion of

𝑦 𝑖𝑗 = 𝛽0𝑗 + 𝑒 𝑖𝑗

variance of the outcome variables explained by the team level variance.
Student Level:
Team Level:

𝛽0𝑗 = 𝛾00 + 𝜇0𝑗

Model 2 (Conditional models with level1-predictors) was specified to examine the
the intercept, 𝛽0𝑗 , and slopes, 𝛽2𝑗 , at the student level were modeled with random

effect of same team exposure with randomized intercepts and slopes at Team 2. Only

effect, which are the

𝜇0𝑗 and 𝜇2𝑗 . The 𝛾00 and 𝛾20 indicate the fixed effects for the

intercept and slopes of same team exposure.

𝑦 𝑖𝑗 = 𝛽0𝑗 + 𝛽1 (prior) 𝑖𝑗 + 𝛽2𝑗 (same team exposure) 𝑖𝑗
+𝛽3 (different team exposure) 𝑖𝑗 + 𝑒 𝑖𝑗

Student Level:

𝛽0𝑗 = 𝛾00 + 𝜇0𝑗
𝛽2𝑗 = 𝛾20 + 𝜇2𝑗

Team Level:

examine the fixed effects of intercept ( 𝛾00 ), same team exposure ( 𝛾20 ), team-level
Model 3 (Conditional models with predictors at both levels) was specified to

predictors ( 𝛾01 ), and cross level interactions between same team exposure and team
level-predictors ( 𝛾21 ). The team-level predictors were P1 (team size), P2 (popularity),

P3 (season), P4 (revenue), P5 (tradition), Q (coach’s regard for academics), R (task-

cohesion), and S (social-cohesion). Due to multicollinearity, each team-level predictor
31

was entered in each model. The

𝜇0𝑗 and 𝜇2𝑗 are for the random effects of intercept

and slope (same team exposure). The

𝑒 𝑖𝑗 is the residual.

𝑦 𝑖𝑗 = 𝛽0𝑗 + 𝛽1 (prior) 𝑖𝑗 + 𝛽2𝑗 (same team exposure) 𝑖𝑗
+𝛽3 (different team exposure) 𝑖𝑗 + 𝑒 𝑖𝑗

Student Level:

𝛽0𝑗 = 𝛾00 + 𝛾01 (team − level predictor) 𝑗 + 𝜇0𝑗
𝛽2𝑗 = 𝛾20 + 𝛾21 (team − level predictor) 𝑗 + 𝜇2𝑗

Team Level:

32

Results
Basic Statistics
Two-hundred and ninety-one and 242 student athletes in 22 athletic teams of one
high school completed the first and second survey respectively (see Table 2.1 & 2.2 for
the participants’ distributions). Table 2.6 and Table 2.7 show the descriptive statistics
and paired t-test result of the outcome variables. When subtracting Time 1 from Time2,
academic achievement, academic efficacy, academic identity, and athletic identity were
increased from Time 1 to Time 2, indicated by the negative signal (-), while college
expectation/ aspiration and physical ability/ appearance were decreased with the
positive signal (+). Among them, significant changes were found in college aspiration
(.052), academic identity (-.122) physical ability (1.115), and appearance (.684).
Specially, the mean differences of physical appearance and ability were almost 10 times
less than the corresponding standard errors.
For the exposure, three different exposures were calculated, all-exposure, same
team-exposure, and different team-exposure. The all-exposure is the mean of the
product between relates (i.e., frequency of interaction with nominees) and nominees’
attribute at Time 1 (i.e., values of outcome variables at Time 1). It was separately
identified as same team-exposure (with same team members) and different teamexposure (with different team members). Table 2.8 shows the descriptive statistics of
the exposures. The paired t-tests were conducted for the outcome variables to see the
difference between same team-exposure and different team-exposure (Table 2.8).
Except for athletic identity, same team-exposure was significantly higher than different
team-exposure, which means that the student athletes were more exposed to friends in
33

a same team. This exposure is the product of frequency of interaction and friends’
attribute.

Basic Influence Models
To examine the effect of exposure (i.e., influence of social network) without
considering variance at team level, two OLS regression models were tested, in which a
only all-exposure ( 𝛽2 ), while same ( 𝛽2−1 ) and different team-exposure ( 𝛽2−2 ) were
mean of all types of interaction were used for the exposures. The first model included

The prior status ( 𝛽1 ) was modeled to control its effect on the outcome variables

included in the second model for each outcome variable (Table 2.9).

at Time 2 in order to examine the effect of the exposures on changes of the outcome
variables from Time 1 to Time 2. And, the 21 dummy variables were entered in the
models to control team’s variance. It makes a stronger claim on the effect of the

exposures. Except for physical appearance, the prior statuses had significant effects on
the outcome variables of Time 2. However, the physical appearance was significantly
influenced by its all-exposure (.192). Also, the different-team exposure was a significant
predictor (.124). The effect of all-exposures was not significant with respect to its effect
on changes of the other outcome variables. For academic efficacy, a significant, positive
effect of different team-exposure (.082) was found at .08 level ofα, which magnitude
was about 9 times less than the effect of the prior (.69).
In sum, these results were made by the overall interaction (i.e., mean of five
types of interaction). The overall interaction with friends positively affects the perception
34

on physical appearance, which is mostly from interactions with friends in a different

team. Also, the interaction with friends in a different team positively influenced change
of their efficacious feeling on academics.
Table 2.10 shows the two OLS regression models with a specific type of
interaction (c.f., Table 2.9). For instance, the exposure for academic identity was
modeled only by a network question (i.e., How often do you interact with the referred
friend on academic topics?), while a network question only on athletic topics was used
for athletic identity.
Using a specific type of interaction for the exposures, the positive effects of allexposure were significant on academic achievement (.062, p<.05), college aspiration
(.094, p<.05), physical ability (.145, p<.08), and physical appearance (.20, p<.01), which
were respectively 18, 6, and 1.5 times less than their prior status, except for physical
appearance. In addition, the changes in academic achievement (.038) and physical
appearance (.16) were positively influenced by different team-exposure.
In sum, using a specific type of interaction, I found somewhat different results
than using an overall interaction as a mean of all type of interactions. Specifically, the
specific interactions about academic or athletic topics with all referred friends,
regardless team involvement, had positive influences on changes of academic
achievement, college aspiration, and perceived physical ability and appearance. The
interaction about academic or athletic topics with friends in different teams also had
positive impact on the change of academic achievement and perceived physical
appearance only.

35

Multilevel Influence Models
Multilevel modeling approaches were integrated into the basic influence models
to partition the variance of the outcome variables into student-level and team-level
variances (Model 1), and to examine the effects of student-level (Model 2) and teamlevel predictors (Model 3) onto the outcome variables.
2
𝜇0𝑗 to the total

The result of Model 1 (unconditional models) shows the intraclass correlation
2
𝜇0𝑗 + 𝑒 2 (Table, 2. 11).
𝑖𝑗

coefficient (ICC), which indicates the proportion of team-level variance,
variance,

A common rule of thumb is to model predictors

(i.e., random slope) at Level-1 and Level-2 when ICC of the null model is greater than
0.05. Among the outcome variables, only academic achievement, athletic identity, and
physical ability and appearance exceeded the criteria of .05, however, the conditional
multilevel modeling (Model 2 & Model 3) was conducted for the all outcome variables to
examine the effect of the exposures (i.e., fixed effects of group-level factors) after
controlling for team-level variance.
In Model 2, predictors at student-level, such prior status and same team- and
different team-exposure, were added with random intercept and slope to examine the
fixed and random effects of the predictors. In Model 3, each predictor (i.e., characteristic
of a team) at team-level was added separately into Model 2 to examine the fixed and
random effects of the predictors at student- and team- level, and cross level interaction.
The all-exposure was not included in the models because a specific team that a student
and a referred friend belonged to could not be identified. A likelihood ratio test was
conducted to test whether the effect of same team-exposure varied across team for
36

each of the outcome variables. However, no significant effects were found for all of the

outcome variables, which led to the decision not to interpret the random effects of teams
exposure ( 𝛾20 ), different team-exposure ( 𝛽3 ), predictor at team-level ( 𝛾01 ), and its

on the intercept and slope of the linear relationship. The fixed effect of same team-

cross-level interaction ( 𝛾21 ) were focused for the results of multilevel modeling (Model
2 and Model 3).

For academic achievement, the team size (-.004) negatively influenced academic
achievement (Table 2.12a). After accounting for the task cohesion as the team level
predictor, same team exposure was significant (-.136) and its cross-level interaction
with task cohesion was also significant (.020) (Table 2.12g). These results indicated that
the effect of same team-exposure negatively affected academic achievement, which
was positively moderated by team’s task cohesion.
1

For academic efficacy, participating in a winter season sport had negative effect
on the change of academic efficacy from Time 1 and Time 2 (-1.12), which was
positively moderated by same team-exposure (.059) (Table 2.13c). Also, participating in
a revenue generating sport had negative effect on academic efficacy (-.82) (Table
2.13d). These results indicated that participation in a revenue generating and winter
season sport had negative effect on academic efficacy; however peer interactions in
their team moderated the negative effect on academic efficacy.
College aspiration and expectation appeared to be positively related to different
team-exposure. With exception of team size, after accounting for each team-level
predictor (Table 2.14b-h), different team-exposure positively affected the change of the

1

Data collected during the winter season. So participation in a winter season sport may
mean the current season.
37

aspiration from Time 1 to Time 2 (.042~.047). For college expectation, the magnitudes
of the positive effect of different team-exposure was .028, .026, and .030 after
accounting for the team size, popularity, and coach’s regard for academic respectively
(Table 2.15a, b, f). These relationships were not found in Model 2 (Table 2.9 & 2.10).
While academic identity was significantly influenced by same team- and different
team-exposure, none of significant relationships were shown in athletic identity. Same
team-exposure negatively affected the change of academic identity from Time 1 to Time
2 after accounting for team size (-.059), winter season (-.041), revenue (-.047), task
cohesion (-.38), In Table 2.16a-h, different team exposure positively affected the
change of academic identity from Time 1 to Time 2 after accounting for each team-level
predictors. The magnitude of the coefficient was from .031 to .038. Other fixed effects
were not significant for academic identity. These results meant that interactions with
same team members and friends in a different team were negative and positive sources
of academic identity respectively.
Only when task cohesion was accounted for as a team-level predictor for
physical ability (Table, 2.18g), same team-exposure at the individual level (-.85), and
task cohesion at the team level (-.30) negatively affected the perception of physical
ability while their cross-level interaction (.12) positively moderated the negative effect.
This result meant that as interaction with team members in a team, which was more
oriented to task, negatively influenced the perception of physical ability. None of the
effects were significant for physical appearance (Table 2.19a-h).
In summary, there were significant fixed effects at both levels for the outcome
variables, except for athletic identity and physical appearance. The same team38

exposure had a negative effect on academic achievement and identity, and the
perception of physical ability, while the different team-exposure positively influenced
college aspiration and expectation, and academic identity. Among the team-level
factors, team size was a negative factor for academic achievement; participating in a
revenue generating sport of winter season was a negative factor for academic efficacy;
task cohesion was a negative factor for physical ability. With respect to the moderating
effect of team-level factors (i.e., cross level interaction), task cohesion of teams
positively moderated the effect of same team-exposure on academic achievement. For
academic efficacy, the cross level interaction between participating in winter season
sports and same team-exposure was a positive factor. The negative effect of same
team-exposure on physical ability was moderated by the cross-level interaction with
task cohesion.

39

Discussion
Study I examined the effect of interaction with peers in groups of student athletes
on educational outcomes using the influence model of social network analysis. The
variables were collected longitudinally to provide greater rigor of the test of the effect of
social interaction by controlling their initial status (Frank, 1998). The findings suggest
that student athletes form peer relationships as part of participating in a sport in high
school, which is influential on positively shaping educational outcomes.
Student athletes in high school formed social ties, not only with same team
members, but also with other team members, regardless team membership. Overall
they formed more social ties with other team members, except for the sideline
cheerleading team (see Table 2.4 & 2.5. for same team-degree and different teamdegree). This degree indicates the average number of friends in a same and different
team. Due to more opportunities and time to make friendships among a larger pool of
students in other structures of school, such as class, school bus, cafeteria etc., it makes
sense that athletes make more friends with students who play different sports from their
own. However, when considering they have less time and opportunities to form
friendships within their own sport, the result for the sideline cheerleading team is
interesting. They made more social ties within the team, which means that cheerleading
creates a more socially bonded team. This result has concurrence with a study that
used a mixed gender-dance program for one year in 23 classrooms of primary and
secondary schools in Berlin, Germany (Zander, Kreutzmann, Mettke, & Hannover, in
revision). Zander et al. found that the social ties for collaboration and sympathy
increased over time after the dancing program. Because dance represents the
40

performance part of cheerleading (Grindstaff & West, 2006), it is probable to infer the
activities promote more socially bonded team culture by creating a clique within a team.
This result is also consistent with the findings of Cohen (1977), and Urberg,
Degirmencioglu, Tolson, and Halliday-Scher (1995) for peer network of adolescents,
which reported that a larger percentage of female students’ friendship list had a same
social affiliation. This convergence may suggest that female students, who are involved
in performing aesthetic physical activity, not like playing basketball on a female team,
create a clique within a team. Also, the nature of the cheerleading team (i.e., cheer
leading team mostly does not have the inter-team competitions) may play a role on this
differences.
The focal hypothesis was on the effect of social interaction with peers in
changing educational outcomes embedded in social capital theory. That is, peers in a
social context of athletic participation were hypothesized as a form of social capital in
school for their educational experience. I found that academic achievement, efficacy,
and college aspiration were increased by the interaction with peers in athletic teams,
which is a function of frequency of interaction and peers’ attribute. For instance, as one
interacts more frequently with peers who have a higher aspiration for going to college,
one’s own college aspiration is expected to increase when other factors are held
constant.
With respect to the improvement of academic achievement through the function
of peer interaction without considering the team-level factors (see Table 2.10), the
finding reinforces the streamline of research on peer social capital and educational
achievement (e.g., Angrist & Lang, 2004; Burke & Sass, 2008; Carrell, Fullerton, &
41

West, 2009; Lavy, Silva, & Weinhardt, 2009), which highlights the important role of
peers in school. Unfortunately, the effect of peer interaction in a same team was not
significant, but the specific interaction regarding academics with peers in different teams
was a positive factor in improvement of academic achievement, which indicates that
rather than being on a same team, athletes socialize more with peers on different teams
regarding academic achievement. Despite the caution placed on interpretation (i.e., selfreported G.P.A.), this may show a mediating mechanism in the relationship between
athletic participation and academic achievement, which has been investigated mostly
for the direct positive relationship by correlation and regression (e.g., Marsh & Kleitman,
2003; Miller, Melnick, Barnes, Farrell, & Sabo, 2005; Rees & Sabia, 2010). However, in
relation to the team-level factors, team size negatively influenced academic
achievement, and participating in a revenue generating- and (or) winter season-sport

2

was a negative factor for academic efficacy.
With respect to increases of academic efficacy, the effect of overall interaction
with peers in a different team was significantly positive (see Table 2.9). Similar to
academic achievement (see Table 2.10), peers in different teams were more influential
in shaping efficacious beliefs for schoolwork. Although no significant effect from peers in
a same team was found, this result may extend the theory of modeling in self-efficacy
by using social network analysis. Bandura (1986) theorized that observation of a model
can strengthen or weaken the likelihood that the observer will adopt the model’s belief in
the future. The theory of modeling has been tested mostly by experiments as controlling
and intervening a setting, in which an experimental group has a protocol for subjects to
2

Winter sport may be interpreted as sport in season because the data collected during
the winter season.
42

observe manipulated models with higher or lower levels of self-efficacy (e.g., Schunk,
Hanson, & Cox, 1987; Schunk & Zimmerman, 1996). However, the generalization of the
results from those experiments may have limitations for a random setting in school.
Students not only observe, but also actually interact with peers in school. That is, the
process of modeling a peer (i.e., observing), which is a source of development of selfefficacy, is a part of social interaction with a peer. Thus, it is probable to suggest social
interaction, including modeling, is a source of students’ sense of self-efficacy in
academics. When interacting with a peer, the peer’s attribute can be observed and
simultaneously transmitted to an adolescent through interaction. The influence model of
a social network analysis provides a quantitative insight for the transmission by social
interaction, including modeling.
The limitations of this study guide future considerations. Firstly, this study did not
include the general body of students that might be in the network. The network measure
was limited to those who were enrolled in an athletic program. Thus the distinction could
not be made between peers in athletic teams and those not in any athletic team. It is
worthwhile to see the difference in the effect of peers from the two different groups due
to the popularity of athletic participation in high school. The National Federation of State
High School Association (NFHA) reported that more than 55.5 % of all high school
students played sports during the 2010-2011 school year (Koebler, 2011).
Secondly, this study did not account for reciprocal relationship because the
analysis used an ego-centric matrix, which cannot distinguish between reciprocal and
one-directional relationship. The impact of reciprocal relationships may be stronger than
one direction. In calculating ‘exposure’, adding an additional weight, such as quality of
43

relationship, by asking how much the interaction with a referred friend is valuable
(adaptable), or ranking the degree of closeness among referred friends, may be a good
idea to more validly evaluate the impact of interaction.
Thirdly, it is common to see students playing more than one sport in high school.
Unfortunately, this study did not statistically model students who were involved in
multiple athletic teams. Only major one team that they referred was considered as their
team-involvement; however there were 40% of samples, who reported they were
involved with two or three athletic teams regardless season. Hypothetically, the social
relationship is expected to be stronger if peers play two or more sports together, which
leads a challenging question on how to statistically model the complex sociometrics.
Lastly, it is arguable that more competitive teams foster negative effects on
academics. A valid quantification on competitiveness of teams as a team characteristic
is needed to test the arguable statement
In light of the paucity of current studies on the influence of peers in athletic teams
on educational achievement factors, this study fills an important gap for the relationship
between athletic participation and educational experience in a school setting. This study
provides another viewpoint on athletic programs in school, which can be a social
context wherein students make social ties. The ties act as resources that student
athletes may access and benefit education in different places, such as the classroom,
as well as in gyms or fields, which is supported by Coleman (1988)’s argument that
social capital developed in one environment can be applicable in another where both
agents (i.e., peer network) exist.

44

Therefore, these results provide evidence that athletic participation promotes
academic success through peer relationship in athletic teams. The effect is not huge
given a short period time of this study, but it would be accumulative if they interacted for
a long period time, when holding other variables are fixed, because the amount of
interaction is a weight of exposure in the influence model. But in real settings, the effect
may be saturated over time. So, the influence model requires a longitudinal design with
multiple data collection points to see whether (or when) the effect is accumulative or
saturated.
Moreover, the study provides indirect insight that athletic participation is not a
negative determinant at least as a form of peer social capital, which is in conflict with a
notion that athletic participation is a time-consuming activity that detracts from time
spent on education (Eide & Ronan, 2001).

45

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46

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Chapter III: PEER SELECTION IN ATHLETIC TEAMS (STUDY II)
Introduction
Research on peer relationships in adolescence has two phases: (a) peer
influence (e.g., depicted in Study I) and (b) peer selection (i.e., how students construct
their peer group) (Frank, 1998; Ryan, 2000, 2001). In peer selection, students choose
peers to interact with in school based on their similar attributes (Frank & Fahrbach,
1999; Robins, Elliott, & Pattison, 2001; Ryan, 2001). This process is embodied in a
social network analysis that governs why students choose to affiliate with particular
peers, and how these interaction patterns influence their experience in school.
However, no prior research has examined how student athletes construct their peer
group by an analytical frame of social network analysis (i.e., selection model of social
network analysis). Thus, it is worthwhile to investigate the process of peer selection in
athletic teams for their academic success because student athletes spend more time
with peers, who have the same interest in playing a sport, beyond a required school
curriculum, and develop their own tight bonds and sub-cultures (Broh, 2002; McNeal,
1995; Philips & Schafer, 1971; Schneider & Stevenson, 1999). In this regard, in Study II,
I investigated the function (or process) that governs why students select particular peers
within a group of student athletes, as emphasizing the similarity of peers’ attributes.
Research has documented that peer groups of adolescence exhibit similarity on
personal attributes, and that adolescents are significantly similar to their friends with
regard to behaviors, attributes, and personality (Gillford-Smith & Brownell, 2003). This
tendency to affiliate with similar peers is called homophily, which refers to the tendency
for people to have ties with people who are similar to themselves in socially significant
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ways. It is considered as the principle of the formation of personal relationships (Frank,
Muller, & Muller, 2013).
Homophily of peer group in adolescence has been found in demographical
attributes, such as gender and race, which affect the selective formation of social
relationships (Lomi, Snijders, Steglich, & Torlo, 2011; Mollica, Gray, & Trevino, 2003;
Moolenaar, 2010). Women tend to have more homophilious relationships than men
(Frydenberg & Lewis, 1993; Mehra, Kilduff, & Brass, 1998), and both men and women
were found to select men as their network to achieve their goals and acquire information
(Aldrich, Reese, & Dubini, 1989). Also, African-Americans were more likely than whites
to seek out racial homophily (Ibarra, 1993; Mollica et al., 2003). However, adolescents
do not form their peer network only by these predetermined background characteristics
(Frank et al., 2013).
Not only limited to background characteristics, homophilious relationships also
have been found in various behavioral characteristics and personal attributes of
adolescents. For example, homophily of peer group has been reported in smoking,
drinking, and drug use (Cohenn, 1977; Ennett & Bauman, 1994; Urberg, Luo, Pilgrim, &
Degirmncioglu, 2003; Urberg, Tolson, & Degirmencioglu, 1998). And, homophily in
relation to academics in school has been found in academic achievement (Epstein,
1983), college aspirations (Epstein, 1983; Hallinan & Williams, 1990), time investment
for homework (Cohen, 1977), and engagement in school (Kindermann, 1993). However,
these studies addressed above were conducted by correlation analysis with crosssectional data. Using a correlational approach, it is unclear to whether similarity is a
result of peer selection or peer influence (Lomi et al., 2011; Ryan, 2000, 2001). That is,
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homophily involves a two-part process of peer relationship (i.e., peer selection and peer
influence). Students in school could select peers because of similarity, which also could
be the result of peer socialization. This ambiguity calls for a longitudinal design to
predict changes in outcome variables, as controlling for the initial status, and selection
process, which is considered fixed over the time interval (Frank, 1998; Ryan, 2000,
2001). For instance, using a longitudinal design, Lomi et al. (2011) found that students
who have attained similar levels of academic performance are more likely to form social
ties with each other, and also low performing students have a much higher tendency to
choose other low-performing students as friends.
More specifically for these homophily, Frank et al. (2013) employed the selection
model of social network analysis, and used the data from Adolescent Health and
Academic Achievement (AHAA) and the National Longitudinal Study of Adolescent
Health (Add Health) in order to study how adolescents form their peer group and which
factors are associated with those friendship formations. For formation of new friends in
high school, Frank et al. estimated the effect of the following independent variables:
homophily (race, gender, parental education, age, GPA), structural constraints (grade
level), micro friendship structures (mutual friends), shared activities (sports, academic,
arts), course overlap (extent of course overlap), and local positions (membership in
same local position). Frank et al. defined the clusters of students who took sets of
courses together as local positions, which memberships are identified by an algorithm
developed by Field, Frank, Schiller, Riegle-Crumb, and Muller (2006) for identifying nonoverlapping clusters from affiliate networks. As the result, Frank et al. found local
positions was the strongest predictors in the model, along with other significant
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predictors, such race, GPA, grade level, and number of mutual friends. Interestingly, the
coefficient for common sports played was nearly zero, but they noted that for common
extracurricular activities, such as, sport, academic, and arts, prior friendship (e.g., Wave
I) was controlled to test the effect on changes from Time I and Time 2 in friendship,
which might reduce coefficients (Frank et al, 2013).
Also, the research literature on peer acceptance provides insight regarding
factors (similarity/ homophily) that predict the process of peer selection. Peer
acceptance and selection have a common origin of peer network and conceptual
overlap (Gifford-Smith & Brownell, 2003; Master & Furman, 1981). The complement to
peer selection is peer acceptance. To be part of a peer group requires selecting peers
and being accepted by peers. Peer acceptance (or sociometric popularity) refers to the
general degree of liking by the peer group, which is usually measured by sociometric
procedures. Students are given a list of the limited (or unlimited) number of randomly
selected names of classmates, and for each name, they are asked to respond to the
question, for instance “how much would you like (or dislike) to be in school activities
with this person?” This assessment is used to create a continuum of social preference
score ranging from well-accepted to rejected, or categories of sociometric status, such
as popular, rejected, neglected, controversial, and average status (e.g., Bukowski,
Pizzamiglio, Newcomb, & Hoza, 1996; de Bruyn & Cillessen, 2006; Lubbers, Van Der
Werf, Kuyper, & Offringa, 2006; Wentzel, 1991; Wentzel & Erdley, 1993).
With this measurement, correlational studies have showed consistent results that
popular students are more cooperative, helpful, and sociable, and demonstrate better
leadership skills (Wentzel, 2005). Peer acceptance is also related to academic
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achievement; the popular status is positively related to successful academic
achievement (i.e., standardized test score) and low level of acceptance to academic
difficulty (Buhs & Ladd, 2001; Wentzel, 2005; Wentzel & Caldwell, 1997). Similarly,
literature in sport supports the association of athletic ability and competency (which can
be observable by peers in athletic teams) with popularity during adolescent years (e.g.,
Adler, Kless, & Adler, 1992; Buchanan, Blankenbaker, & Cotten, 1976; Vannatta,
Gartstein, Zeller, & Noll, 2009; Weiss & Duncan, 1992). However, this sociometric
methodology does not account for data dependency because the nominated individuals
have an aggregated rating score (i.e., this is used as a popularity variable correlated
with their personal attribute), which eliminates the dependent information on the
nominated individuals (Wellman & Frank, 2000). That is, such an aggregated score
cannot identify (or model) a specific score of a specific rater.
The nature of network data is not independent. The social ties can be formed
either from i to i’ or from i’ to i. Such dependencies are accounted for in P1 models of
selection (Fienberg, Meyer, & Wasserman, 1985). However, this model specifies only
the set of relationships among the dyad (i.e., direct relationship only between two) as
the unit of analysis. It does not account for dependencies among pairs outside the dyad,
for example, there may be multiple nominees (i’1 – k), but they may not indicate i as their
network. A new estimation approach for theses conditioned models has been developed
based on maximization of the pseudo-likelihood (Frank & Strauss, 1986; Strauss &
Ikeda, 1990), which shows that estimates from a logit model can be used to obtain
estimates while conditioning the relation between each pair of people on the relation
between every other pair of people in the network (see Frank, 1998 for review). This
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approach enables us to model “whether two people are friends as a function of the
number of friends they have in common, the number of friends of friends they have in
common, and so forth.” (Frank, 1998, p. 195). Frank (1998) suggested this statistical
model and procedure be used to establish whether given factors are linked to how
individuals construct their social contexts (i.e., referring friends), and to differentiate
among factors (i.e., multiple homophily) that affect how students construct their peer
network by using a logistic regression.
In addition, the integration of multilevel models and the selection model of social
network analysis has been suggested to characterize individual- and group- level
characteristics, as well as the interaction of them (Frank, 1998). It seems reasonable to
apply the multilevel framework into the selection model because nominators are nested
in nominators. This integrated model enables us to account for the variance of
nominators’ characteristics onto the effect of homophily in constructing peer networks.
Friendship forms within social constraints created by structural institutes (i.e.,
school, classroom, athletic team, etc.), in which adolescents have opportunities to
choose their social interaction (Frank et al., 2013; Zeng & Xie, 2008). Research on peer
selection has been conducted almost exclusively in school; however no prior study has
focused on groups of student athletes, in which they may select peers to engage in
relationship for their academic success given the similarity of peers in athletic groups in
school. By reviewing literatures on homophily and peer acceptance among students in
high school, it was hypothesized that characteristics of high school student athletes
affect forming friendship in their teams. Therefore, the purpose of Study II was to
examine the homophily effect of the academic and athletic characteristics of student
61

athletes (i.e., academic achievement, academic efficacy, college aspiration/
expectation, academic/athletic identity, perception of physical appearance/ ability, and
attitude toward their team), their demographics (i.e., gender, race, and grade level), and
effect of shared other activities and course overlap to select peers to interact with in
groups of student athletes in school for their academic success. Further, the network
data are ego-centric in which an ego (nominator) is a focus of analysis to be accounted
for in terms of how an ego chooses alters (nominees). The data do not include a dyadic
network. Thus, ties are independently nested in an ego. By specifying the conditional
variance at two levels (i.e., tie and ego) using a random intercept multilevel model, the
effects of the predictors in peer selection were evaluated by odd ratio of logistic
regression.

62

Method
Participants and Procedures
Data were collected from a local high school in which approximately 500 students
are enrolled, and 350 students play at least one sport for the school. The school has a
total of 22 athletic teams regardless season. After getting approvals from the athletic
director of the school and the University Committee on Research Involving Human
Subjects (UCRIHS), the meeting with all student athletes was made in an auditorium for
data collection. The data were collected longitudinally to examine the social interaction
during a certain period and control the initial status on the outcome variables. The first
data set was collected in the beginning of 12-13 Winter season (i.e., the first week of
November), and the second data set was collected in the end of 12-13 Winter season
(i.e., the fourth week of February). Participants were told that they would receive $5 by
completing the two surveys. Two-hundred and ninety-one and 242 student athletes
completed the first and second survey respectively. Table 2.1 shows participants’
distribution on each team. This distribution is based only on the primary sports team
reported by them regardless of season (i.e., one belongs to one sport team). There
were students who reported multiple sports in the two surveys (137 and 91
respectively).
Two-hundred and thirteen student athletes completed the both surveys, 79 and
29 completed only the first survey and second survey respectively. Three-hundred and
twenty-one student athletes participated in at least one survey, among which 82.5% are
White. The distributions of gender and school years are in Table 2.2.

63

Dependent Variable
Our dependent variable was dichotomous from the network data at Time 2,
taking a value of 1 if nominator (i) indicates nominee (i’) as a friend in the group of
athletes, 0 otherwise in ego-central network for all pairs between nominators and
nominees. Only ego-centric data were treated because reciprocity is difficult to interpret
(Frank et al., 2013). The all-possible pairs are 47,525, in which 745 were tied (i.e.,
coded as 1) at Time 2.

Independent Variables
Demographic Information: Gender, race, team, and grade level, were collected.
These are the predetermined factors of peer relationship (Frank et al., 2013). These
variables are dichotomous, taking a value of 1 if pairs were same in this demographic
information, 0 otherwise. Among pairs, about 38 %, 10%, and 53% were same gender,
team, and race, respectively.
Prior Network at Time 1. This dummy variable (1= tied and 0= not tied at Time 1)
was used for the first selection model as a predictor, while for the second selection
model, I conditioned our samples by selecting only those who did not have a friendship
at Time 1, using this variable, which enables to model how predictors affect forming new
friendships over the time frame (Frank et al., 2013). The number of ties at Time 1 was
1,025. About 2% of all pairs in Time 2 were identifies as the prior friendship.
Courses and Other Extracurricular Activities. Friendship can be formed in various
school activities, such as same course taking, art club, and academic clubs (Frank et
al., 2013), which need to be set as predictors of friendship. Participants were asked to
64

list courses that they were taking, and choose extracurricular activities in the list of
extracurricular activities obtained from the National Longitudinal Study of Adolescent
Health (Add Health): French Club, German Club, Latin Club, Spanish Club, Book Club,
Computer Club, Debate team, Newspaper, Honor Society, Student Council, Yearbook,
Drama club, band, Chorus or Choir, Orchestra. Beside athletic team enrollment, the
numbers of shared extracurricular activities and overlapped courses were set as
predictors. The means of the number of shared extra activities and overlapped courses
were 14. 80 (SD=1.12) and 3.78 (SD=2.69).
Similarity in Attributes. The absolute value of the difference in attributes Time 1
between all pairs was used to represent similarity of between pairs for their attributes.
The attributes included grade level, academic achievement/ efficacy, college aspiration/
expectation, academic/ athletic identity, perception of coach’s regard for academics,
physical appearance/ ability, and task/ social cohesion. The descriptions on the
measures for the abovementioned variables are in Chapter 2. The descriptive statistics
of the similarity are in Table 3.1. The larger value indicates less similar attributes
between pairs.

Data Analysis and Statistical Model
Basic (Single level) Selection Models. The selection model of a social network
analysis was employed to examine how to construct the peer network of student
athletes in high school. It is based on logistic regression in which the dependent

𝑤 𝑖𝑖 ′ 𝑡1→𝑡2 represents the presence of a social tie

variable is dichotomous (tie: 1 or 0). Also, the dependent variables described above
were entered in the following model.

65

at Time 2 between nominator (i) and nominee (i’), and

𝜋0−19 indicate the effects of the

grade level ( 𝜋5 ), the more we would infer that similar grade level affects forming peer

independent variables to forming the ties. For instance, the larger coefficient of similar
networks. In addition, the prior network ( 𝜋1 ) was removed to model the tendency of

forming new networks in the second (single level) model, as removing Time 1 networks

𝑝�𝑤 𝑖𝑖 ′ 𝑡1→𝑡2 = 1�
log �
� = 𝜋0 + 𝜋1 prior networks 𝑖𝑖 ′ 𝑡1
1 − 𝑝[ 𝑤 𝑖𝑖 ′ 𝑡1→𝑡2 = 1]

in Time 2 network.

+𝜋2 same gender 𝑖𝑖 ′ 𝑡1 + 𝜋3 same team 𝑖𝑖 ′ 𝑡1 + 𝜋4 same race 𝑖𝑖 ′ 𝑡1

+𝜋5 − �grade 𝑖𝑡1 − grade 𝑖 ′ 𝑡1 �

+𝜋6 − �academic acheivement 𝑖𝑡1 − academic acheivement 𝑖 ′ 𝑡1 �
+𝜋7 − �aspiration 𝑖𝑡1 − aspiration 𝑖 ′ 𝑡1 �

+𝜋8 − �expectation 𝑖𝑡1 − expectation 𝑖 ′ 𝑡1 �

+𝜋9 − �coach regard 𝑖𝑡1 − coach regard 𝑖 ′ 𝑡1 �

+𝜋10 − �others ′ edu. expe. 𝑖𝑡1 − others ′ edu. expe. 𝑖 ′ 𝑡1 �

+𝜋11 − �academic efficacy 𝑖𝑡1 − academic efficacy 𝑖 ′ 𝑡1 �
+𝜋12 − �athletic identity 𝑖𝑡1 − athletic identity 𝑖 ′ 𝑡1 �

+𝜋13 − �academic idenity 𝑖𝑡1 − academic identity 𝑖 ′ 𝑡1 �

+𝜋14 − �physical appearance 𝑖𝑡1 − physical appearance 𝑖 ′ 𝑡1 �

+𝜋15 − �physical ability 𝑖𝑡1 − physical ability 𝑖 ′ 𝑡1 �
+𝜋16 − �task cohesion 𝑖𝑡1 − task cohesion 𝑖 ′ 𝑡1 �
66

+𝜋17 − �social cohesion 𝑖𝑡1 − social cohesion 𝑖 ′ 𝑡1 �

+𝜋18 number of shared activity 𝑖𝑖 ′ 𝑡1→𝑡2

+𝜋18 number of course overlap 𝑖𝑖 ′ 𝑡1→𝑡2

Multilevel Selection Model. To account for nominators’ characteristic, which
cannot be modeled with the single-level model, a multilevel modeling (i.e., ties are
nested in nominators) was applied into the selection model described above. Model 1
(Null Model) was specified as follows without any predictors and Model 2 was specified
with Level-1 predictors with random intercept. Finally, the characteristics of nominators
were added in Model 2 for Model 3 as follows:

log �

𝑝�𝑤 𝑖𝑖 ′ 𝑡1→𝑡2 = 1�
� = 𝜋0𝑖 + 𝜋1𝑖 prior networks 𝑖𝑖 ′ 𝑡1
1 − 𝑝[ 𝑤 𝑖𝑖 ′ 𝑡1→𝑡2 = 1]

At tie level:

+𝜋2𝑖 same gender 𝑖𝑖 ′ 𝑡1 + 𝜋3𝑖 same team 𝑖𝑖 ′ 𝑡1 + 𝜋4𝑖 same race 𝑖𝑖 ′ 𝑡1
+𝜋5𝑖 − �grade 𝑖𝑡1 − grade 𝑖 ′ 𝑡1 �

+𝜋6𝑖

− �academic acheivement 𝑖𝑡1 − academic acheivement 𝑖 ′ 𝑡1 �
+𝜋7𝑖 − �aspiration 𝑖𝑡1 − aspiration 𝑖 ′ 𝑡1 �

+𝜋8𝑖 − �expectation 𝑖𝑡1 − expectation 𝑖 ′ 𝑡1 �

+𝜋9𝑖 − �coach regard 𝑖𝑡1 − coach regard 𝑖 ′ 𝑡1 �

+𝜋10𝑖 − �others′ edu. expe. 𝑖𝑡1 − others′ edu. expe. 𝑖 ′ 𝑡1 �

+𝜋11𝑖 − �academic efficacy 𝑖𝑡1 − academic efficacy 𝑖 ′ 𝑡1 �
67

+𝜋12𝑖 − �athletic identity 𝑖𝑡1 − athletic identity 𝑖 ′ 𝑡1 �

+𝜋13𝑖 − �academic idenity 𝑖𝑡1 − academic identity 𝑖 ′ 𝑡1 �

+𝜋14𝑖 − �physical appearance 𝑖𝑡1 − physical appearance 𝑖 ′ 𝑡1 �

+𝜋15𝑖 − �physical ability 𝑖𝑡1 − physical ability 𝑖 ′ 𝑡1 �

+𝜋16𝑖 − �task cohesion 𝑖𝑡1 − task cohesion 𝑖 ′ 𝑡1 �

+𝜋17𝑖 − �social cohesion 𝑖𝑡1 − social cohesion 𝑖 ′ 𝑡1 �

+𝜋18𝑖 number of shared activity 𝑖𝑖 ′ 𝑡1→𝑡2

+𝜋19𝑖 number of course overlap 𝑖𝑖 ′ 𝑡1→𝑡2

𝜋0𝑖 = 𝛽00 + 𝛽2 gender 𝑖 + 𝛽5 grade 𝑖 𝛽6 academic achievement 𝑖
At ego level:

+ 𝛽7 aspiration 𝑖 + 𝛽8 expectation 𝑖 + 𝛽9 coach regard 𝑖

+ 𝛽10 others educational expectation 𝑖 + 𝛽11 academic efficacy 𝑖

+ 𝛽12 athletic identity 𝑖 + 𝛽13 academic identity 𝑖

+ 𝛽14 physical appearance 𝑖 + 𝛽15 physical ability 𝑖
+ 𝛽16 task cohesion 𝑖

At the tie level,

𝑤 𝑖𝑖 ′ 𝑡1→𝑡2

represents whether i and i’ talked over the time

interval, from Time 1 (t1) to Time 2 (t2), which can be transformed the logit model. The

𝜋0𝑖 represents an intercept and 𝜋1𝑖

dependent variable (i.e., the log odds) expresses for the probability to select peers to

𝜋2𝑖−17𝑖 represent the homophily effects of variables of interest, where

interact with.
Time 1.

68

is the effect of the prior network at

students choose peers in relations with similar attributes, which include, as variables of
interests in the model, gender, team, race, grade level, academic achievement (GPA),
college aspiration and expectation, perception on coach’s regard for academics, others’
educational expectation, academic efficacy, athletic and student identities, physical
appearance and ability, and task- and social-cohesion. For example, academic

𝜋18𝑖 and 𝜋19𝑖

acheivementit1 represents the academic achievement of i at Time 1 and academic
acheivementi’t1 is the academic achievement of i’ at Time 1. Also,

represent the effects of the number of shared activities and course overlap between i

𝛽00 is the average intercept across egos, and 𝜇0𝑖 is the unique

and i’ over the period time.

increment or decrement to the intercept (random intercept). 𝛽2 , and 𝛽5 through 𝛽17
At ego level (i),

are the fixed effect of nominators’ characteristics.

69

Results
Basic Selection Models
The two basic selection models were used to test how students’ demographics
and attributes affect forming friendships. It is based on a logistic regression with a
dichotomous dependent variable (i.e., 1=tied and 0=not tied) along with independent
variables (e.g., same demographics and similar attributes) at Time1.
The result of the first selection model is presented in Table 3. 2. The significant
predictors (i.e., more than twice standard error) for forming peer networks among
student athletes in a high school were the prior friendship, same gender, same team,
similarity in grade level, academic achievement, college aspiration, perception of
coach’s regard on academics, athletic identity, perception of physical appearance, and
number of shared extra activities.
The X-standardized coefficients show the relative importance of Xs. Similarity in
grade level was the strongest factor of friendship formation. The coefficient of 3.97
indicates that as a 1 standard deviation increases in similarity of grade level at Time 1,
3.97 increase in the log odds of getting tied at Time 2. The next stronger predictors
were same gender (1.55), and prior network (1.48). Similarity in academic achievement
(1.25), same team (1.22), and similarity in perception of coach’s regard for academics
(1.20) were also stronger predictors. Relatively speaking, similarity in athletic identity
(.86), college aspiration (.81), and number of shared extra activities (.79) showed
smaller effects on forming friendships. Interestingly, race and number of courses
overlapped were not significant factors to be tied among student athletes.

70

To model forming new friendship over the fixed time frame between Time 1 and
Time 2, the prior 492 ties at Time 1 were removed in the data. Only 492 were tied and
coded as 1 in the dependent variable.
The result was similar to the first model. Similarity in grade level is the most
influential to form new friendships. The coefficient of 5.48 indicates that as a 1 standard
deviation increases in similarity of grade level, 5.48 increase in the log odds of getting
new ties during the time frame. Same gender (1.63), same team (1.25), similar in
academic achievement (1.33), college aspiration (.82), athletic identity (.82), and the
number of shared extra activities (.79) were significant predictors to form new
friendships.
Compared to the first selection model, same race changed to a significant factor,
while similarity in physical appearance became a non-significant factor, which indicates
that same race (e.g., cultural background and similar origins) is more influential in
making a new friend during the short period (i.e., 4 months) than their perception of
physical appearance. Having a similar level of perception of their own physical
appearance is affective for continuing their relationship rather than making a new friend
in athletic groups in a high school.
In summary, student athletes in a high school form and keep their friendships by
structural components of high school (grade level, athletic team, and extra activities),
demographics (gender and race), and other attributes (academic achievement, athletic
identity, and college aspiration).

71

Multilevel Selection Model
The results of Model 1, 2, and 3 are shown in Table 3.4. ICCs (intraclass
correlation) of the Models are .05, .11, and .04, respectively. 5% of the total variance in
the propensity to become a tie (y) is attributable to unobservable nominator’s
characteristics (Model 1). The added predictors at tie-level led to increases in Level-2
variance, resulting in 11% of the between-variance to the total variance. The Level-2
variance in Model 3 decreased with Level-2 predictors (i.e., nominators’ characteristics),
which has 4% of the between-variance in the total variance. The log likelihood for Model
1, 2, and 3 are -3276.8581, -1045.3852, and -1027.90, respectively. Model 2 and Model
3 showed a huge difference, however, a likelihood ratio (LR) test was performed for the
model comparison between Model 2 and Model 3 as follows: LR = 2(-1027.90 - 1045.38) = 36.96 on 14 of d.f., p<.05. The LR test indicates Model 3 is more
parsimonious to interpret the parameters of the fixed effects of Level 1 and 2, which
enables us to make a claim that the effect of similarity is not associated with the
characteristics of nominators. That is, it is possible to interpret the effect of homophily
regardless the characteristics of nominator. A single-level selection model uses a score
of similarity between a nominator and a nominee for a characteristic, but cannot model
a characteristic of nominators (e.g., a nominator is higher and the other nominator is
lower).
The result of Model 3 (Table 3.4) can be compared to the single-level selection
model (Table 3.2) in order to see the changes after accounting for nominators’
characteristics. First, gender (1=male and 2=female) and grade level were significant
factors at Level-2, which means that students upper-level grades and females tend to
72

make more ties. Among Level-1 predictors, prior network, and same demographics (i.e.,
gender, and team) were consistently positive predictors. However, the direction of the
effect from similarity in grade level, academic achievement, aspiration, and coach’s
regard were changed from negative to positive for aspiration, and from positive to
negative for the others. Also, their change of the direction occurred in Model 2. In
addition, the effects of race, college expectation, academic efficacy, athletic identity,
physical appearance, and shared activities changed to non-significant effects in Model
3.
As the result of Model 3, in holding constant of nominator’s characteristics, the
effect of prior network (4.05) and same gender (.87) and team (.44) in demographics
were positively significant to become a tie, which indicates that the chances to become
social ties are greater if athletes are same gender, and play the same sport. Among the
other characteristics, the similarity in grade level (-1.47), academic achievement (-.70),
coach’s regard (-.22) was negative, which indicates that as the chances are greater for
social ties as the similarities are smaller. However, the chances for social ties are
greater if the similarity in aspiration is larger.
In summary, while accounting for nominators’ characteristics, student athletes in
high school tend to choose friends to interact with when they are same gender, and
have similar orientation for going a college. They also form friends who are different (not
similar) in grade level, academic achievement, and perception toward their coach.

73

Discussion
Based on the selection model of social network analysis, the aim of Study II was
to explore factors for student athletes to select peers on the basis of homophily, which
assumed that similarity between peers plays a role in forming a peer network in given a
time period. The sociometric data (i.e., referring a friend) were measured both at Time 1
and Time 2 over the winter season, which was a dependent variable in the selection
model (i.e., logistic regression). The findings were based on selecting new friends
(forming new networks) given the time period since the peer networks at Time1 was
controlled and removed.
Homophily theories suggested that “similarities between adolescents and their
friends are due to youths’ initial tendencies to affiliate with friends who already possess
similar behavioral proclivities and like-minded attitudes (i.e., selection effects).”
(Brechwald & Prinstein, 2011, p. 166). This study provided clear evidence of homophily
effect in selecting peers among student athletes, for example, gender, team
involvement, college aspiration, and number of shared other activities were positive
predictors (see Model 3 in Table 3.4), which means student athletes seek similar friends
in terms of gender, team membership, college aspiration, and seeking same other
activities. Among them, gender showed the strongest homophilious effect, while
aspiration, other activity, and same team involvement relatively showed in order of the
effect. This result is consistent with the previous research that has documented that
adolescents are similar to their peers in behaviors, attributes, and demographic
background.
However, unexpectedly, the present findings showed that student athletes also
74

seek friends who are not similar in grade level and academic achievement. This result
contrasts with a general agreement on tendency to choose similar peers to interact with
(Kiesner, Kerr, & Stattin, 2004), and the recent empirical studies using the analytical
frame of a social network analysis. Frank et al., (2013) used a national longitudinal data,
and showed similarities in grade level and academic performance were strong
predictors of friendship formation. Also, Lomi et al. (2011) found that students who have
attained similar levels of academic performance are more likely to form social ties with
each other, especially for lower performing students. Perhaps because athletic teams
consist of athletes from multiple grade levels and are not formed along academic
performance lines, athletes are more comfortable in seeking friends outside their own
grade level and academic performance category.
Moreover, the present study also did not provide evidence for importance of
same race in selecting new peers; rather, processes of social selection among student
athletes operate across race. Racial homophily has consistently been found as a
significant contributor to the development of social networks (McPherson, Smith-Lovin,
& Cook, 2001; Shurm, Cheek, & Hunter, 1988). Frank et al. (2013) also found racial
homophily as a strong factor in peer selection in school with empirical data. That is,
adolescents are more likely to form friends with peers who have the same ethnicity
background, however, I found student athletes also develop peer relationships across
race, which shows a positive benefit of athletic participation with respect to cross-racial
friendships. Kawabata and Crick (2008) showed cross-racial friendships were
associated with positive development in a school setting, such as social adjustment
(i.e., relational inclusion and leadership). Also they found that European American
75

students displayed a higher frequency of cross-racial/ethnic friendships than African
American children, and Latino children exhibited a lower frequency of these friendships.
Abound, Levy, and Oskamp (2000) contented that cross-racial friendships may be
optimal dyads for cooperation, emotional security, and intimate exchange in school. In
this sense, it may be possible to regard athletic participation as a school activity, beyond
a classroom setting, that increases chances to make cross-racial friendships.
The discrepancy between this study and the major features of research on
homophily effect on developing peer relationships is probably the result of the
characteristic of my samples. This study sampled only student athletes, who were
limited to select peers only among student athletes in the survey. These results may
limit generalizing to the whole body of students, but they may show different
characteristics of a specific group (i.e., student athletes) in terms of developing peer
relationships within a system of athletic programs. This unique finding about ‘wider
range’ of peer relationship of student athletes, not limited to seeking homophilious
relationship, provides insight for the development of peer relationship and athletic
participation during adolescence. One possible theoretical explanation is that athletic
programs offered by schools constitute a social context (Smith, 2003), and establish a
structural constraint (i.e., being in a same place, such as gyms), in which student
athletes explore new friends with similar interest and preference (Frank et al., 2013). In
this regard, Smith (2003) suggested a term ‘sport social context’ that may foster positive
social relationship and developmental outcomes of youths.
There are some limitations with respect to analysis and interpretation. First, only
independent similarity between a pair of samples in attributes and demographics was
76

considered as the bases of analysis. So, the dynamics of interpersonal relationships
need to be further considered in forming new peer networks. For instance, we may
make a new friendship via our prior networks, in which homophily is dependent on our
prior networks. Second, dyadic relationship was not accounted for in this study.
However, it would be interesting to compare factors to predict bi-directional and singledirectional relationships, which can be addressed by adding a variable for the reciprocal
relationship and further controlling for nominee’s characteristics. Finally, the team-level
characteristics were not accounted for in this study, which suggests a future study
regarding the dynamics of peer relationship within a specific group, such as an athletic
team. Multilevel modeling with three levels (i.e., individuals < clique < team) enables us
to investigate why someone selects a specific team member to interact with for a certain
purpose, such social or task in a team.
Although there are some limitations, this study shows the process of forming
peer networks among student athletes, which contributes to the groundwork regarding
the association between athletic participation and development of peer relationships. A
context where adolescents participate in physical activity may enhance the quality of
peer relationship (Smith, 2003). In attempt to better understand peer relationships in
physical activity contexts, the application of the selection model of a social network
analysis used in this study will be a useful model in terms of the process of peer
selection as Smith (2003) suggested.

77

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Chapter IV: THE PSYCHOMETRICAL EVALUATION OF STUDENT
INTERACTION (DEPTH OF INTERACTION) MEASURES – APPLICATION OF
GRADED RESPONSE MULTILEVEL ITEM RESPONSE THEORY (STUDY III)
Introduction
Student interaction in school has been indicated as a key component of the
educational process which as been studied under Social Capital Theory, however, it is
difficult to find a clear and precise definition of student interaction (Anderson, 2003).
Social capital is defined as resources that individuals may access and accumulate
through social interactions (Coleman, 1988, 1990; Frank & Yasumoto, 1998). In this
regard, peer is a type of relation that may provide resources that can be applied to
educational outcomes.
More specifically, Bourdieu (1985) described social capital as the aggregate of
actual and potential resources that an individual has access to through social ties.
Generally, there are two components, structure (embeddedness) and available
resources (contents) of social capital (Vanhoutte & Hooghe, 2009). Also, Lin (2001)
made a distinction between the access through network and the action-related use of
social capital. Access refers to an individual’s collection of potential resources, while
use refers to actions. That is, social ties are channels for information and resources flow
within embedded structures with respect to social capital. This suggests research
should focus on the resources available through social relations (i.e., information or
material exchange; Coleman, 1990). In measuring peer social capital, for example, what
do student discuss with their peers and ask for within their school social network.

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Since there are a large number of different definitions and descriptions of social
capital in a given social context, and general standardized direct measures do not exist,
various types of measures (or indicators) have been used previously in social science,
economics, and business (Vanhoutte & Hooghe, 2009). First of all, attitudinal measures
of social capital, within socialization, social support, and trust, have been used as
manifestation of social capital in its own way. King and Furrow (2004) defined a threedimensional model of social capital, social interaction, trust, and shared vision, using
structural equation modeling, using attitudinal measures, such as Parent and Peer Trust
subscales from the Inventory for Parent and Peer Attachment (e.g., my parent trust my
judgment; Armsden & Greenberg, 1987), Family-Shield Shared Activity Scale (e.g., how
often do you do something active together like playing sports?; Furstenberg et al.,
1999), and a subscale of the American Institutes for Researcher’s Community
Assessment Instrument (e.g., many of my personal values are shared by my
parents/friends/ other adults in the community; Royal & Rossi, 1996). Particularly in
school settings, self-reported questionnaires have been used, which provide general
information about students’ evaluations of group interaction (e.g., whether students find
explanations to be understandable or helpful) (Webb, 1982). Rugutt and Chemosit
(2009) assessed attitudes about student-student relations, using the following 6 items:
1) I make friendships with other students. 2) I know other students. 3) I do favors for
members of this class. 4) Students help me with my learning. 5) I help other class
members who are having trouble with their work. 6) In this class, I am able to depend on
other students for help. This attitudinal component of social capital is generally
measured by a questionnaire indicating the degree to which one believes people are
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trustworthy in general. These questions ask subjective feelings about individuals’
general attitude toward social relationship, and have seldom been tested in relation
under specific social ties (Vanhoutte & Hooghe, 2009).
In addition to measuring attitude, social capital of students has been measured
by a variety of indicators in education, such as number of siblings, parental education,
parental involvement in school, parent-child discussion, etc. in family, and participation
in religious and sporting activities, number of school changes, and number of
organizations belonged to, etc, in community (e.g., Hao & Bonstead-Burns, 1998; Israel,
Beauliew, & Hartless, 2001; McNeal, 1999; Muller & Ellison, 2001; Smith-Maddoz,
1999; Sun, 1999). However, Stanton-Salazar (2001) suggested that these conventional
measures (e.g., number of parents, parent-child discussion, etc.) are poor and
unreliable indicators of social capital, and they give little information about dynamics of
relationships or quality of the interaction. This type of measures also cannot be tested
under specific social ties.
Measures of social capital showed draw on network analysis that has been
developed to measure aspects of social relations. The method of ‘Name Generator’
(McCallister & Fischer, 1978) has been used, which requires identifying names with
whom an individual interacts, for example ‘With whom do you talk about your personal
matters?’ Such measures can be used for egocentric analysis (Van der Gaag &
Snigiders, 2005) or extended to include indicators, such as size, intensity (i.e.,
frequency of contacts), diversity of network (i.e., number of friends who have different
characteristics), and density (Vanhoutte & Hooghe, 2009). But these extensions focus
only on the structural part of social capital. Also, Lin, Fu, and Sung (2001) have
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developed ‘Position Generator’ as a measurement technique for social capital with a list
of job related resources. This method measures access through network members to
occupation, seen as representing social resource collections based on job prestige.
Range of accessed prestige, highest accessed prestige, and number of different
positions accessed are indicators of the social capital. However, it does not contain
specific information of their social structure (i.e., names of their networks). These
methods have referred only to social structure of their relationship, not the actual
resources that may become available through their social network.
With emphasis on resources, Van der Gaag and Snigiders, (2005) developed
‘Resource Generator’, which asks about access to a fixed list of resources, each
representing collection of social capital in several domains of general life. Van der Gaag
and Snigiders defined social capital as latent traits using IRT analysis. Resource
Generator has a list of resources that question the availability of each of these
resources checked by measuring the tie through which the resources are accessed,
indicated by the role of these ties (family members, friends, or acquaintances). The
questions begin with a stem ‘Do you know anyone who…’ followed by a list of
resources, such as ‘can help when moving house’, ‘can give advice on matters of law’,
‘can repair a car’, etc.
In light of identifying and analyzing specific ties, social network analysis can be
one to quantify the flow of resources through social ties. For instance, Frank, Muller,
and Muller (2013) analyzed friendship nomination from sociometric data because they
have the potential to convey resources, and found that nomination were affected by
common course takings, homophily (e.g., race, age, GPA, etc.), and a structural
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constraint (e.g., grade level). The sociometric data only provides dichotomous
information only about ‘quantity (i.e., 1 or 0) of the interaction with whom one endorsed’,
such as who his/her friends are (i.e., network ties), or how often they interact regarding
a certain matter (i.e., quantity of their interaction). This limited information suggests the
following questions: ‘what topic do students talk with their social ties?’, ‘what resources
(or contents) actually flow through social ties for students in school?’, and ‘which ties
have more deep interaction?’
Although teachers’ social capital is not the focus of this study, studies by Penuel,
Riel, Krause, and Frank (2009), and Sun (2011) inform us on how to measure flows
through social relations within network theory. Penuel et al. used a social network
analysis, combined with qualitative data, to analyze structure and resources of teachers’
interactions as social capital; Sun (2011) applied Rasch based-multilevel item response
theory (Kamata, 2001; Kamata, Bauer, Miyazaki, 2008) to estimate the psychometric
properties of interaction among teachers who responded to a social network survey
based on dichotomous items (yes or no) with respect to instructional tasks (e.g., doing
mathematics problems together, discussing students’ work, sharing instructional
materials, and so on.). Also, Sun estimated the depth of interaction (i.e., a latent trait of
item response theory), and discussed the possibility of use of polytomous items, such
as the partial credit model (PCM) and rating scale model (RSM).
Similar to Sun, this study investigated the potential use of multilevel Rasch
based-PCM and RSM (Bacci & Caviezel, 2011) to evaluate a measurement for social
interaction used in Study I, and further estimated the depth of interaction, defined as the
propensity of endorsing collaborative relationships regarding academic, athletic, social,
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and emotional interactions. The depth of interaction is the latent trait estimated by the
measurement model, which indicates the likelihood to be connected to friends, and is a
form of social capital based on Lin (2001)’s definition of social capital. The estimated
depth of interaction indicates individuals’ propensity with respect to being connected to
peers, and higher propensity indicates higher potential to carry resource through social
ties.
A combined model from Multilevel Modeling and IRT is useful when the effects of
multilevel covariate on a latent trait need to be estimated. A combined model allows us
to analyze covariates at the different levels that affect the latent trait; it yields a more
accurate standard error estimate (Maier, 2001). Also, the total variance of the latent trait
is decomposed into level-specific variance of a latent trait (Fox, 2005). For example,
items are nested in students, which are nested in schools. Personal characteristics
(e.g., concentrating skill on exams) at student-level, and types of schools (e.g., public or
private) at school-level are related to the person ability.
Several kinds of multilevel structure of IRT have been proposed. For
dichotomous response data, Kamata (2001) proposed the multilevel formulation of
Rasch model as a hierarchical generalized linear model. Maier (2001) defined a Rasch
model with a hierarchical model imposed on the person parameters but without
additional covariates. Also, Fox and Glas (2001, 2003) used a normal ogive model to
estimate two item parameters in multilevel structure, with covariates on both levels. For
dichotomous response data, Maier (2002) developed the partial credit hierarchical
measurement model with Gibbs sampling and used the Netropolis-Hastings algorithm to
estimate the parameters of the model. Natesan, Limbers, and Varni (2010) defined
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graded response multilevel model, using cumulative logit model. Also Bacci and
Caviezel (2011) demonstrated the multilevel 2PL-partial credit model, partial credit, and
rating scale model with empirical data.
Due to the nested structure of network data (i.e., items are nested in ties within
nominators), it is logical to adopt the analytical frame of multilevel IRT onto network data
to diagnose the psychometrical quality of the instrument used to collect empirical data
for social network of students. Specifically, Sun (2011) addressed benefits of use of
multilevel IRT in network data. First, it can estimate latent traits at different levels
simultaneously, such as the depth of student interaction between a pair at tie-level, and
the extent to which a student is embedded in the network at ego-level. Second, it can
accommodate dependencies in the nested structure. Responses at item-levels are
dependent (i.e., items are correlated within a tie) on ties, which are also dependent on
egos (nominators), but they are conditionally independent across ties and egos. Third, it
can proportion the total variance and covariance into separate components at the item-,
tie-, and ego-levels, which helps more accurate estimation for standard error. Lastly, the
measurement model can be combined with predictors and covariates at any level to
increase the power of analysis (Sun 2011).
Therefore, the purpose of Study III was to conduct a psychometrical evaluation
for the social interaction measure in Study I using multilevel item response theory, and
to estimate the latent trait, which is defined as the depth of interaction. For the
application (i.e., external validity) of the latent score estimated by a measurement
model, which represents the depth of interaction between nominators and nominee, the

90

influence model (Study I) was used to investigate the difference of using the raw score
(i.e., sum or mean) of interaction and the standardized score of the depth of interaction.

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Method
Participants and Instrument
I used the network measure used in Study I and Study II, which was collected
from student athletes in a local high school over two time periods (i.e., in the beginning
and ends of 12-13 Winter season). Approximately, 350 students played at least one
sport for the school. Two-hundred and ninety-one and 242 student athletes completed
and reported 1,179 and 855 ties in the first and second network measure, respectively.
In the network measure, they were asked to refer their friends’ names on their team and
other teams whom they are interacting with, and rate how often they interact with about
five types of contents, such as general, academic, athletic, social, and emotional topics.
The degree of the interaction between egos (nominators) and alters (nominees) were
assessed using a 5-point Likert scale, 1 = ‘Daily’, 3 = ‘Weekly’, and 5= ‘Monthly’. The
following is the list of five items:
1) How often do you interact with this friend in general?
2) How often do you interact with this friend on academic topics (exam, projects,
classes, etc.)?
3) How often do you interact with this friend on athletic topics (sports skill, practices,
game schedule and strategies, etc.)?
4) How often do you interact with this friend on social topics (other friends, social
events, parties, etc.)?
5) How often do you receive emotional support from this friend?

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Analytic Strategy and Measurement Model
Before performing the IRT analysis, I needed to confirm a latent dimension of the
five items, for which exploratory and confirmatory factor analyses were performed. Also,
reliability was checked under the classical testing theory and item response theory.
In addition, single-level IRT models for polytomous items, such as the 2-parmeter
partial-credit model (2PL-PCM; Muraki, 1992), partial-credit model (PCM; Master,
1982), and rating scale model (RSM; Andrich, 1978), were used to select the best
goodness of fit of a measurement model by comparing Akaike’s information coefficient
(AIC), Bayesian information coefficient (BIC), and a likelihood ratio test (i.e., chi-square
difference).
Then, the multilevel frame was added into the selected measurement model
because the analytic framework is under an ego-centric network structure, which does
not model reciprocal relationships. The unique characteristics of an ego-centric network
that assume independence across egos and relative independence across ties within
each ego’s network make of a generalized multilevel model plausible for the network
measure. That is, items (level 1 is item-level) are nested in social ties (level 2 is tielevel), which are nested in egos (level 3 is ego-level).
For this ego-centric network data, multilevel 2PL-PCM (Bacci & Caviezel, 2011)
were adapted to fit the data and to simultaneously estimate item characteristics and the
depth of interaction, as controlling for variance of tie- and ego-level. Bacci and Caviezel
showed the transformation of generalized 2PL-PCM (Muraki, 1992) to logit-linear
function for model specification of specify model multilevel data as follows:

93

𝑃�𝑌𝑖𝑗𝑘 = 𝑚�𝜃0𝑗𝑘 , 𝜃00𝑘 �

Level 1-model (item level):

=

𝑚
𝑒𝑥𝑝 �∑ 𝑘=0 𝜆 𝑖 �𝜃0𝑗𝑘 + 𝜃00𝑘 − ( 𝛽 𝑖 + 𝜏 𝑖𝑘 )��

𝑀−1
1 + ∑ 𝑙=1 𝑒𝑥𝑝 �∑ 𝑙𝑘=0 𝜆 𝑖 �𝜃0𝑗𝑘 + 𝜃00𝑘 − ( 𝛽 𝑖 + 𝜏 𝑖𝑘 )��

𝑖 = 1, … , 𝐼;

𝑚 = 0, … , 𝑀;

𝑗 = 1, … , 𝑛;

ℎ = 1, … , 𝐻

𝑙𝑜𝑔𝑖𝑡 �𝑃(𝑌𝑖𝑗ℎ = 𝑚)� = 𝛾0𝑖𝑗ℎ + �𝛾1𝑖𝑗ℎ + 𝛾 𝑖𝑚𝑗ℎ � ∙ 𝐼 𝑖𝑗ℎ
𝛾0𝑖𝑗ℎ = 𝜆 𝑖 ∙ �𝛾00ℎ + 𝜃0𝑗ℎ �

Level-2 model (tie level):

𝛾1𝑖𝑗ℎ = 𝜆 𝑖 ∙ 𝛾1𝑖0ℎ

𝛾 𝑖𝑚𝑗ℎ = 𝜆 𝑖 ∙ 𝛾 𝑖𝑚0ℎ

𝛾00ℎ = 𝛾000 + 𝜃00ℎ

Level-3 model (ego level):

𝛾1𝑖0ℎ = 𝛽 𝑖

𝛾 𝑖𝑚0ℎ = 𝜏 𝑖𝑚

𝑙𝑜𝑔𝑖𝑡 �𝑃(𝑌𝑖𝑗ℎ = 𝑚)� = 𝜆 𝑖 ∙ �𝛾000 + �𝜃0𝑗ℎ + 𝜃00ℎ � − (𝛽 𝑖 + 𝜏 𝑖𝑚 �

The combined model of the three levels:
94

where

𝑌𝑖𝑗ℎ represents the responses to item i (i=1,…,I) from ties (j=1,…,n) within
𝜃0𝑗ℎ at level 2 (i.e., deviation of the latent

ego network (h=1,,,H); θ indicates the level of the latent trait (depth of interaction) of

variable θ for tie j in ego h), and 𝜃00ℎ at level 3 (i.e., deviation of the latent variable for

ego, which is divided into two random effect,

𝛽𝑖

ego h from average of the population). They are assumed to be normally distributed
with mean equal to 0 and constant variance.
th

item i

indicates the average difficulty of the

item; a threshold difficulty parameter (𝜏 𝑖𝑚 ) indicates the scoring in the m
th

th

𝜆 𝑖 indicates the discrimination of item i. 𝛾0𝑖𝑗ℎ is

the random intercept where 𝛾1𝑖𝑗ℎ is the slope of the i
category rather than (m-1)

to item i;

th

th

th

𝛾 𝑖𝑚𝑗ℎ is the slope of

item. 𝛾000 is the intercept of 𝛾00ℎ at level 3. The sum of the
item, and

residuals at Level 2 and 3 ( 𝜃0𝑗ℎ and 𝜃00ℎ , respectively) was defined as the estimate of
the m category of the i

the depth of interaction to represent the latent trait of tie j nominated by ego h in ego-

𝜆 𝑖 = 0 for each item i and 𝜆 𝑖 = 0 and 𝜏 𝑖𝑚 = 𝜏

centric network data (c.f., Sun 2011). The PCM and RSM, which are special cases of
2PL-PCM, can be obtained by imposing
for each item i, respectively.

For the estimation procedure, Bacci and Caviezel suggested to firstly use
numerical integration method (e.g., Breslow & Clayton, 1993; Breslow & Lin, 1995;
Pinheiro & Bates, 1995; Skrondal & Rabe-Hesketh, 2004) because of the fact that the
marginal likelihood function obtained by integrating out the random effects in
95

𝑚

multidimensional integrals. Then, they suggested using maximum marginal likelihood
with suitable algorithms, such as Newton-Raphson and Fisher Scoring in terms of direct
optimization method, and EM as an indirect optimization method.
For the application of the latent trait score (i.e., the depth of interaction) obtained
by the measurement model, the result of the influence model (Study I) was compared to
see the difference in the estimated coefficients of the exposure when using the latent
score versus the mean of frequency.

96

Results
Preliminary Analysis: Dimensionality and Reliability
The five items on general, academic, athletic, social, and emotional topics
measured interaction among friends with a 5-point Likert scale, ranging from 1 (Daily) to
5 (Monthly). However, the values reversely coded to indicates a larger value means
more frequent (i.e., 1=Monthly and 5=Daily). Table 4.1 shows the descriptive statistics
of the five items. The means of interaction on general and social topics were higher than
other topics, and all responses were negatively skewed.
To test if the five items were converged onto a latent factor (i.e., interaction), an
exploratory factor analysis was firstly performed, which revealed an Eigenvalue of 2.19
for a one-factor model. Also, a confirmatory factor analysis was performed to confirm a
one-factor model and check the model fit. Table 4.2 shows the standardized factor
loadings with standard errors. The item on social topics was the greatest predictor (.84),
while the item on academics was the lowest (.55). The one-factor model was confirmed
2

with the following fit index: χ (5) = 30.26, p<.000, CFI=.978, TLI=.955, RMSEA=.080
(90% CI: .055 ~ .110), and SRMR=.024. It sufficed Hu and Bentler (1999)’s cut-off
values, which are CFI and TLI >.95 and RMSEA and SRMR < .08. The coefficient of
determination (R-squared) is .837. In addition to the factor analysis, the
3

unidimensionality of the five items was also tested by DIMTEST (Stout, 1987;
Nandakumar, Yu, Li, & Stout, 1998), which is used to decide whether the data satisfy
the assumption of a unidimensional model based on the item response theory. This test
3

Poly-DIMTEST is more appropriate for the polytomous items; however the author has
no access to the program. Instead, the author dichotomized the items by each item’s
mean, and used DIMTEST to check the nuances of the unidimensionality as suggested
by committee.
97

uses two subtests, an assessment subtest (AT) and a partitioning subtest (PT), in which
the null hypothesis is that the appropriately selected AT and PT are under a same
dimension. The selection can be done either by the program using explorative factor
analysis or by the user. Since the number of items should be at least 20 for the
explorative factor analysis (Stout, Nandakumar, Junker, Chang, & Steidinger, 1992), I
selected AT (item 1, 4, and 5) and PT (item 2 and 3) based on bivariate correlations
between the items and a subjective judgment (Table, 4.3). The item 2 and 3 asked
about more specific interaction on academics and athletics; however item 1, 4, and 5
indicated interactions in general. Also, the correlations between item 1 and 4 (.43), and
item 4 and 5 (.50) were relatively higher than the other correlations. The test results
were TL= 1.63, TGbar= 1.72, T=-.08, and p=.53, which did not warrant rejecting the null
hypothesis (i.e., AT and PT are under one latent dimension). Other selecting
combinations did not show sufficient evidence to reject the null hypothesis as well.
Thus, the unidimensionality of the five items was confirmed both by the classical testing
theory and item response theory.
For the reliability of this measure under the classical testing theory, Cronbach’s
alpha of the test scale is .79 (Table, 4.4). In addition, item-test correlation and inter-item
covariance for all items are larger than .64.

Multilevel 2PL-PCM
In Table 4.5, the result of LR test showed significant differences between 2PLPCM and PCM. PCM was also significantly different from RSM. This result suggested
that 2PL-PCM is the most parsimonious model than the other two models to fit the data,
98

which allows estimating respectively threshold difficulty and discrimination parameters
of the five items. The reliability of a set of the five items under 2PL-PCM is .60, which

𝜎2
𝜃

2
𝜎� − (𝑆𝐸𝑀)2
𝜃

. 01672 −. 01122
=
= .60
. 01672

was obtained by Samejima (1994)’s formula as followed:

𝜌 𝜃𝜃 =
�

2
𝜎�
𝜃

=

2
𝜎�
𝜃

The LR test between multilevel 2PL-PCM and 2PL-PCM (2 times of the
difference of the two log likelihoods) provided chi-square of 3798.88 (df = 4), which
rejected the null hypothesis (i.e., the two models are equivalent). This result warranted
that multilevel 2PL-PCM is the more acceptable and parsimonious measurement model
for this empirical data. Finally, the multilevel 2PL-PCM was selected to estimate the
latent trait of the depth of interaction, while accounting for variances at tie- and egolevel.
multilevel 2PL-PCM. The coefficients are the estimated step parameters for item i ( 𝛽 𝑖 )
Table 4.6 provides the coefficients and standard errors estimated by the

and category j+1 ( 𝜏1 ), which indicates relative difficulty of each step needed to

transition from one category to the next within an item. In Item 1, the transition from
category 3 to category 4 is the most difficult (3.48), and the transition from category 4 to
category 5 is the least difficulty (1.71); In Item 2, the transition from category 3 to
category 4 is the most difficult (1.11), and the transition from category 2 to category 3 is
the least difficult (.26); In Item 3, the transition from category 4 to category 5 is the most
difficult (1.34), and the transition from category 2 to category 3 is the least difficult (.23);
In Item 4, the transition from category 4 to category 5 is the most difficult (4.04), and the
99

transition from category 1 to category 2 is the least difficult (.78); In item 5, the transition
from category 4 to category 5 is the most difficult (1.85), and the transition from
category 1 to category 2 is the least difficult (.29). Overall, respondents felt the difficulty
of endorsing category 4 (More than Weekly) and 5 (Daily).
The discrimination parameter is interpreted as “the degree to which categorical
responses vary among items as a latent trait changes” (Muraki, 1992, p. 162). Among
the five items, while fixing to 1 for Item 1 for model specification, item 4 (1.697) has the
biggest discrimination ability (i.e., steepest slope), which distinguishes the most
effectively between individuals with different levels of the latent trait. Item 2 (.341)
showed at least ability to discriminate individuals with different levels of the depth of
The depth of interaction is defined as the sum of 𝜃0𝑗ℎ and 𝜃00ℎ , which

interaction.

represent the estimated latent trait of tie j nominated by ego h in an ego-centric network
data. The range of the depth of interaction was from -3.63 to 2.66 with a mean of .08
and a standard deviation of 1.09 in a conventional scale of IRT models. To shift this
scale in a positive manner for interpretation, I added 5 to the estimated latent, which
gave the range from 1.37 to 7.66. Figure 4.1 shows the distributions of the shifted scale
of the depth of interaction (Mean=5.08, SD=1.09, Min.=1.37, Max.=7.66, Skewness=.19,
Kurtosis=.24). Figure 4.2 is the distribution of the mean of the raw frequency on the five
items (Mean=3.99, SD=.95, Min.=1, Max.=5, Skewness=-1.01, Kurtosis=.72). The
distribution of the latent score (depth of interaction) shows a normal distribution
although the distribution of the mean of the raw frequency is not, which shows a
100

negatively skewed distribution with a standard criterion of ± 1 of Skewness and
Kurtosis.

The Application of the Latent Score on the Depth of Interaction

𝑤 𝑖𝑖′ ,

This part of the analysis was to compare the results of influence models in Study
I and the results of influence models when using the estimated latent score for

which indicates the extent of relation between i (nominator) and i’ (nominee). The

correlation between the latent score and the raw mean of frequency was high (.88,
p<.001).
exposure ( 𝛽2 and 𝛽2

𝐿) was very similar in all variables, except for academic identity.

Comparing the magnitude of the influence in the two models (Table, 4.7), the all-

When using the latent score, each magnitude in academic achievement, college

aspiration and expectation, and athletic identity was little increased, while decreased in
academic efficacy, and physical ability and appearance. The academic identity showed
considerable increases, and the signal was changed from (-) to (+) when using the
latent score, which is rooted in the changes in the different team-exposure. In the
different team-exposure, the changes to positive influence were observed in academic
achievement, college aspiration, and academic identity, while athletic identity was
changed to negative influence.
In summary, the network measure with the five items was confirmed with a onelatent factor model for student interaction. In the single level comparison of IRT models,
2PL-PCM was found to be more parsimonious, which determined the use of multilevel
101

2PL-PCM as a measurement model for this data. The measurement model was

psychometrically acceptable, and the latent trait (depth of interaction) was estimated,
which was highly correlated with a raw mean of interaction frequency. However, the
latent score was normally distributed, but the raw mean was not, which was negatively
skewed. Applying the latent score in the influence model showed a considerable change
in academic identity for the all-exposure. Also for the different team-exposure, many
changes occurred in academic achievement, college aspiration, and identity. The effect
in academic identity was changed to positive while athletic identity was changed to
negative.

102

Discussion
In an attempt to validate a measurement for social network, I applied multilevel
item response theory to network data in order to account for the difference in items and
the nested data structure (i.e., items are nested within ties, which are further nested in
and Level 3 (nominators), and their sum ( 𝜃0𝑗ℎ and 𝜃00ℎ ) was hypothetically defined as

nominators). Multilevel 2PL-PCM was selected to estimate the latent trait at Level 2 (tie)

depth of student interaction. Moreover, I demonstrated the application of the latent

depth of interaction using the influence model (Study I), which conventionally uses a
raw score (i.e., sum or mean of interaction), to model ‘exposure’ for each nominator. As
Sun (2011) suggested, this study contributes to the development of a measurement
model of polytomous network data, which contains the degree of interaction (i.e.,
frequency of discussing) as well as dichotomous occurrence of interaction.
One feature of IRT is that the estimated latent trait is normally distributed, which
is continuous on a common IRT scale. In this study, the distribution of the latent depth
of interaction was normal while the mean of frequency showed a negatively skewed
distribution. Despite of a lot of observations near a category of 5 (i.e., everyday
interacting with all ties about all topics), the index of skewness was not very large
because of a larger sample size, which is supported by central limit theorem stating that
when sample size is sufficiently large, the sampling distribution of a random variable is
well approximated by a normal curve, even when the population distribution is not itself
normal (Devore & Peck, 1997). Therefore, the scale transformation into a common IRT
scale (i.e., a standardized scale) yields a normal distribution of the trait, which
surpasses using the traditional methods, such as the mean of frequency of interaction,
103

because Individuals may refer only a few friends with whom they are interacting very
frequently in a real setting. Also, it is possible to equate multiple survey instruments and
put different estimates for the same tie on the same scale for comparing the depth of
interaction across ties using equivalent survey instruments (Sun, 2011).
As an application, I incorporated the latent depth of interaction into modeling the
exposures in the influence model of social network analysis (see Table 4.7). The
magnitude of the coefficients slightly decreased, but the considerable change occurred
in the coefficients of all-exposure in college expectation, academic and athletic identity,
which is the consequence of the score calibration by the IRT model although they are
not statistically different (i.e., paired t-test). The interpretation of the coefficients by the
latent depth of interaction is more valid due to features of IRT models in calibrating raw
scores. An IRT model postulates that a single continuous factor underlies responses,
and this factor is subject to error of each item; an estimated latent score is dependent
on item characteristics (de Ayala, 2009). In conjunction of IRT and a network
measurement, Van der Gaag and Snijder (2004) also point out the caution of using raw
information on a very low or a very high frequency of responses, and claim that IRT
yields a better representation of a set of items and their associations than factor
analysis.
There are limitations guiding future studies. This measurement model is wellsuited to ego-centric network data, which assumes that egos are independent. That is,
egos are not related each other, but related to nominees and corresponding items.
Therefore, this measurement model does not account for reciprocal relationships
between egos. This limitation suggests developing a measurement model to account for
104

the dependency of egos because the estimated depth of interaction may be different
when egos have a dyadic interaction. The depth of interaction between egos may be
expected to be higher when they have dyadic ties.
This measurement model has not been extended for covariates. Covariates can
be added in Multilevel IRT models to explain more variance at different levels and see
their effect on the latent trait (Maier, 2001; Sun, 2011). This point suggests a
mathematical development of polytomous multilevel IRT models to add covariates at
different levels, which potentially reduce the standard errors (Maier, 2001).
Conceptually, the negatively skewed data indicate that few subjects selected little
interaction for some nominees, which was coded as 1 (monthly interaction), however,
considering the context of school, students come to school every day and have more
chances to interact often with friends, not like adults’ interactions for professional
development (e.g., teaching workshop). Because adolescents tend to spend more time
with peers for socialization (Fuligni, Yip, & Tseng, 2002; Richards, Crowe, Larson, &
Swarr, 1998), the category about the monthly interaction arises a question if inclusion of
little interaction is appropriate for adolescents as an indication of their friends and
networks. From adolescents’ perspective, little interaction, for instance once in a month,
may not be included to define a social network of adolescents.
Finally, this study used only five items about social interaction in school, such as
talking about academics and athletics. They may be too broad to capture students’
interactions. Thus, measuring items can be further detailed in terms of interaction with
peers in school, which will require a lot of time for subjects to complete the questions for
each referred peer. It may yield biased information with missing data, but it will have
105

merit to have more items because the number of items is related to test information,
which represents reliability of a test in IRT. The test information is the sum of items’
information (de Ayala, 2009). More items lead to more reliability of a whole test. It is
also probable to select items demonstrating more information for a specific range of a
trait level because information varies by a trait level. Moreover, various latent
constructs can be formed depending on a research question, such as depth of
interaction on courses or athletics. For future studies, I suggest the following
dimensions and items based on literature reviews on student interaction and social
capital in school (e.g., Furstenberg, Cook, Eccles, Elder, & Sameroff, 1999; King &
Furrow, 2004):
Contents-related
Sharing materials for courses
Discussing what you have learned in courses
Discussing what you expect to learn in courses
Discussing your progress in courses
Asking what you did not understand in contents of courses

MotivationDiscussing your class engagement
Discussing your attitude in courses
Discussing your motivation in courses
Discussing your interest in courses

106

TaskTalking about exam/ quiz
Talking about homework
Talking about group projects

Classroom EnvironmentTalking about classroom settings.
Talking about classroom organization.
Talking about classroom policy.
Talking about course schedule

FacultyTalking about teachers’ leadership
Talking about teachers’ instructional strategy
Talking about teachers’ behavior
Talking about teaching methods
Talking about ways to interact with students

AthleticTalking about your coach’s leadership style.
Talking about your team’s schedule.
Talking about team’s practice/ training.
Talking about team’s competition
107

Talking about sport skill improvement

108

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109

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113

CHAPTER V: CONCLUSION AND IMPLICATION OF THIS DISSERTATION

By conducting a series of three studies, this dissertation enriches the
understandings of educational consequences of athletic participation with emphasis on
peers who participate together in athletic programs. Study I provides evidence that
social interactions with peers on a same team and different teams positively influence
student athletes’ academic related variables, such as academic achievement. Study II
provides information regarding personal attributes used in forming peer networks.
Multiple sources play the role in initiating peer relationships. Student athletes form peer
networks based not only on similar attributes, such as gender, team membership, and
college aspiration, but also different attributes in grade level and achievement.
Taken together, these results imply that an athletic program is a social institution
in which students produce and distribute social capital not only for athletics but also for
academics. Similarly, Frank, Muller, and Muller (2013) emphasized an emergent cluster
of course-taking pattern as social institution to formulate ‘local position’ where students
develop peer relationships. Attending the same social institutions, such as courses and
sports, provides more time for students to be in a same place and share personal and
group norms and values, which facilitates effective peer relationships. The effective
peer relationships, which are formed in athletic programs, are a form of social capital
that student athletes can access for their academics.
These implications add more weight to the value of athletic participation on
education in school. There has been an ongoing debate to unpack the causal factors
and actual mechanisms of the athletic participation/education value relationship
114

(Hartmann, 2008). That is, athletic participation facilitates social relationships

throughout t which students can develop capitals to achieve their goals in school both
for academic and athletic success. This optimistic outcome by athletic participation for
academic and athletic success is aligned with the mission of the National Collegiate
Athletic Association (“Academics”, 2013), which is an organization established to create
an atmosphere to pursue a balance of academic and athletic excellence in school.
In addition to educational consequences of athletic participation, this study
contributes to the argument that sport participation facilitates social relationships. In this
regard, Smith (2003) suggested a term ‘sport social context’, and Hills (2007) argued as
follows:
“Physical education represents a dynamic social space where students
experience and interpret physicality in contexts that accentuate peer
relationships and privilege particular forms of embodiment. It represents a
distinctive area within schools with regard to its focus on the body and physical
skills and its unique opportunities for social interactions between peers.” (p. 317318).
These quotes, along with this study, provide insights that sport participation is a
source for students in high school to build peer relationships. However, the study leaves
a question on how peer relationship is positive for athletes’ well-being in high school.
How athletic programs are designed and delivered by coaches, athletic directors, and
community is critical to making a positive impact on peer relationships formed in school
and athletic programs on athletes’ well-being.
Methodologically, the statistical models of social network analysis provide a
prospective analytical frame for socialization, peer relationship, social network, and
115

group dynamics in the psychosocial aspect of sport. The influence and selection model
of social network analysis can be more extensively utilized in sports to assess the effect
of social network in terms of attitude, emotion, cognition, and behavior of individuals
fluctuated by interpersonal relationship and interaction. Also, the IRT-based
measurement model for the polytomous network data, as far as I am aware, is the first
attempt, which enriches issues on measurements in conjunction with social network
analysis.
Finally, this dissertation provides a policy-related implication that athletic
participation, as an extracurricular activity, is not detrimental with respect to
development of adolescents. Instead, it ameliorates social relationships with peers in
school, which is a social capital for adolescents to achieve their goals for academic,
social, and physical wellbeing in school and future. However, these findings and
implications can only be generalized to religiously based-private high schools due to the
sample’s characteristics of this study. Public and private schools have different figures
with respect to individuals (students, parents, teachers, and administrators), academics,
educational aspiration, and economics (Altonji, Elder, & Taber, 2005), which may result
in differences of peer relationship in school. In public (urban or rural) schools, student
athletes may represent different patterns in initiating and capitalizing peer relationship
for academics.

116

REFERENCES

117

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Academics. (2013). Retrieved May 5, 2013, from
http://www.ncaa.org/wps/wcm/connect/public/ncaa/academics/index.html
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variables: assessing the effectiveness of catholic schools. Journal of Political
Economy, 113, 151-184.
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Recognizing, assessing, and utilizing the relationship. Los Angeles: LA84
Foundation.
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118

APPENDICES

119

APPENDIX A: Tables
Table 2.1. Participants’ distributions on teams
Fall Sports
N
n1
n2
1 Football (Varsity, JV, Freshmen)
150
32
22
2 Boys Tennis(Varsity, JV)
20
22
16
3 Boys Soccer (Varsity, JV)
30
19
5
4 Boys & Girls Cross Country (Varsity, JV)
20
26
21
5 Girls Volleyball (Varsity, JV & Freshmen)
45
23
13
6 Girls Golf (Varsity, JV)
15
3
2
7 Sideline Cheer Team (Varsity, JV)
20
18
13
8 Girls Swimming & Diving (Varsity)
20
3
4
Winter Sports
9 Boys Basketball (Varsity, JV, Freshmen)
45
31
26
10 Hockey (Varsity)
30
1
1
11 Boys Swimming & Diving (Varsity)
15
3
3
12 Boys & Girls Bowling (Varsity, JV)
10
0
0
13 Girls Basketball (Varsity, JV & Freshmen)
45
22
22
14 Competitive Cheer Team (Varsity, JV)
20
6
4
15 Boys Wrestling
20
7
6
Spring Sports
16 Baseball (Varsity, JV, Freshmen)
45
11
12
17 Boys & Girls Track & Field (Varsity)
40
9
10
18 Boys Golf(Varisty, JV)
20
7
2
19 Softball (Varsity, JV, Freshmen)
45
6
10
20 Girls Tennis (Varsity, JV)
15
10
9
21 Girls Soccer (Varsity, JV)
25
8
10
22 Boys & Girls Lacrosse (Varsity)
25
4
9
Note. N is the total number students on team. n1 and n2 are the numbers of students
who completed the first and second survey respectively.

120

Table 2.2. Gender and school years of samples in the first and second survey.
Freshman
Sophomore
Junior
Senior
Male

39 (38)

55 (45)

38 (24)

31 (18)

Female

46 (42)

36 (38)

20 (18)

24 (15)

Note. The numbers in parenthesis indicate the number of samples in the second survey.

121

Table 2.3. Teams’ characteristics and norms
Fall Sports
Size Pop. Sea.
1 Football (D1)
150
1
0

Tra.
1

Rev.
1

CoR.
5.58

Task
7.59

Social
7.25

2

Boys Tennis (D2)

20

4

0

1

1

5.13

6.46

5.93

3

Boys Soccer (D3)
Boys & Girls Cross
Country (D4)

30

3

0

0

0

5.05

7.12

6.93

20

7

0

0

0

5.8

7.76

8.27

5

Girls Volleyball (D5)

45

2

0

0

0

5

7.13

6.99

6

Girls Golf (D6)
Sideline Cheer Team
(D7)
Girls Swimming &
Diving (D8)
Winter Sports

15

5

0

1

1

6.33

8.82

8.46

20

6

0

0

0

6.13

7.74

7.58

20

8

0

0

0

5.33

8.01

7.82

Boys Basketball (D9)

45

1

1

1

1

5.64

7.36

7.05

10 Hockey (D10)
Boys Swimming &
11
Diving (D11)
Boys & Girls Bowling
12
(reference)
13 Girls Basketball (D12)
Competitive Cheer
14
Team (D13)
15 Boys Wrestling (D14)
Spring Sports
16 Baseball (D15)
Boys & Girls Track &
17
Field (D16)
18 Boys Golf (D17)

30

4

1

1

1

1

6.81

8.25

15

6

1

0

0

6

6.81

7.63

10

7

1

0

0

0

0

0

45

2

1

1

1

5.72

6.13

6.21

20

8

1

0

0

6.33

7.80

7.05

20

3

1

1

1

5.28

7.93

7.31

45

2

0

1

0

5.45

7.42

7.13

40

1

0

1

1

6.22

7.39

7.11

20

3

0

1

0

6.14

7.64

6.99

19 Softball (D18)
20 Girls Tennis (D19)

45

4

0

0

0

5

6.71

6.45

15

5

0

1

0

5.7

7.24

7.00

4

7
8

9

25
7
0
0
0
6
6.82
6.13
21 Girls Soccer (D20)
Boys & Girls
22
25
6
0
0
0
5.66 7.06
6.45
Lacrosse (D21)
Note. Size=total number of students on each team; Pop.= the order of popularity;
Sea. = season (1=winter season & 0=other seasons); Rev. = revenue (1=revenue
generating team & 0=others); Tra.=tradition (1=state championship banner & 0=no
banner); CoR.=coach’s regard on academics; Task= average of task-related cohesion;
Social=average of social-related cohesion.
122

Table 2.4. The descriptive statistics of the network at time1.
Ties in Same
Total
Ave.
Sports Team n1
same
teamtie
degree
team degree
1 Football
32 119
3.71
64
2
2 B. Tennis
22
60
2.73
21
0.95
3 B. Soccer
19
67
3.53
27
1.42
B. & G.
4 Cross
26 120
4.62
67
2.58
Country
5 G. Volleyball 23 116
5.04
46
2
6 G. Golf
3
13
4.33
4
1.33
Sideline
7
18 112
6.22
78
4.33
Cheer Team
G. Swim. &
3
15
5
8
2.66
8
Diving
9 B. Basketball 31
95
3.06
30
0.97
10 Hockey
1
4
4
3
3
B. Swim. &
11
3
12
4
7
2.33
Diving
B. & G.
0
0
0
0
0
12
Bowling
13 G.Basketball 22 105
4.77
24
1.09
Competitive
14
6
34
5.67
8
1.33
Cheer Team
15 B. Wrestling
7
34
4.86
10
1.43
16 Baseball
11
35
3.18
12
1.09
B. & G.Track
17
9
50
5.56
11
1.22
& Field
18 B. Golf
7
21
3
1
0.14
19 Softball
6
24
4
8
1.33
20 G. Tennis
10
34
3.4
14
1.4
21 G. Soccer
8
35
4.38
15
1.88
B. & G.
22
4
17
4.25
1
0.25
Lacrosse

Ties in
different
team
55
39
40

different
teamdegree
1.72
1.77
2.10

53

2.04

70
9

3.04
3

34

1.89

7

2.33

65
1

2.10
1

5

1.67

0

0

81

3.68

26

4.33

24
23

3.43
2.09

39

4.33

20
16
20
20

2.86
2.67
2
2.5

16

4

Note. B.=Boys. G.=Girls n1 is the number of nominators in each team. Average degree
is the average number of nominees, which is obtained by dividing the total ties with n1.
Same team-degree is the average number of nominees within a same team, while
different team-degree is the average number of nominees outside of a same team (the
number of ties in a same team or other teams is to be divided by the number of
nominators).
123

Table 2.5. The descriptive statistics of the network at time 2..
Ties in Same
Ties in
Total
Ave.
Sports Team n2
same
team- different
tie
degree
team degree
team
1 Football
22 103
3.22
59
1.84
44
2 B. Tennis
16
46
2.09
15
0.68
31
3 B. Soccer
5
21
1.11
11
0.58
10
B. & G.
4 Cross
21
76
2.92
34
1.31
42
Country
5 G. Volleyball 13
52
2.26
25
1.09
27
6 G. Golf
2
5
1.67
0
0
5
Sideline
7
13
73
4.06
44
2.44
29
Cheer Team
G. Swim. &
4
18
6
6
2
12
8
Diving
9 B. Basketball 26
77
2.48
22
0.71
55
10 Hockey
1
6
6
1
1
5
B. Swim. &
11
3
7
2.33
2
0.67
5
Diving
B. & G.
0
0
0
0
0
12
Bowling
13 G.Basketball 22
74
3.36
29
1.32
45
Competitive
14
4
14
2.33
12
2
2
Cheer Team
15 B. Wrestling
6
26
3.71
8
1.14
18
16 Baseball
12
36
3.27
14
1.27
22
B. & G.Track
17
10
32
3.56
11
1.22
21
& Field
18 B. Golf
2
6
0.86
1
0.14
5
19 Softball
10
35
5.83
9
1.5
26
20 G. Tennis
9
34
3.4
12
1.2
22
21 G. Soccer
10
38
4.75
13
1.63
25
B. & G.
22
9
21
5.25
2
0.5
19
Lacrosse

different
teamdegree
1.38
1.41
0.53
1.62
1.17
1.67
1.61
4
1.77
5
1.67
0
2.05
0.33
2.57
2
2.33
0.71
4.33
2.2
3.13
4.75

Note. B.=Boys. G.=Girls n2 is the number of nominators in each team. Average degree
is the average number of nominees, which is obtained by dividing the total ties with n1.
Same team-degree is the average number of nominees within a same team, while
different team-degree is the average number of nominees outside of a same team (the
number of ties in a same team or other teams is to be divided by the number of
nominators).
124

Table 2.6. Descriptive statistics of outcome variables at Time1 and Time2.
Variables (Time1)
N
Mean
SD
Skewness Kurtosis
1 Academic achievement
225
3.63
.41
-1.62
6.91
2

Academic efficacy

289

4.27

.66

-1.14

4.91

3

College expectation

286

4.84

.47

-3.75

22.40

4

College aspiration

285

4.86

.41

-3.42

16.43

5

Academic identity

280

4.96

1.02

-.38

2.62

6

Athletic identity

284

4.87

1.15

-.22

2.54

7

Physical ability

284

5.61

.68

.08

2.66

8

Physical appearance

284

5.19

.65

.59

3.23

N

Mean

SD

Skewness

Kurtosis

Variables (Time2)
1

Academic achievement

199

3.66

.36

-1.36

5.02

2

Academic efficacy

240

4.32

.67

-1.11

4.76

3

College expectation

234

4.83

.54

-3.82

20.59

4

College aspiration

233

4.81

.56

-3.78

19.37

5

Academic identity

231

5.01

1.06

-.20

2.53

6

Athletic identity

231

4.94

1.16

-.34

2.82

7

Physical ability

235

4.48

1.34

-.32

2.63

8

Physical appearance

235

4.45

.84

-.10

2.99

125

Table 2.7. Paired t-test of outcome variables
Variables
N
Mean-D

SE-D

t

p

1

Academic achievement

153

-.018

.01

-1.74

.08

2

Academic efficacy

211

-.047

.03

-1.38

.16

3

College expectation

208

.004

.028

.17

.86

4

College aspiration

208

.052

.027

1.93

.05

5

Academic identity

204

-.122

.053

-2.28

.02

6

Athletic identity

204

-.020

.044

-.46

.64

7

Physical ability

206

1.115

.100

11.15

.00

8

Physical appearance

206

.684

.074

9.14

.00

Note. Mean-D is the mean difference between Time1 and Time2 (Time1-Time2); SE-D
is the difference of standard errors.

126

Table 2.8. Descriptive statistics of three exposures, and paired t-test between same and
different team-exposure.
Same teamDifferent teamAll-exposure
exposure
exposure
Variables
n
M
SD
n
M
SD
n
M
SD
Academic
184 14.98 3.16 107 15.34 3.18 144 16.94 4.31
achievement**
Academic efficacy**

202 17.11 4.11

115

17.83 4.04 144 16.94 4.31

College expectation**

201 19.31 4.15

115

20.09 3.88 143 18.98 4.37

College aspiration**

201 19.48 3.98

115

20.17 3.89 143 19.19 4.24

Academic identity*

201 19.63 4.90

116

20.29 5.04 143 19.33 5.46

Athletic identity

200 19.51 5.51

115

20.63 5.39 143 19.03 6.03

Physical ability**

201 22.44 4.72

114

23.06 4.67 144 22.17 5.14

Physical appearance*

201 20.59 4.42

114

21.09 4.33 144 20.23 4.60

Note. M=mean; SD=standard deviation; n is the number of cases, which are different for
each exposure because all-exposure included all ties, but one may have either the
same team-exposure or different team-exposure. The result of the paired t-test between
same and different team-exposure were indicated by asterisk (*: p<.05, **: p<.01).

127

Table 2.9. Regression models of the outcome variables (y) with overall interactions
y

Academic
achievement
Academic
efficacy
College
aspiration
College
expectation
Academic
identity
Athletic
identity
Physical
ability
Physical
appearance

n

β0

127

.37(.13)

.93(.02)**

138

.45(.09)

.93(.02)**

175

.69(.30)

.68(.05)**

182

.96(.28)

.69(.05)**

172

.78(.42)

.66(.08)**

180

1.1(.42)

.67(.08)*

172

1.6(.37)

.67(.05)**

180

1.6(.35)

.67(.05)**

171

2.9(.44)

.74(.05)**

179

2.3(.41)

.74(.05)**

170

.73(.56)

.79(.04)**

179

.76(.51)

.78(.04)**

172

2.6(1.3)

.16(.17)*

180

3.3(1.1)

.17(.16)*

172

2.3(.88)

β2

β1

.06(.11)

β2-1

β2-2
.03(.003)

-.011
(.001)

.029
(.001)

.071(.007)
.045
(.003)

.082
(.003)+

.077(.007)
-.009
(.00)

.011
(.00)

-.040(.006)
-.025
(.002)

-.041
(.002)

-.002(.01)
-.018
(.005)

.035
(.005)

.015(.009)
.067
(.004)

-.041
(.004)

.066(.02)
.016
(.008)

.023
(.008)

.192(.014)*

2

β3

R

.08(.01)**

.90

.07(.01)*

.90

.94(.05)

.55

.042(.06)

.52

-.12(.05)*

.42

.11(.05)+

.40

.038(.04)

.41

.033(.04)

.40

-.15(.09)*

.52

-.14(.09)*

.5

-.00(.08)

.69

.00(.08)

.69

-.09(.16)

.13

-.12(.16)*

.12

.06(.11)

.12

.001
.124
.05(.10)
.09
(.005)
(.006)+
Note. The exposures were obtained with overall interaction (i.e., average of all type of
interactions). The β0 is the intercept; β1 is the effect of the prior status; β2 is the effect of
64

3.9(.70)

.09(.10)

all exposures from all ties; β3 was set as a controlling variable; β2-1 and β2-2 is the
effect of exposure from ties in a same team and different team. The coefficients are
standardized values, except for intercept. The coefficients of the 21 dummy variables
(D1 through D21) are not presented in this table for less importance of interpretation. +
(p<.08); *(p<.05); **(p<.01)

128

Table 2.10. Regression models of the outcome variables (y) with a specific type of
interaction
y

Academic
achievement
Academic
efficacy
College
aspiration
College
expectation
Academic
identity
Athletic
identity
Physical
ability
Physical
appearance

n

β0

127

.37(.13)

.93(.02)**

127

.43(.10)

.93(.03)**

175

.77(.35)

.68(.05)**

175

.77(.34)

.68(.06)**

172

.81(.48)

.66(.08)**

172

.83(.48)

.68(.08)**

172

1.6(.37)

.67(.05)**

172

1.6(.36)

.67(.05)**

171

2.8(.53)

.73(.05)**

171

2.9(.43)

.74(.05)**

170

.62(.54)

.78(.04)**

170

.80(.53)

.79(.05)**

172

2.6(1.2)

.15(.17)*

172

3.0(1.3)

.16(.17)**

172

2.5(.86)

β2

β1

.07(.11)

β2-1

β2-2

.062(.002)*
.012
(.001)

.038
(.001)+

.054(.006)
.082
(.003)

.075
(.003)

.094(.005)*
.067
(.002)

.022
(.002)

.01(.004)
.012
(.002)

-.047
(.002)

.068(.009)
-.016
(.005)

.038
(.005)

.067(.007)
.045
(.004)

-.039
(.005)

.145(.014)+
.014
(.008)

.048
(.009)

.20(.011)**

2

β3

R

.08(.02)**

.91

.08(.01)**

127

.09(.06)

.55

.09(.05)

175

-.11(.05)+

.42

-.12(.04)+

172

.03(.04)

.40

.03(.05)

172

-.15(.09)*

.52

-.15(.09)*

171

-.01(.09)

.70

-.01(.086)

170

-.08(.17)+

.15

.-.09(.17)+

172

.08(.11)

.12

.05
.16
.07(.11)
172
(.005)
(.006)*
Note. The exposures were obtained with overall interaction (i.e., average of all type of
interactions). The β0 is the intercept; β1 is the effect of the prior status; β2 is the effect of
172

2.9(.85)

.09(.11)

all exposures from all ties; β3 was set as a controlling variable; β2-1 and β2-2 is the
effect of exposure from ties in a same team and different team. The coefficients are
standardized values, except for intercept. The coefficients of the 21 dummy variables
(D1 through D21) are not presented in this table for less importance of interpretation. +
(p<.08); *(p<.05); **(p<.01)

129

𝛾00

𝜇0𝑗

𝑒 𝑖𝑗

ICC

Table 2.11. Model 1: Null multilevel (unconstrained) models of the outcome variables
n
Academic achievement

153

3.69

.090(.04)

.351(.02)

.06

Academic efficacy

180

4.35

.110(.08)

.617(.03)

.03

College expectation

189

4.86

.016(.18)

.448(.02)

.00

College aspiration

189

4.83

.090(.04)

.499(.02)

.03

Academic identity

189

4.96

.197(.11)

1.00(.05)

.04

Athlete identity

178

4.83

.381(.11)

.996(.05)

.13

Physical ability

192

4.54

.379(.14)

1.25(.06)

.08

Physical appearance

192

4.48

.193(.09)

.837(.04)

.05

Note. ICC = intraclass correlation coefficient

130

Table 2.12a. Model 2 and 3 for academic achievement with team size for the team level
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.792**

.040

.001

-.004

.007

.001

.000

.005

-.004*

.001

.000

Same team exposure X P1 𝛾21

.023

.001

Team size (P1) 𝛾01

S.E.

-.000

Different team exposure 𝛾30

Coef.

.83**

Same team exposure 𝛾20

S.E.

.000

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

.658**

SD (Residual)

S.E.

Est.

S.E.

.002

.008

.009

.006

.021

.079

.129

.101**

𝑒 𝑖𝑗

.178

.003

SD (constant) 𝜇0𝑗

.895**

Est.

Random Effect

.083

.006

.099**

.015

Note. No. of observations=131; No. of groups=20. The average of observations per
group=6.5 (Min.=1 & Max=15). + (p<.08); *(p<.05); **(p<.01)

131

Table 2.12b. Model 2 and 3 for academic achievement with popularity for the team level
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.760**

.046

.001

.010

.011

.001

.000

.005

.056

.039

-.002

Same team exposure X P2 𝛾21

.023

.001

Popularity (P2) 𝛾01

S.E.

-.000

Different team exposure 𝛾30

Coef.

.83**

Same team exposure 𝛾20

S.E.

.002

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

.658**

SD (Residual)

S.E.

Est.

S.E.

.002

.001

.007

.006

.021

.071

.122

.101**

𝑒 𝑖𝑗

.207

.003

SD (constant) 𝜇0𝑗

.649**

Est.

Random Effect

.083

.006

.105**

.013

Note. No. of observations=131; No. of groups=20. The average of observations per
group=6.5 (Min.=1 & Max=15). + (p<.08); *(p<.05); **(p<.01)

132

Table 2.12c. Model 2 and 3 for academic achievement with winter season for the team
level
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.787**

.046

.001

.004

.006

.001

.000

.005

.081

.199

-.007

Same team exposure X P3 𝛾21

.023

.001

Winter season (P3) 𝛾01

S.E.

-.000

Different team exposure 𝛾30

Coef.

.83**

Same team exposure 𝛾20

S.E.

.011

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

.658**

SD (Residual)

S.E.

Est.

S.E.

.002

.002

.006

.006

.021

.115

.105

.101**

𝑒 𝑖𝑗

.212

.003

SD (constant) 𝜇0𝑗

.747**

Est.

Random Effect

.083

.006

.094**

.013

Note. No. of observations=131; No. of groups=20. The average of observations per
group=6.5 (Min.=1 & Max=15). + (p<.08); *(p<.05); **(p<.01)

133

Table 2.12d. Model 2 and 3 for academic achievement with revenue for the team level
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.749**

.049

.001

-.000

.007

.001

.001

.005

-.228

.176

.010

Same team exposure X P4 𝛾21

.023

.001

Revenue (P4) 𝛾01

S.E.

-.000

Different team exposure 𝛾30

Coef.

.83**

Same team exposure 𝛾20

S.E.

.010

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

.658**

SD (Residual)

S.E.

Est.

S.E.

.002

.001

.009

.006

.021

.067

.144

.101**

𝑒 𝑖𝑗

.223

.003

SD (constant) 𝜇0𝑗

.960**

Est.

Random Effect

.083

.006

-.999

.035

Note. No. of observations=131; No. of groups=20. The average of observations per
group=6.5 (Min.=1 & Max=15). + (p<.08); *(p<.05); **(p<.01)

134

Table 2.12e. Model 2 and 3 for academic achievement with tradition for the team level
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.776**

.045

.001

.005

.012

.001

-.000

.005

-.062

.005

-.000

Same team exposure X P5 𝛾21

.023

.001

Tradition (P5) 𝛾01

S.E.

-.000

Different team exposure 𝛾30

Coef.

.83**

Same team exposure 𝛾20

S.E.

.017

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

.658**

SD (Residual)

S.E.

Est.

S.E.

.002

.020

.014

.006

.021

.332

.221

.101**

𝑒 𝑖𝑗

.274

.003

SD (constant) 𝜇0𝑗

.803**

Est.

Random Effect

.083

.006

.103**

.015

Note. No. of observations=131; No. of groups=20. The average of observations per
group=6.5 (Min.=1 & Max=15). + (p<.08); *(p<.05); **(p<.01)

135

Table 2.12f. Model 2 and 3 for academic achievement with coach’s regard for
academics for the team level
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.759**

.043

.001

.021

.084

.001

.000

.004

-.057

.262

-.003

Same team exposure X Q 𝛾21

.023

.001

Coach’s regard for academics (Q) 𝛾01

S.E.

-.000

Different team exposure 𝛾30

Coef.

.83**

Same team exposure 𝛾20

S.E.

.015

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

.658**

SD (Residual)

S.E.

Est.

S.E.

.002

.001

.001

.006

.021

.108

.105

.101**

𝑒 𝑖𝑗

1.474

.003

SD (constant) 𝜇0𝑗

1.474

Est.

Random Effect

.083

.006

.103**

.015

Note. No. of observations=131; No. of groups=20. The average of observations per
group=6.5 (Min.=1 & Max=15). + (p<.08); *(p<.05); **(p<.01)

136

Table 2.12g. Model 2 and 3 for academic achievement with task cohesion for the team
level
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.779**

.046

.001

-.136+

.082

.001

.001

.005

-.291

.190

.020+

Same team exposure X R 𝛾21

.023

.001

Task cohesion (R) 𝛾01

S.E.

-.000

Different team exposure 𝛾30

Coef.

.83**

Same team exposure 𝛾20

S.E.

.011

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

.658**

SD (Residual)

S.E.

Est.

S.E.

.002

.013

.011

.006

.021

.243

.169

.101**

𝑒 𝑖𝑗

1.377

.003

SD (constant) 𝜇0𝑗

2.76*

Est.

Random Effect

.083

.006

.104**

.014

Note. No. of observations=131; No. of groups=20. The average of observations per
group=6.5 (Min.=1 & Max=15). + (p<.08); *(p<.05); **(p<.01)

137

Table 2.12h. Model 2 and 3 for academic achievement with social cohesion for the team
level
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.781**

.046

.001

-.061

.069

.001

.001

.005

-.145

.163

.009

Same team exposure X S 𝛾21

.023

.001

Social cohesion (S) 𝛾01

S.E.

-.000

Different team exposure 𝛾30

Coef.

.83**

Same team exposure 𝛾20

S.E.

.009

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

.658**

SD (Residual)

S.E.

Est.

S.E.

.002

.016

.013

.006

.021

.270

.209

.101**

𝑒 𝑖𝑗

1.157

.003

SD (constant) 𝜇0𝑗

1.699

Est.

Random Effect

.083

.006

.106**

.015

Note. No. of observations=131; No. of groups=20. The average of observations per
group=6.5 (Min.=1 & Max=15). + (p<.08); *(p<.05); **(p<.01)

138

Table 2.13a. Model 2 and 3 for academic efficacy with team size at both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.605**

.080

.004

-.006

.018

.003

.009

.013

-.005

.004

.000

Same team exposure X P1 𝛾21

.049

.008*

Team size (P1) 𝛾01

S.E.

.007

Different team exposure 𝛾30

Coef.

.703**

Same team exposure 𝛾20

S.E.

.000

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

1.15**

SD (Residual)

S.E.

Est.

S.E.

.004

.005

.013

.063

.061

.147

.244

.408**

𝑒 𝑖𝑗

.492

.011**

SD (constant) 𝜇0𝑗

1.867**

Est.

Random Effect

.223

.022

.340**

.035

Note. No. of observations=131; No. of groups=20. The average of observations per
group=6.5 (Min.=1 & Max=15). + (p<.08); *(p<.05); **(p<.01)

139

Table 2.13b. Model 2 and 3 for academic efficacy with popularity at both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.603**

.080

.004

.018

.023

.003

.010

.013

.130

.101

-.004

Same team exposure X P2 𝛾21

.049

.008*

Popularity (P2) 𝛾01

S.E.

.007

Different team exposure 𝛾30

Coef.

.703**

Same team exposure 𝛾20

S.E.

.005

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

1.15**

SD (Residual)

S.E.

Est.

S.E.

.004

.009

.013

.063

.061

.032

.239

.408**

𝑒 𝑖𝑗

.506

.011**

SD (constant) 𝜇0𝑗

1.135**

Est.

Random Effect

.223

.022

.339**

.035

Note. No. of observations=131; No. of groups=20. The average of observations per
group=6.5 (Min.=1 & Max=15). + (p<.08); *(p<.05); **(p<.01)

140

Table 2.13c. Model 2 and 3 for academic efficacy with winter season at both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.625**

.081

.004

-.005

.015

.003

.006

.013

-1.124*

.488

.059*

Same team exposure X P3 𝛾21

.049

.008*

Winter season (P3) 𝛾01

S.E.

.007

Different team exposure 𝛾30

Coef.

.703**

Same team exposure 𝛾20

S.E.

.027

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

1.15**

SD (Residual)

S.E.

Est.

S.E.

.004

.021

.015

.063

.061

.185

.287

.408**

𝑒 𝑖𝑗

.460

.011**

SD (constant) 𝜇0𝑗

1.778**

Est.

Random Effect

.223

.022

.338**

.036

Note. No. of observations=131; No. of groups=20. The average of observations per
group=6.5 (Min.=1 & Max=15). + (p<.08); *(p<.05); **(p<.01)

141

Table 2.13d. Model 2 and 3 for academic efficacy with revenue at both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.596**

.080

.004

-.011

.017

.003

.011

.013

-.829+

.434

.038

Same team exposure X P4 𝛾21

.049

.008*

Revenue (P4) 𝛾01

S.E.

.007

Different team exposure 𝛾30

Coef.

.703**

Same team exposure 𝛾20

S.E.

.024

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

1.15**

SD (Residual)

S.E.

Est.

S.E.

.004

.014

.013

.063

.061

.035

.250

.408**

𝑒 𝑖𝑗

.493

.011**

SD (constant) 𝜇0𝑗

1.987**

Est.

Random Effect

.223

.022

.335**

.035

Note. No. of observations=131; No. of groups=20. The average of observations per
group=6.5 (Min.=1 & Max=15). + (p<.08); *(p<.05); **(p<.01)

142

Table 2.13e. Model 2 and 3 for academic efficacy with tradition at both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.623**

.080

.004

-.003

.019

.003

.008

.013

-.416

.470

.012

Same team exposure X P5 𝛾21

.049

.008*

Tradition (P5) 𝛾01

S.E.

.007

Different team exposure 𝛾30

Coef.

.703**

Same team exposure 𝛾20

S.E.

.025

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

1.15**

SD (Residual)

S.E.

Est.

S.E.

.004

.009

.060

.063

.061

.112

1.355

.408**

𝑒 𝑖𝑗

.504

.011**

SD (constant) 𝜇0𝑗

1.791**

Est.

Random Effect

.223

.022

.344**

.038

Note. No. of observations=131; No. of groups=20. The average of observations per
group=6.5 (Min.=1 & Max=15). + (p<.08); *(p<.05); **(p<.01)

143

Table 2.13f. Model 2 and 3 for academic efficacy with coach’s regard for academics at
both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.669**

.088

.004

-.053

.210

.003

.007

.015

-.183

.735

.011

Same team exposure X Q 𝛾21

.049

.008*

Coach’s regard for academics (Q) 𝛾01

S.E.

.007

Different team exposure 𝛾30

Coef.

.703**

Same team exposure 𝛾20

S.E.

.038

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

1.15**

SD (Residual)

S.E.

Est.

S.E.

.004

.000

.025

.063

.061

.098

.460

.408**

𝑒 𝑖𝑗

4.099

.011**

SD (constant) 𝜇0𝑗

2.276

Est.

Random Effect

.223

.022

.393**

.012

Note. No. of observations=131; No. of groups=20. The average of observations per
group=6.5 (Min.=1 & Max=15). + (p<.08); *(p<.05); **(p<.01)

144

Table 2.13g. Model 2 and 3 for academic efficacy with task cohesion at both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.604**

.081

.004

-.093

.170

.003

.011

.013

.015

.428

.013

Same team exposure X R 𝛾21

.049

.008*

Task cohesion (R) 𝛾01

S.E.

.007

Different team exposure 𝛾30

Coef.

.703**

Same team exposure 𝛾20

S.E.

.023

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

1.15**

SD (Residual)

S.E.

Est.

S.E.

.004

.027

.030

.063

.061

.474

.507

.408**

𝑒 𝑖𝑗

3.043

.011**

SD (constant) 𝜇0𝑗

1.424

Est.

Random Effect

.223

.022

.345**

.038

Note. No. of observations=131; No. of groups=20. The average of observations per
group=6.5 (Min.=1 & Max=15). + (p<.08); *(p<.05); **(p<.01)

145

Table 2.13h. Model 2 and 3 for academic efficacy with social cohesion at both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.606**

.080

.004

-.099

.118

.003

.010

.013

-.062

.316

.014

Same team exposure X S 𝛾21

.049

.008*

Social cohesion (S) 𝛾01

S.E.

.007

Different team exposure 𝛾30

Coef.

.703**

Same team exposure 𝛾20

S.E.

.016

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

1.15**

SD (Residual)

S.E.

Est.

S.E.

.004

.016

.030

.063

.061

.332

.467

.408**

𝑒 𝑖𝑗

2.223

.011**

SD (constant) 𝜇0𝑗

2.012

Est.

Random Effect

.223

.022

.341**

.036

Note. No. of observations=131; No. of groups=20. The average of observations per
group=6.5 (Min.=1 & Max=15). + (p<.08); *(p<.05); **(p<.01)

146

Table 2.14a. Model 2 and 3 for college aspiration with team size at both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.499**

.208

.003

-.046

.027

.002

.047*

.021

-.013

.008

.000

Same team exposure X P1 𝛾21

.078

.001

Team size (P1) 𝛾01

S.E.

.000

Different team exposure 𝛾30

Coef.

.852**

Same team exposure 𝛾20

S.E.

.000

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

.675+

SD (Residual)

S.E.

Est.

S.E.

.003

.001

.000

.016

.044

.098

.078

.350**

𝑒 𝑖𝑗

1.096

.007**

SD (constant) 𝜇0𝑗

2.538**

Est.

Random Effect

.385

.019

.538**

.054

Note. No. of observations=131; No. of groups=20. The average of observations per
group=6.5 (Min.=1 & Max=15). + (p<.08); *(p<.05); **(p<.01)

147

Table 2.14b. Model 2 and 3 for college aspiration with popularity at both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.527**

.216

.003

.006

.039

.002

.042*

.020

.100

.192

-.005

Same team exposure X P2 𝛾21

.078

.001

Popularity (P2) 𝛾01

S.E.

.000

Different team exposure 𝛾30

Coef.

.852**

Same team exposure 𝛾20

S.E.

.008

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

.675+

SD (Residual)

S.E.

Est.

S.E.

.003

.027

.026

.016

.044

.787

.607

.350**

𝑒 𝑖𝑗

1.342

.007**

SD (constant) 𝜇0𝑗

1.290

Est.

Random Effect

.385

.019

.514**

.056

Note. No. of observations=131; No. of groups=20. The average of observations per
group=6.5 (Min.=1 & Max=15). + (p<.08); *(p<.05); **(p<.01)

148

Table 2.14c. Model 2 and 3 for college aspiration with winter season at both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.597**

.215

.003

-.007

.023

.002

.049*

.020

1.121

.877

-.043

Same team exposure X P3 𝛾21

.078

.001

Winter season (P3) 𝛾01

S.E.

.000

Different team exposure 𝛾30

Coef.

.852**

Same team exposure 𝛾20

S.E.

.040

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

.675+

SD (Residual)

S.E.

Est.

S.E.

.003

.018

.021

.016

.044

.628

.457

.350**

𝑒 𝑖𝑗

1.130

.007**

SD (constant) 𝜇0𝑗

1.050

Est.

Random Effect

.385

.019

.501**

.052

Note. No. of observations=131; No. of groups=20. The average of observations per
group=6.5 (Min.=1 & Max=15). + (p<.08); *(p<.05); **(p<.01)

149

Table 2.14d. Model 2 and 3 for college aspiration with revenue at both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.078

.597**

.220

.003

-.027

.028

.001

.002

.044*

.021

-.388

.851

.017

.038

1.646

Revenue (P4) 𝛾01

S.E.

.000

Different team exposure 𝛾30

Coef.

.852**

Same team exposure 𝛾20

S.E.

1.178

Same team exposure X P4 𝛾21
Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

Random Effect

Est.

SD (Residual)

S.E.

.003

.021

.022

.016

.044

.677

.487

.350**

𝑒 𝑖𝑗

Est.

.007**

SD (constant) 𝜇0𝑗

S.E.

.019

.515**

.053

Note. No. of observations=131; No. of groups=20. The average of observations per
group=6.5 (Min.=1 & Max=15). + (p<.08); *(p<.05); **(p<.01)

150

Table 2.14e. Model 2 and 3 for college aspiration with tradition at both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.593**

.220

.003

-.017

.029

.002

.044*

.021

.097

.883

-.001

Same team exposure X P5 𝛾21

.078

.001

Tradition (P5) 𝛾01

S.E.

.000

Different team exposure 𝛾30

Coef.

.852**

Same team exposure 𝛾20

S.E.

.039

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

.675+

SD (Residual)

S.E.

Est.

S.E.

.003

.021

.022

.016

.044

.678

.477

.350**

𝑒 𝑖𝑗

1.206

.007**

SD (constant) 𝜇0𝑗

1.390

Est.

Random Effect

.385

.019

.514**

.052

Note. No. of observations=131; No. of groups=20. The average of observations per
group=6.5 (Min.=1 & Max=15). + (p<.08); *(p<.05); **(p<.01)

151

Table 2.14f. Model 2 and 3 for college aspiration with coach’s regard for academics at
both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.499**

.207

.003

-.110

.292

.002

.047*

.020

-.776

1.174

.017

Same team exposure X Q 𝛾21

.078

.001

Coach’s regard for academics (Q) 𝛾01

S.E.

.000

Different team exposure 𝛾30

Coef.

.852**

Same team exposure 𝛾20

S.E.

.053

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

.675+

SD (Residual)

S.E.

Est.

S.E.

.003

.024

.022

.016

.044

.658

.505

.350**

𝑒 𝑖𝑗

6.599

.007**

SD (constant) 𝜇0𝑗

6.096

Est.

Random Effect

.385

.019

.509**

.052

Note. No. of observations=131; No. of groups=20. The average of observations per
group=6.5 (Min.=1 & Max=15). + (p<.08); *(p<.05); **(p<.01)

152

Table 2.14g. Model 2 and 3 for college aspiration with task cohesion at both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.544**

.215

.003

-.166

.207

.002

.044*

.020

-.528

.616

.021

Same team exposure X R 𝛾21

.078

.001

Task cohesion (R) 𝛾01

S.E.

.000

Different team exposure 𝛾30

Coef.

.852**

Same team exposure 𝛾20

S.E.

.029

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

.675+

SD (Residual)

S.E.

Est.

S.E.

.003

.020

.028

.016

.044

.636

.636

.350**

𝑒 𝑖𝑗

4.402

.007**

SD (constant) 𝜇0𝑗

5.366

Est.

Random Effect

.385

.019

.515**

.057

Note. No. of observations=131; No. of groups=20. The average of observations per
group=6.5 (Min.=1 & Max=15). + (p<.08); *(p<.05); **(p<.01)

153

Table 2.14h. Model 2 and 3 for college aspiration with social cohesion at both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.595**

.219

.003

-.140

.172

.002

.047*

.020

-.385

.544

.017

Same team exposure X S 𝛾21

.078

.001

Social cohesion (S) 𝛾01

S.E.

.000

Different team exposure 𝛾30

Coef.

.852**

Same team exposure 𝛾20

S.E.

.024

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

.675+

SD (Residual)

S.E.

Est.

S.E.

.003

.019

.023

.016

.044

.617

.50

.350**

𝑒 𝑖𝑗

3.896

.007**

SD (constant) 𝜇0𝑗

4.128

Est.

Random Effect

.385

.019

.516**

.053

Note. No. of observations=131; No. of groups=20. The average of observations per
group=6.5 (Min.=1 & Max=15). + (p<.08); *(p<.05); **(p<.01)

154

Table 2.15a. Model 2 and 3 for college expectation with team size at both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.783**

.111

.002

-.018

.017

.002

.028*

.014

.007

.005

-.000

Same team exposure X P1 𝛾21

.057

-.000

Team size (P1) 𝛾01

S.E.

.000

Different team exposure 𝛾30

Coef.

.667**

Same team exposure 𝛾20

S.E.

.000

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

1.63**

SD (Residual)

S.E.

Est.

S.E.

.007

.000

.000

.016

.101

.000

.000

.322**

𝑒 𝑖𝑗

.676

.002

SD (constant) 𝜇0𝑗

.839

Est.

Random Effect

.286

.018

.353**

..024

Note. No. of observations=131; No. of groups=20. The average of observations per
group=6.5 (Min.=1 & Max=15). + (p<.08); *(p<.05); **(p<.01)

155

Table 2.15b. Model 2 and 3 for college expectation with popularity at both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.749**

.112

.002

-.042

.025

.002

.026+

.014

-.081

.115

.003

Same team exposure X P2 𝛾21

.057

-.000

Popularity (P2) 𝛾01

S.E.

.000

Different team exposure 𝛾30

Coef.

.667**

Same team exposure 𝛾20

S.E.

.005

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

1.63**

SD (Residual)

S.E.

Est.

S.E.

.007

.009

.050

.016

.101

.163

.894

.322**

𝑒 𝑖𝑗

.673

.002

SD (constant) 𝜇0𝑗

1.649**

Est.

Random Effect

.286

.018

.356**

.042

Note. No. of observations=131; No. of groups=20. The average of observations per
group=6.5 (Min.=1 & Max=15). + (p<.08); *(p<.05); **(p<.01)

156

Table 2.15c. Model 2 and 3 for college expectation with winter season at both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.745**

.112

.002

-.034*

.015

.002

.023

.015

-.273

.530

.014

Same team exposure X P3 𝛾21

.057

-.000

Winter season (P3) 𝛾01

S.E.

.000

Different team exposure 𝛾30

Coef.

.667**

Same team exposure 𝛾20

S.E.

.025

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

1.63**

SD (Residual)

S.E.

Est.

S.E.

.007

1.06

1.05

.016

.101

2.01

2.06

.322**

𝑒 𝑖𝑗

.618

.002

SD (constant) 𝜇0𝑗

1.492*

Est.

Random Effect

.286

.018

.361

.357

Note. No. of observations=131; No. of groups=20. The average of observations per
group=6.5 (Min.=1 & Max=15). + (p<.08); *(p<.05); **(p<.01)

157

Table 2.15d. Model 2 and 3 for college expectation with revenue at both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.565**

.112

.002

-.031

.015

.002

.023

.015

-.273

.530

.014

Same team exposure X P4 𝛾21

.057

-.000

Revenue (P4) 𝛾01

S.E.

.000

Different team exposure 𝛾30

Coef.

.667**

Same team exposure 𝛾20

S.E.

.025

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

1.63**

SD (Residual)

S.E.

Est.

S.E.

.007

1.06

1.05

.016

.101

2.01

2.06

.322**

𝑒 𝑖𝑗

.618

.002

SD (constant) 𝜇0𝑗

1.430**

Est.

Random Effect

.286

.018

.361

.357

Note. No. of observations=131; No. of groups=20. The average of observations per
group=6.5 (Min.=1 & Max=15). + (p<.08); *(p<.05); **(p<.01)

158

Table 2.15e. Model 2 and 3 for college expectation with tradition at both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.752**

.111

.002

-.027

.019

.002

.025

.015

.107

.522

-.000

Same team exposure X P5 𝛾21

.057

-.000

Tradition (P5) 𝛾01

S.E.

.000

Different team exposure 𝛾30

Coef.

.667**

Same team exposure 𝛾20

S.E.

.024

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

1.63**

SD (Residual)

S.E.

Est.

S.E.

.007

.002

.196

.016

.101

.048

3.65

.322**

𝑒 𝑖𝑗

.693

.002

SD (constant) 𝜇0𝑗

1.24+

Est.

Random Effect

.286

.018

.359**

.040

Note. No. of observations=131; No. of groups=20. The average of observations per
group=6.5 (Min.=1 & Max=15). + (p<.08); *(p<.05); **(p<.01)

159

Table 2.15f. Model 2 and 3 for college expectation with coach’s regard for academics at
both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.695**

.116

.002

.141

.188

.002

.030*

.014

.542

.721

-.031

Same team exposure X Q 𝛾21

.057

-.000

Coach’s regard for academics (Q) 𝛾01

S.E.

.000

Different team exposure 𝛾30

Coef.

.667**

Same team exposure 𝛾20

S.E.

.034

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

1.63**

SD (Residual)

S.E.

Est.

S.E.

.007

.017

.022

.016

.101

.297

.435

.322**

𝑒 𝑖𝑗

4.09

.002

SD (constant) 𝜇0𝑗

-1.37

Est.

Random Effect

.286

.018

.348**

.037

Note. No. of observations=131; No. of groups=20. The average of observations per
group=6.5 (Min.=1 & Max=15). + (p<.08); *(p<.05); **(p<.01)

160

Table 2.15g. Model 2 and 3 for college expectation with task cohesion at both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.729**

.111

.002

.145

.133

.002

.025

.014

.470

.368

-.025

Same team exposure X R 𝛾21

.057

-.000

Task cohesion (R) 𝛾01

S.E.

.000

Different team exposure 𝛾30

Coef.

.667**

Same team exposure 𝛾20

S.E.

.018

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

1.63**

SD (Residual)

S.E.

Est.

S.E.

.007

.016

.032

.016

.101

.170

.577

.322**

𝑒 𝑖𝑗

2.62

.002

SD (constant) 𝜇0𝑗

-1.80

Est.

Random Effect

.286

.018

.352

.040

Note. No. of observations=131; No. of groups=20. The average of observations per
group=6.5 (Min.=1 & Max=15). + (p<.08); *(p<.05); **(p<.01)

161

Table 2.15h. Model 2 and 3 for college expectation with social cohesion at both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.679**

.112

.002

.015

.107

.002

.021

.013

.096

.336

-.005

Same team exposure X S 𝛾21

.057

-.000

Social cohesion (S) 𝛾01

S.E.

.000

Different team exposure 𝛾30

Coef.

.667**

Same team exposure 𝛾20

S.E.

.015

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

1.63**

SD (Residual)

S.E.

Est.

S.E.

.007

.013

.033

.016

.101

.474

.808

.322**

𝑒 𝑖𝑗

2.40

.002

SD (constant) 𝜇0𝑗

.958

Est.

Random Effect

.286

.018

.324**

.049

Note. No. of observations=131; No. of groups=20. The average of observations per
group=6.5 (Min.=1 & Max=15). + (p<.08); *(p<.05); **(p<.01)

162

Table 2.16a. Model 2 and 3 for student identity with team size at both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.759**

.076

.005

-.059*

.027

.005

.034*

.016

-.008

.009

.000

Same team exposure X P1 𝛾21

.000

.002

Team size (P1) 𝛾01

S.E.

.000

Different team exposure 𝛾30

Coef.

.709**

Same team exposure 𝛾20

S.E.

.000

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

1.48**

SD (Residual)

S.E.

Est.

S.E.

.008

.027

.019

.240*

.12

.701

.412

.647**

𝑒 𝑖𝑗

.703

.012

SD (constant) 𝜇0𝑗

1.85**

Est.

Random Effect

.276

.039

.596**

.057

Note. No. of observations=131; No. of groups=20. The average of observations per
group=6.5 (Min.=1 & Max=15). + (p<.08); *(p<.05); **(p<.01)

163

Table 2.16b. Model 2 and 3 for student identity with popularity at both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.775**

.074

.005

-.027

.036

.005

.033*

.016

.010

.185

-.002

Same team exposure X P2 𝛾21

.000

.002

Popularity (P2) 𝛾01

S.E.

.000

Different team exposure 𝛾30

Coef.

.709**

Same team exposure 𝛾20

S.E.

.008

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

1.48**

SD (Residual)

S.E.

Est.

S.E.

.008

.031

.019

.240*

.12

.749

.408

.647**

𝑒 𝑖𝑗

.842

.012

SD (constant) 𝜇0𝑗

1.275

Est.

Random Effect

.276

.039

.598**

.057

Note. No. of observations=131; No. of groups=20. The average of observations per
group=6.5 (Min.=1 & Max=15). + (p<.08); *(p<.05); **(p<.01)

164

Table 2.16c. Model 2 and 3 for student identity with winter season at both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.773**

.075

.005

-.041+

.023

.005

.038*

.016

.282

.827

-.005

Same team exposure X P3 𝛾21

.000

.002

Winter season (P3) 𝛾01

S.E.

.000

Different team exposure 𝛾30

Coef.

.709**

Same team exposure 𝛾20

S.E.

.037

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

1.48**

SD (Residual)

S.E.

Est.

S.E.

.008

.030

.023

.240*

.12

.694

.506

.647**

𝑒 𝑖𝑗

.619

.012

SD (constant) 𝜇0𝑗

1.31*

Est.

Random Effect

.276

.039

.615**

.059

Note. No. of observations=131; No. of groups=20. The average of observations per
group=6.5 (Min.=1 & Max=15). + (p<.08); *(p<.05); **(p<.01)

165

Table 2.16d. Model 2 and 3 for student identity with revenue at both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.773**

.074

.005

-.047+

.027

.005

.034*

.016

-.183

.839

.018

Same team exposure X P4 𝛾21

.000

.002

Revenue (P4) 𝛾01

S.E.

.000

Different team exposure 𝛾30

Coef.

.709**

Same team exposure 𝛾20

S.E.

.038

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

1.48**

SD (Residual)

S.E.

Est.

S.E.

.008

.036

.019

.240*

.12

.857

.410

.647**

𝑒 𝑖𝑗

.715

.012

SD (constant) 𝜇0𝑗

1.44*

Est.

Random Effect

.276

.039

.587**

.056

Note. No. of observations=131; No. of groups=20. The average of observations per
group=6.5 (Min.=1 & Max=15). + (p<.08); *(p<.05); **(p<.01)

166

Table 2.16e. Model 2 and 3 for student identity with tradition at both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.774**

.074

.005

-.032

.029

.005

.035*

.016

.249

.853

-.003

Same team exposure X P5 𝛾21

.000

.002

Tradition (P5) 𝛾01

S.E.

.000

Different team exposure 𝛾30

Coef.

.709**

Same team exposure 𝛾20

S.E.

.039

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

1.48**

SD (Residual)

S.E.

Est.

S.E.

.008

.035

.020

.240*

.12

.828

.419

.647**

𝑒 𝑖𝑗

.753

.012

SD (constant) 𝜇0𝑗

1.12

Est.

Random Effect

.276

.039

.594**

.057

Note. No. of observations=131; No. of groups=20. The average of observations per
group=6.5 (Min.=1 & Max=15). + (p<.08); *(p<.05); **(p<.01)

167

Table 2.16f. Model 2 and 3 for student identity with coach’s regard for academics at
both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.769**

.074

.005

.257

.278

.005

.033*

.016

1.02

1.07

-0.52

Same team exposure X Q 𝛾21

.000

.002

Coach’s regard for academics (Q) 𝛾01

S.E.

.000

Different team exposure 𝛾30

Coef.

.709**

Same team exposure 𝛾20

S.E.

.049

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

1.48**

SD (Residual)

S.E.

Est.

S.E.

.008

.026

.019

.240*

.12

.644

.426

.647**

𝑒 𝑖𝑗

6.06

.012

SD (constant) 𝜇0𝑗

-4.33

Est.

Random Effect

.276

.039

.603**

.058

Note. No. of observations=131; No. of groups=20. The average of observations per
group=6.5 (Min.=1 & Max=15). + (p<.08); *(p<.05); **(p<.01)

168

Table 2.16g. Model 2 and 3 for student identity with task cohesion at both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.766**

.071

.005

-.385*

.161

.005

.031*

.015

-1.238**

.462

.047*

Same team exposure X R 𝛾21

.000

.002

Task cohesion (R) 𝛾01

S.E.

.000

Different team exposure 𝛾30

Coef.

.709**

Same team exposure 𝛾20

S.E.

.022

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

1.48**

SD (Residual)

S.E.

Est.

S.E.

.008

.000

.005

.240*

.12

.001

.002

.647**

𝑒 𝑖𝑗

3.32

.012

SD (constant) 𝜇0𝑗

10.41**

Est.

Random Effect

.276

.039

.589**

.054

Note. No. of observations=131; No. of groups=20. The average of observations per
group=6.5 (Min.=1 & Max=15). + (p<.08); *(p<.05); **(p<.01)

169

Table 2.16h. Model 2 and 3 for student identity with social cohesion at both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.774**

.073

.005

-.260

.176

.005

.033*

.016

-.812

.540

.031

Same team exposure X S 𝛾21

.000

.002

Social cohesion (S) 𝛾01

S.E.

.000

Different team exposure 𝛾30

Coef.

.709**

Same team exposure 𝛾20

S.E.

.024

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

1.48**

SD (Residual)

S.E.

Est.

S.E.

.008

.028

.023

.240*

.12

.626

.491

.647**

𝑒 𝑖𝑗

3.80

.012

SD (constant) 𝜇0𝑗

7.09+

Est.

Random Effect

.276

.039

.595**

.057

Note. No. of observations=131; No. of groups=20. The average of observations per
group=6.5 (Min.=1 & Max=15). + (p<.08); *(p<.05); **(p<.01)

170

Table 2.17a. Model 2 and 3 for athletic identity with team size at both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.794**

.083

.004

.005

.026

.004

-.001

.015

.003

.008

.000

Same team exposure X P1 𝛾21

.046

-.000

Team size (P1) 𝛾01

S.E.

.006

Different team exposure 𝛾30

Coef.

.811**

Same team exposure 𝛾20

S.E.

.000

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

.832**

SD (Residual)

S.E.

Est.

S.E.

.010

.018

.049

.198

.115

.327

1.10

.606**

𝑒 𝑖𝑗

.574

.005

SD (constant) 𝜇0𝑗

.703

Est.

Random Effect

.235

.035

.630**

.063

Note. No. of observations=171; No. of groups=20. The average of observation per
group=8.6 (Min.=1 & Max=19). + (p<.08); *(p<.05); **(p<.01)

171

Table 2.17b. Model 2 and 3 for athletic identity with popularity at both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.819**

.082

.004

.020

.036

.004

-.000

.015

-.003

.169

.890

Same team exposure X P2 𝛾21

.046

-.000

Popularity (P2) 𝛾01

S.E.

.006

Different team exposure 𝛾30

Coef.

.811**

Same team exposure 𝛾20

S.E.

.007

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

.832**

SD (Residual)

S.E.

Est.

S.E.

.010

.000

.000

.198

.115

.001

.001

.606**

𝑒 𝑖𝑗

.899

.005

SD (constant) 𝜇0𝑗

.898

Est.

Random Effect

.235

.035

.637**

.045

Note. No. of observations=171; No. of groups=20. The average of observation per
group=8.6 (Min.=1 & Max=19). + (p<.08); *(p<.05); **(p<.01)

172

Table 2.17c. Model 2 and 3 for athletic identity with winter season at both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.845**

.085

.004

-.001

.020

.004

-.002

.016

-.918

.806

.039

Same team exposure X P3 𝛾21

.046

-.000

Winter season (P3) 𝛾01

S.E.

.006

Different team exposure 𝛾30

Coef.

.811**

Same team exposure 𝛾20

S.E.

.038

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

.832**

SD (Residual)

S.E.

Est.

S.E.

.010

.005

.023

.198

.115

.115

.495

.606**

𝑒 𝑖𝑗

.568

.005

SD (constant) 𝜇0𝑗

.882

Est.

Random Effect

.235

.035

.634**

.062

Note. No. of observations=171; No. of groups=20. The average of observation per
group=8.6 (Min.=1 & Max=19). + (p<.08); *(p<.05); **(p<.01)

173

Table 2.17d. Model 2 and 3 for athletic identity with revenue at both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.830**

.080

.004

-.007

.022

.004

-.002

.014

-.372

.775

.042

Same team exposure X P4 𝛾21

.046

-.000

Revenue (P4) 𝛾01

S.E.

.006

Different team exposure 𝛾30

Coef.

.811**

Same team exposure 𝛾20

S.E.

.035

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

.832**

SD (Residual)

S.E.

Est.

S.E.

.010

.023

.026

.198

.115

.554

.604

.606**

𝑒 𝑖𝑗

.547

.005

SD (constant) 𝜇0𝑗

.839

Est.

Random Effect

.235

.035

.604**

.058

Note. No. of observations=171; No. of groups=20. The average of observation per
group=8.6 (Min.=1 & Max=19). + (p<.08); *(p<.05); **(p<.01)

174

Table 2.17e. Model 2 and 3 for athletic identity with tradition at both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.845**

.081

.004

.027

.027

.004

.004

.016

1.07

.743

-.039

Same team exposure X P5 𝛾21

.046

-.000

Tradition (P5) 𝛾01

S.E.

.006

Different team exposure 𝛾30

Coef.

.811**

Same team exposure 𝛾20

S.E.

.036

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

.832**

SD (Residual)

S.E.

Est.

S.E.

.010

.024

.026

.198

.115

.332

.571

.606**

𝑒 𝑖𝑗

.678

.005

SD (constant) 𝜇0𝑗

-.031

Est.

Random Effect

.235

.035

.628**

.062

Note. No. of observations=171; No. of groups=20. The average of observation per
group=8.6 (Min.=1 & Max=19). + (p<.08); *(p<.05); **(p<.01)

175

Table 2.17f. Model 2 and 3 for athletic identity with coach’s regard for academics at both
levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.923**

.083

.004

.242

.290

.004

.004

.016

.408

1.09

-.042

Same team exposure X Q 𝛾21

.046

-.000

Coach’s regard for academics (Q) 𝛾01

S.E.

.006

Different team exposure 𝛾30

Coef.

.811**

Same team exposure 𝛾20

S.E.

.051

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

.832**

SD (Residual)

S.E.

Est.

S.E.

.010

.035

.031

.198

.115

.698

.649

.606**

𝑒 𝑖𝑗

6.15

.005

SD (constant) 𝜇0𝑗

-2.07

Est.

Random Effect

.235

.035

.637**

.064

Note. No. of observations=171; No. of groups=20. The average of observation per
group=8.6 (Min.=1 & Max=19). + (p<.08); *(p<.05); **(p<.01)

176

Table 2.17g. Model 2 and 3 for athletic identity with task cohesion at both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.843**

.087

.004

-.149

.230

.004

.004

.017

-.530

.619

.021

Same team exposure X R 𝛾21

.046

-.000

Task cohesion (R) 𝛾01

S.E.

.006

Different team exposure 𝛾30

Coef.

.811**

Same team exposure 𝛾20

S.E.

.031

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

.832**

SD (Residual)

S.E.

Est.

S.E.

.010

.013

.026

.198

.115

.051

.569

.606**

𝑒 𝑖𝑗

4.47

.005

SD (constant) 𝜇0𝑗

4.42

Est.

Random Effect

.235

.035

.636**

.063

Note. No. of observations=171; No. of groups=20. The average of observation per
group=8.6 (Min.=1 & Max=19). + (p<.08); *(p<.05); **(p<.01)

177

Table 2.17h. Model 2 and 3 for athletic identity with social cohesion at both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.866**

.085

.004

-.153

.201

.004

.005

.017

-.612

.529

.022

Same team exposure X S 𝛾21

.046

-.000

Social cohesion (S) 𝛾01

S.E.

.006

Different team exposure 𝛾30

Coef.

.811**

Same team exposure 𝛾20

S.E.

.028

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

.832**

SD (Residual)

S.E.

Est.

S.E.

.010

.019

.024

.198

.115

.205

.519

.606**

𝑒 𝑖𝑗

3.75

.005

SD (constant) 𝜇0𝑗

4.83

Est.

Random Effect

.235

.035

.630**

.062

Note. No. of observations=171; No. of groups=20. The average of observation per
group=8.6 (Min.=1 & Max=19). + (p<.08); *(p<.05); **(p<.01)

178

Table 2.18a. Model 2 and 3 for physical ability with team size at both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.254

.270

.005

.024

.079

.006

.013

.038

.040

.030

-.001

Same team exposure X P1 𝛾21

.104

.008

Team size (P1) 𝛾01

S.E.

-.000

Different team exposure 𝛾30

Coef.

.022

Same team exposure 𝛾20

S.E.

.001

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

4.24

SD (Residual)

S.E.

Est.

S.E.

.007

.118

.072

.176

.118

3.08

1.76

.820**

𝑒 𝑖𝑗

2.35

.003

SD (constant) 𝜇0𝑗

1.79

Est.

Random Effect

.561

.046

1.17

1.25

Note. No. of observations=172; No. of groups=20. The average of observation per
group=8.6 (Min.=2 & Max=19). + (p<.08); *(p<.05); **(p<.01)

179

Table 2.18b. Model 2 and 3 for physical ability with popularity at both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.225

.262

.005

-.013

.099

.006

.016

.037

-.120

.552

-.002

Same team exposure X P2 𝛾21

.104

.008

Popularity (P2) 𝛾01

S.E.

-.000

Different team exposure 𝛾30

Coef.

.022

Same team exposure 𝛾20

S.E.

.021

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

4.24

SD (Residual)

S.E.

Est.

S.E.

.007

.108

.063

.176

.118

3.02

1.58

.820**

𝑒 𝑖𝑗

2.94

.003

SD (constant) 𝜇0𝑗

3.99

Est.

Random Effect

.561

.046

1.13**

.118

Note. No. of observations=172; No. of groups=20. The average of observation per
group=8.6 (Min.=2 & Max=19). + (p<.08); *(p<.05); **(p<.01)

180

Table 2.18c. Model 2 and 3 for physical ability with winter season at both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.291

.272

.005

.021

.058

.006

.007

.038

2.08

2.31

-.084

Same team exposure X P3 𝛾21

.104

.008

Winter season (P3) 𝛾01

S.E.

-.000

Different team exposure 𝛾30

Coef.

.022

Same team exposure 𝛾20

S.E.

.092

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

4.24

SD (Residual)

S.E.

Est.

S.E.

.007

.078

.046

.176

.118

2.42

1.16

.820**

𝑒 𝑖𝑗

2.08

.003

SD (constant) 𝜇0𝑗

2.36

Est.

Random Effect

.561

.046

1.17**

.122

Note. No. of observations=172; No. of groups=20. The average of observation per
group=8.6 (Min.=2 & Max=19). + (p<.08); *(p<.05); **(p<.01)

181

Table 2.18d. Model 2 and 3 for physical ability with revenue at both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.271

.268

.005

-.007

.072

.006

.008

.037

.925

2.46

-.012

Same team exposure X P4 𝛾21

.104

.008

Revenue (P4) 𝛾01

S.E.

-.000

Different team exposure 𝛾30

Coef.

.022

Same team exposure 𝛾20

S.E.

.095

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

4.24

SD (Residual)

S.E.

Est.

S.E.

.007

.093

.056

.176

.118

2.73*

1.39

.820**

𝑒 𝑖𝑗

2.27

.003

SD (constant) 𝜇0𝑗

2.83

Est.

Random Effect

.561

.046

1.16**

.120

Note. No. of observations=172; No. of groups=20. The average of observation per
group=8.6 (Min.=2 & Max=19). + (p<.08); *(p<.05); **(p<.01)

182

Table 2.18e. Model 2 and 3 for physical ability with tradition at both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.029

.147

.005

-.007

.039

.006

.003

.038

-2.02

1.43

.080

Same team exposure X P5 𝛾21

.104

.008

Tradition (P5) 𝛾01

S.E.

-.000

Different team exposure 𝛾30

Coef.

.022

Same team exposure 𝛾20

S.E.

.055

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

4.24**

SD (Residual)

S.E.

Est.

S.E.

.007

.063

.043

.176

.118

2.05

1.36

.820**

𝑒 𝑖𝑗

2.473

.003

SD (constant) 𝜇0𝑗

3.783

Est.

Random Effect

.561

.046

1.18**

.121

Note. No. of observations=172; No. of groups=20. The average of observation per
group=8.6 (Min.=2 & Max=19). + (p<.08); *(p<.05); **(p<.01)

183

Table 2.18f. Model 2 and 3 for physical ability with coach’s regard for academics at both
levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.254

.270

.005

.024

.079

.006

.013

.038

.040

.030

-.001

Same team exposure X Q 𝛾21

.104

.008

Coach’s regard for academics (Q) 𝛾01

S.E.

-.000

Different team exposure 𝛾30

Coef.

.022

Same team exposure 𝛾20

S.E.

.001

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

4.24

SD (Residual)

S.E.

Est.

S.E.

.007

.118

.72

.176

.118

3.08

1.76

.820**

𝑒 𝑖𝑗

2.35

.003

SD (constant) 𝜇0𝑗

1.79

Est.

Random Effect

.561

.046

1.17**

.125

Note. No. of observations=172; No. of groups=20. The average of observation per
group=8.6 (Min.=2 & Max=19). + (p<.08); *(p<.05); **(p<.01)

184

Table 2.18g. Model 2 and 3 for physical ability with task cohesion at both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.262

.276

.005

-.857+

.486

.006

.004

.038

-3.00+

1.69

.120+

Same team exposure X R 𝛾21

.104

.008

Task cohesion (R) 𝛾01

S.E.

-.000

Different team exposure 𝛾30

Coef.

.022

Same team exposure 𝛾20

S.E.

.067

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

4.24

SD (Residual)

S.E.

Est.

S.E.

.007

.078

.055

.176

.118

2.49

1.42

.820**

𝑒 𝑖𝑗

12.5

.003

SD (constant) 𝜇0𝑗

24.4

Est.

Random Effect

.561

.046

1.16**

.128

Note. No. of observations=172; No. of groups=20. The average of observation per
group=8.6 (Min.=2 & Max=19). + (p<.08); *(p<.05); **(p<.01)

185

Table 2.18h. Model 2 and 3 for physical ability with social cohesion at both levels
Model2
Model3
Prior status 𝛽1

Fixed Effect

Coef.

.289

.269

.005

-.571

.399

.006

.003

.038

-2.02

1.43

.080

Same team exposure X S 𝛾21

.104

.008

Social cohesion (S) 𝛾01

S.E.

-.000

Different team exposure 𝛾30

Coef.

.022

Same team exposure 𝛾20

S.E.

.055

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

4.24

SD (Residual)

S.E.

Est.

S.E.

.007

.063

.053

.176

.118

2.03

1.36

.820**

𝑒 𝑖𝑗

10.3

.003

SD (constant) 𝜇0𝑗

17.3

Est.

Random Effect

.561

.046

1.18**

.123

Note. No. of observations=172; No. of groups=20. The average of observation per
group=8.6 (Min.=2 & Max=19). + (p<.08); *(p<.05); **(p<.01)

186

Table 2.19a. Model 2 and 3 for physical appearance with team size at both levels
Model2
Prior status 𝛽1

Fixed Effect

Model3

Coef.

.006

.166

.008

.007

.042

.009

.009

.29

-.006

.011

.000

Same team exposure X P1 𝛾21

.161

.010

Team size (P1) 𝛾01

S.E.

.008

Different team exposure 𝛾30

Coef.

.249

Same team exposure 𝛾20

S.E.

.000

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

2.89**

SD (Residual)

S.E.

Est.

S.E.

.001

.006

.038

.389*

.149

.019

.806

1.25**

𝑒 𝑖𝑗

1.09

.000

SD (constant) 𝜇0𝑗

3.79**

Est.

Random Effect

.899

.072

.783**

.079

Note. No. of observations=172; No. of groups=20. The average of observation per
group=8.6 (Min.=1 & Max=19). + (p<.08); *(p<.05); **(p<.01)

187

Table 2.19b. Model 2 and 3 for physical appearance with popularity at both levels
Model2
Prior status 𝛽1

Fixed Effect

Model3

Coef.

-.008

.162

.008

.076

.055

.009

.023

.029

.203

.246

-.012

Same team exposure X P2 𝛾21

.161

.010

Popularity (P2) 𝛾01

S.E.

.008

Different team exposure 𝛾30

Coef.

.249

Same team exposure 𝛾20

S.E.

.011

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

2.89**

SD (Residual)

S.E.

Est.

S.E.

.001

.026

.029

.389*

.149

.190

.585

1.25**

𝑒 𝑖𝑗

1.24

.000

SD (constant) 𝜇0𝑗

2.65*

Est.

Random Effect

.899

.072

.741**

.076

Note. No. of observations=172; No. of groups=20. The average of observation per
group=8.6 (Min.=1 & Max=19). + (p<.08); *(p<.05); **(p<.01)

188

Table 2.19c. Model 2 and 3 for physical appearance with winter season at both levels
Model2
Prior status 𝛽1

Fixed Effect

Model3

Coef.

-.058

.162

.008

.016

.034

.009

.022

.029

-1.26

1.23

.047

Same team exposure X P3 𝛾21

.161

.010

Winter season (P3) 𝛾01

S.E.

.008

Different team exposure 𝛾30

Coef.

.249

Same team exposure 𝛾20

S.E.

.061

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

2.89**

SD (Residual)

S.E.

Est.

S.E.

.001

.037

.028

.389*

.149

.467

.590

1.25**

𝑒 𝑖𝑗

1.02

.000

SD (constant) 𝜇0𝑗

4.01**

Est.

Random Effect

.899

.072

.740**

.073

Note. No. of observations=172; No. of groups=20. The average of observation per
group=8.6 (Min.=1 & Max=19). + (p<.08); *(p<.05); **(p<.01)

189

Table 2.19d. Model 2 and 3 for physical appearance with revenue at both levels
Model2
Prior status 𝛽1

Fixed Effect

Model3

Coef.

-.012

.174

.008

.009

.040

.009

.009

.029

-1.22

1.06

.059

Same team exposure X P4 𝛾21

.161

.010

Revenue (P4) 𝛾01

S.E.

.008

Different team exposure 𝛾30

Coef.

.249

Same team exposure 𝛾20

S.E.

.051

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

2.89**

SD (Residual)

S.E.

Est.

S.E.

.001

.022

.031

.389*

.149

.146

.663

1.25**

𝑒 𝑖𝑗

1.13

.000

SD (constant) 𝜇0𝑗

4.11**

Est.

Random Effect

.899

.072

.764**

.077

Note. No. of observations=172; No. of groups=20. The average of observation per
group=8.6 (Min.=1 & Max=19). + (p<.08); *(p<.05); **(p<.01)

190

Table 2.19e. Model 2 and 3 for physical appearance with tradition at both levels
Model2
Prior status 𝛽1

Fixed Effect

Model3

Coef.

.012

.175

.008

.019

.043

.009

.008

.030

-.711

1.12

.037

Same team exposure X P5 𝛾21

.161

.010

Tradition (P5) 𝛾01

S.E.

.008

Different team exposure 𝛾30

Coef.

.249

Same team exposure 𝛾20

S.E.

.054

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

2.89**

SD (Residual)

S.E.

Est.

S.E.

.001

.020

.018

.389*

.149

.123

.231

1.25**

𝑒 𝑖𝑗

1.13

.000

SD (constant) 𝜇0𝑗

3.79**

Est.

Random Effect

.899

.072

.774**

.074**

Note. No. of observations=172; No. of groups=20. The average of observation per
group=8.6 (Min.=1 & Max=19). + (p<.08); *(p<.05); **(p<.01)

191

Table 2.19f. Model 2 and 3 for physical appearance with coach’s regard for academics
at both levels
Model2
Prior status 𝛽1

Fixed Effect

Model3

Coef.

-.018

.169

.008

-.478

.419

.009

.023

.029

-2.19

1.60

.092

Same team exposure X Q 𝛾21

.161

.010

Coach’s regard for academics (Q) 𝛾01

S.E.

.008

Different team exposure 𝛾30

Coef.

.249

Same team exposure 𝛾20

S.E.

.075

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

2.89**

SD (Residual)

S.E.

Est.

S.E.

.001

.020

.026

.389*

.149

.047

.565

1.25**

𝑒 𝑖𝑗

9.04

.000

SD (constant) 𝜇0𝑗

15.4

Est.

Random Effect

.899

.072

.738**

.076

Note. No. of observations=172; No. of groups=20. The average of observation per
group=8.6 (Min.=1 & Max=19). + (p<.08); *(p<.05); **(p<.01)

192

Table 2.19g. Model 2 and 3 for physical appearance with task cohesion at both levels
Model2
Prior status 𝛽1

Fixed Effect

Model3

Coef.

.011

.181

.008

-.244

.316

.009

.020

.030

-.504

.879

.035

Same team exposure X R 𝛾21

.161

.010

Task cohesion (R) 𝛾01

S.E.

.008

Different team exposure 𝛾30

Coef.

.249

Same team exposure 𝛾20

S.E.

.043

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

2.89**

SD (Residual)

S.E.

Est.

S.E.

.001

.021

.036

.389*

.149

.186

.781

1.25**

𝑒 𝑖𝑗

6.43

.000

SD (constant) 𝜇0𝑗

6.88

Est.

Random Effect

.899

.072

.776**

.078

Note. No. of observations=172; No. of groups=20. The average of observation per
group=8.6 (Min.=1 & Max=19). + (p<.08); *(p<.05); **(p<.01)

193

Table 2.19h. Model 2 and 3 for physical appearance with social cohesion at both levels
Model2
Prior status 𝛽1

Fixed Effect

Model3

Coef.

.001

.179

.008

-.143

.247

.009

.018

.030

-.339

.679

.025

Same team exposure X S 𝛾21

.161

.010

Social cohesion (S) 𝛾01

S.E.

.008

Different team exposure 𝛾30

Coef.

.249

Same team exposure 𝛾20

S.E.

.034

Cross Level Interaction
Constant 𝛾00

SD (slope) 𝜇2𝑗

2.89**

SD (Residual)

S.E.

Est.

S.E.

.001

.028

.034

.389*

.149

.288

.735

1.25**

𝑒 𝑖𝑗

4.92

.000

SD (constant) 𝜇0𝑗

5.73

Est.

Random Effect

.899

.072

.769**

.077

Note. No. of observations=172; No. of groups=20. The average of observation per
group=8.6 (Min.=1 & Max=19). + (p<.08); *(p<.05); **(p<.01)

194

Table 3.1. Descriptive statistics of independent variables of selection models
Variables

No. of all pairs

Mean

Std. Dev.

Min

Max

Network at Time1

46897

0.02

0.13

0.00

1.00

Same gender

46897

0.38

0.49

0.00

1.00

Same team

47525

0.10

0.29

0.00

1.00

Same race

47106

0.53

0.50

0.00

1.00

Similarity of grade

33128

1.18

0.94

0.00

3.00

Similarity of GPA

21179

0.42

0.39

0.00

2.00

Similarity of aspiration

32924

0.20

0.42

0.00

2.00

Similarity of expectation

32924

0.28

0.56

0.00

3.00

Similarity of coach’s regard

32964

1.43

1.13

0.00

6.00

Similarity of other’s expectation

30767

0.53

0.59

0.00

5.00

Similarity of academic efficacy

33658

0.69

0.56

0.00

3.00

Similarity of athlete identity

32559

1.31

0.96

0.00

5.22

Similarity of academic identity

32559

1.19

0.88

0.00

5.00

Similarity of physical appearance

33167

0.72

0.57

0.00

3.00

Similarity of physical ability

33167

0.73

0.55

0.00

3.00

Similarity of task cohesion

33699

1.53

1.26

0.00

8.00

Similarity of social cohesion

33699

1.76

1.47

0.00

7.38

No. of shared extra activities

46897

0.05

0.21

0.00

3.00

No. of shared courses

46897

3.78

2.69

1.00

8.00

195

Table 3.2. Selection model for friendship network at Time2 (n=18505).
XOdds
Std.
Predictors
Stan.
Ratio
Coef.
Err.
coef.

z

Prior network

47.86

3.87

0.39

0.19

20.71*
*

Same gender

2.26

0.81

0.41

0.15

5.51**

team

2.11

0.75

0.20

0.17

4.40**

race

0.74

-0.31

-0.14

0.15

-2.11*

Si. of grade

4.28

1.45

1.35

0.12

12.44*
*

academic achiev.

1.94

0.66

0.21

0.23

2.84**

aspiration

0.57

-0.56

-0.23

0.19

-2.96**

expectation

1.39

0.33

0.16

0.18

1.87+

coach’s regards

1.19

0.18

0.18

0.08

2.32*

others’ edu. expec.

0.96

-0.04

-0.02

0.11

-0.38

academic efficacy

1.28

0.24

0.12

0.14

1.72

athletic identity

0.85

-0.16

-0.15

0.07

-2.17*

academic identity

0.95

-0.05

-0.05

0.08

-0.70

physical appear.

1.34

0.29

0.15

0.14

2.12*

physical ability

1.01

0.01

0.00

0.12

0.07

task cohesion

1.08

0.07

0.08

0.07

1.04

social cohesion

1.05

0.05

0.08

0.05

1.00

No. of shared other acti.

1.76

0.57

0.16

0.16

3.54**

No. of overlapped classes

1.04

0.04

0.08

0.03

1.20

Intercept

0.05

-2.95

0.30

-9.68

Note. Si.=similarity. Odd ratio = exp (coefficient). X-standardized=coefficient * SD of
each variables. + (p<.08); *(p<.05); **(p<.01)
196

Table 3.3. Selection model for forming new friendships (Time1->Time2)
Odds
X-Stan.
Std.
Predictors
Coef.
Ratio
coef.
Err.
Same gender
2.67
0.98
1.63
0.44

z
5.98**

team

2.45

0.90

1.25

0.45

4.92**

race

0.74

-0.30

0.87

0.12

-1.93*

Si. of grade

6.24

1.83

5.48

0.90

12.64**

academic achiev.

2.48

0.91

1.33

0.65

3.47**

aspiration

0.63

-0.46

0.8

0.12

-2.35*

expectation

1.23

0.21

1.10

0.23

1.11

coach’s regards

1.14

0.13

1.14

0.09

1.65

others’ edu. expec.

0.94

-0.06

0.96

0.11

-0.50

academic efficacy

1.25

0.22

1.11

0.19

1.43

athletic identity

0.81

-0.21

0.81

0.07

-2.57*

academic identity

0.94

-0.06

0.94

0.08

-0.72

physical appear.

1.32

0.27

1.15

0.20

1.83+

physical ability

1.01

0.01

1.00

0.13

0.05

task cohesion

1.04

0.04

1.04

0.08

0.55

social cohesion

1.10

0.10

1.15

0.06

1.63

No. of shared other acti.

0.82

-0.20

0.79

0.05

-3.53**

No. of overlapped classes

1.06

0.06

1.12

0.04

1.67

Intercept

0.91

0.98

0.74

-0.11

Si.=similarity. Odd ratio = exp (coefficient). X-standardized=coefficient * SD of each
variables. + (p<.08); *(p<.05); **(p<.01)

197

Table 3.4. Multilevel analysis of selection model with network data at Time2
Model1
Model2
Model3
Fixed Effect-Level1
Coef. S.E. Coef.
S.E.
Coef.
S.E.
Prior network 𝜋1𝑖
4.05** 0.20 3.97**
0.20
0.87** 0.15 0.93**
0.15
Same gender 𝜋2𝑖
0.44** 0.10 0.45**
0.10
team 𝜋3𝑖
-0.28
0.17
-0.22
0.16
race 𝜋4𝑖
Si. of grade 𝜋5𝑖
-1.47** 0.12 -1.50** 0.12
-0.70** 0.25 -0.61*
0.26
academic achiev. 𝜋6𝑖
0.59** 0.21 0.67**
0.24
aspiration 𝜋7𝑖
-0.25
0.19
-0.09
0.21
expectation 𝜋8𝑖
coach’s regards 𝜋9𝑖
-0.22** 0.08 -0.22** 0.08
0.07
0.12
0.10
0.12
others’ edu. expec. 𝜋10𝑖
-0.16
0.15
-0.15
0.16
academic efficacy 𝜋11𝑖
-0.15* 0.08
-0.10
0.08
athletic identity 𝜋12𝑖
academic identity 𝜋13𝑖
0.07
0.08
0.08
0.08
-0.30* 0.15
-0.25
0.15
physical appear. 𝜋14𝑖
-0.01
0.13
0.00
0.13
physical ability 𝜋15𝑖
-0.05
0.08
-0.03
0.08
task cohesion 𝜋16𝑖
-0.07
0.06
-0.06
0.06
social cohesion 𝜋17𝑖
No. of shared other acti. 𝜋18𝑖
0.46** 0.18
0.25
0.18
0.06
0.04
0.06
0.04
No. of overlapped classes 𝜋19𝑖
Fixed Effect-Level2
(nominators’ characteristic)
Gender 𝛽2
0.48**
0.17
0.34**
0.08
Grade 𝛽5
0.39
0.28
Academic achiev. 𝛽6
0.02
0.35
Aspiration 𝛽7
0.16
0.33
Expectation 𝛽8
Coach’s regards 𝛽9
-0.02
0.09
-0.02
0.15
Others’ edu. expec. 𝛽10
0.16
0.18
Academic efficacy 𝛽11
0.00
0.09
Athletic identity 𝛽12
Academic identity 𝛽13
0.09
0.08
-0.09
0.16
Physical appear. 𝛽14
0.09
0.14
Physical ability 𝛽15
0.00
0.10
Task cohesion 𝛽16
Social cohesion 𝛽17
0.05
0.08
-4.18** .055 -3.93
.409
-9.40
2.11
Intercept 𝛽00
Random Effect- Intercept
Est.
S.E.
Est.
S.E.
Est.
S.E.
.189 .052
.384
.145
.145
.106
Var. Level-2 𝜇0𝑖
No. of ties
36852
17766
17766
No. of nominators
196
144
144
Note. Si.=similarity. *(p<.05) **(p<.01).
198

Table 4.1. Descriptive statistics of the five items
Items on
n
Mean
S.D.
Min
Max
interaction
General
770
4.59
.92
1
5

Skew.

Kur.

-2.61

9.41

Academic

839

3.75

1.38

1

5

-.80

2.36

Athletic

837

3.81

1.31

1

5

-.77

2.36

Social

834

4.14

1.19

1

5

-1.33

3.74

Emotional

831

3.67

1.47

1

5

-.68

2.00

Mean of
five items

763

4.03

.92

1

5

-1.09

4.06

199

Table 4.2. The coefficient of one factor model
Items on
Standardized
S.E.
interaction
coefficient

Z

General

.65

.025

26.00***

Academic

.55

.029

37.56***

Athletic

.65

.025

26.16***

Social

.84

.018

45.56***

Emotional

.63

.025

24.82***

*** (p<.000).

200

Table 4.3. Bivariate correlations between the items
1
2
3
4
General
Academic

.320**

Athletic

.286**

.249**

Social

.434**

.311**

.389**

Emotional

.301**

.335**

.358**

.504**

**: p<.01

201

5

Table 4.4. Item-test correlation and reliability
Items on
interaction

n

Item-test
correlation

Average
inter-item
covariance

Cronbach’s
alpha

General

770

.69

.82

.76

Academic

839

.70

.73

.78

Athletic

837

.75

.69

.75

Social

834

.83

.64

.70

Emotional

831

.76

.67

.76

.71

.79

Test scale

202

Table 4.5. Comparison of single-level IRT models
Log
df
AIC
Models
likelihood
2PL-PCM

BIC

LR-test

-6352.34

25

12754.69

12952.96

-

PCM

-6359.61

21

12761.22

12927.77

16.66 (4)**

RSM

-6383.57

9

12785.14

12856.31

47.92 (12)**

Note. 2PL-PCM is the 2-parameter partial-credit model. PCM is the partial-credit model.
RSM is the rating scale model. 2PL-PCM is nested in PCM. PCM is nested in RSM. LRtest is the likelihood ratio test following chi-square distribution. The parenthesis is a
degree of freedom for LR-test. **: p<.01. The criteria of chi-square are 13.28 and 26.22
at df=4 and df=12, respectively, at .01 of type I error.

203

Table 4.6. The results of Multilevel 2PL-PCM
Parameters
Coefficient
S.E.
Z
2.240
.172
12.98**
𝛽1 + 𝜏1
1.968
.340
5.79**
𝛽1 + 𝜏2
3.481
.507
2.85**
𝛽1 + 𝜏3
1.718
.603
2.85**
𝛽1 + 𝜏4
.534
.105
5.08**
𝛽2 + 𝜏1
.268
.122
2.20*
𝛽2 + 𝜏2
1.11
.163
6.84**
𝛽2 + 𝜏3
.070
.181
.39
𝛽2 + 𝜏4
.533
.121
4.37**
𝛽3 + 𝜏1
.233
.137
1.71
𝛽3 + 𝜏2
1.169
.166
7.00**
𝛽3 + 𝜏3
1.344
.215
6.24**
𝛽3 + 𝜏4
.783
.209
3.74**
𝛽4 + 𝜏1
2.302
.426
5.40**
𝛽4 + 𝜏2
3.697
.608
6.08**
𝛽4 + 𝜏3
4.045
.826
4.90**
𝛽4 + 𝜏4
.294
.220
1.34
𝛽5 + 𝜏1
.783
.251
3.12**
𝛽5 + 𝜏2
1.669
.308
5.42**
𝛽5 + 𝜏3
1.854
.411
4.51**
𝛽5 + 𝜏4
1 (fixed)
𝜆1
.341
.060
5.68**
𝜆2
.530
.097
5.46**
𝜆3
1.697
.511
3.32**
𝜆4
.589
.171
3.44**
𝜆5
Variance (tie-level)
2.034 (.637)
Variance (ego-level)
.547 (.244)
Fit index
Log likelihood: -4452.902 df: 30, AIC: 8965.80, BIC: 9203.72

𝛽 𝑖 is the estimated difficulty parameters of item i for the lowest category. 𝜏 𝑗 is the
threshold difficulty for changing category j to j+1 of each item. 𝜆 𝑖 is the discriminant
Note.

parameters (factor loadings) of item i. The parenthesis is the standard error of the
variance of random effect at tie- and ego-level. ***(p<.000), **(p<.01), *(p<.05)
204

𝛽2

𝛽2 𝐿

Table 4.7. Comparison of the two influence models with the raw frequency and the
depth of interaction.
y

n

Academic
achievement

127

Academic
efficacy

175

College
aspiration

172

College
expectation

172

Academic
identity

171

Athletic
identity

170

Physical
ability

172

127

182

180

180

179

179

180
172

𝛽2−1

.03(.003)

-.011 (.001)

𝛽2−2

-.011 (.001)

.071(.007)
.045(.003)

.045(.003)

.077(.007)
-.009(.00)

-.009(.00)

-.040(.006)
-.025(.002)

-.025(.002)

-.002(.01)
-.018(.005)

-.018(.005)

.015(.009)
.067(.004)

.067(.004)

.066(.02)
.016(.008)

.016(.008)

.192(.014)*

𝛽2−1 𝐿

𝛽2−2 𝐿

.033(.002)

-.011(.001)

.029(.001)

.064(.006)
.043(.002)

.077(.002)

.085(.007)
-.013(.002)

.001(.002)

-.044(.005)
-.016(.002)

.-057(.002)

.014(.009)
-.013(.004)

.040(.004)

.029(.007)
.071(.003)

-.034(.003)

.055(.016)
.002(.006)

.027(.007)

.171(.012)*

Note. The exposures ( 𝛽2 , 𝛽2−1 , and 𝛽2−2 ) were obtained with the mean of
frequencies of the overall interaction. 𝛽2 𝐿, 𝛽2−1 𝐿, and 𝛽2−2 𝐿 are the exposures
obtained using the latent score of depth of interaction. + (p<.08); *(p<.05); **(p<.01)
Physical
appearance

64

.001(.005)

.001(.005)

205

-.017(.004)

.118(.005)+

APPENDIX B: Figures

Figure 4.1. The distribution of the depth of interaction.

Note. For interpretation of the references to color in this and all other figures, the reader
is referred to the electronic version of this dissertation.

206

Figure 4.2. The distribution of the mean of frequency of interactions.

Note. For interpretation of the references to color in this and all other figures, the reader
is referred to the electronic version of this dissertation.

207

APPENDIX C: Questionnaires
Name:
First
Date :

Last
/

/

/

E-mail: __________________@______________
Are you (BOY/ GIRL)?
How old are you? (

) years old

What grade are you in?
1) Freshmen 2) Sophomore

3) Junior

4) Senior

What is your race?
1) White/ Caucasian
2) Black/ African American
3) Hispanic
4) American Indian/ Alaska Native
5) Hawaiian/ Pacific Islander
6) Asian American
7) Multiracial/ Mixed (
)
What sports are you currently playing for your school? (___________)
Which level are you playing in? (_______________)
Which are you participating in? (Select all (v) that apply to you)
French Club
German Club
Latin Club

Spanish Club

Book Club

Computer Club

Debate Team

Newspaper

Society

Student Council

Yearbook

Drama Club

Band

Chorus/ Choir

Orchestra

Others

List all courses that you are taking this semester.

What is your current GPA? (

)

208

What is the highest degree that your parents hold?
1) High school
2) Trade school
3) Two year college (Associate Degree)
4) Four year college (Bachelor Degree)
5) Master degree
6) Doctoral degree
7) Others________
Others’ education expectations
1. How far in school does your father want you to go after high school?
2. How far in school does your mother want you to go after high school?
3. How far in school do your teachers want you to go after high school?
4. How far in school does your coach want you to go after high school?
1) Get a job after high school
2) Enter a trade school
3) Go to community college
4) Go to four years college
5) Go to graduate school
6) Others________
Coach’s regard for academics
1. I think my coach has a high opinion of my academic ability
(Anchor: 1=strongly disagree through 7=strongly agree)
College aspiration
2. How much do you want to go to college?
College expectation
3. How likely is it that you will go to college?
(Anchor: 1=low through 5=high).
Academic efficacy
1. I'm certain I can master the skills taught in class this year.
2. I'm certain I can figure out how to do the most difficult class work.
3. I can do almost all the work in class if I don't give up.
4. Even if the work is hard, I can learn it.
5. I can do even the hardest work in this class if I try.
(Anchor: 1 = "Not at all true,” 3 = "Somewhat true,” and 5 = "Very true)

209

Academic /athletic identities
1. I consider myself an athlete (or a student).
2. I have many goals related to sport (or academics).
3. Most of my friends are athletes (or students).
4. Sport (or Academics) is the most important part of my life.
5. I spend more time thinking about sport (or academics) than anything else.
6. I need to participate in sport (or academics) to feel good about myself.
7. Other people see me mainly as an athlete (or a student).
8. I feel bad about myself when I do poorly in sport (or academics).
9. Sport (or Academics) is the only important thing in my life.
10. I would be very depressed if I were injured or could not compete in sport (or
were sick or could not attend academics).
(Anchor: 1=strongly disagree through 7=strongly agree)
Self-regard on physical appearance and ability
1. How confident are you that others see you as being physically appealing?
2. Have you ever thought of yourself as physically uncoordinated?
3. When trying to do well at a sport and you know other people are watching, how
rattled or flustered to you get?
4. Have you ever felt inferior to most other people in athletic ability?
5. Do you often feel that most of your friends or peers are more physically
attractive than yourself?
6. When involved in sports requiring physical coordination, are you often
concerned that you will not do well?
7. Have you ever felt ashamed of your physique or figure?
8. Do you often wish or fantasize that you were better looking?
9. Have you ever thought that you lacked the ability to be a good dancer or do well
at recreational activities involving coordination?
10. Have you ever been concerned or worried about your ability to attract
members of the opposite sex?
(Anchor: 1=almost never through 7=very often)
Social Interaction Questionnaire
Directions: Think about the interactions that you have with other members on your
team. You may add up to TEN friends in your team. Friends in other athletic teams
maybe added. Please write the first and last name of your friend with whom you are
interacting (i.e., verbal communication, texting, Internet chat, Facebook, email, etc.)
about you and school. If you are not sure about his or her full name, please put the
initials. Also please write the sports that he or she is playing in for school.
Full name of your friend____________________________
Sports__________________________________________
Did you firstly meet this friend in this season? Yes_____ No_____
1. How often do you interact with this friend in general?
210

2. How often do you interact with this friend on academic topic (ex, exams, projects,
classes, etc.)?
3. How often do you interact with this friend on athletic topics (ex, sports skills,
practice, game strategies)?
4. How often do you interact with this friend on social topics (ex, other friends, parties,
social events, etc.)?
5. How often do you receive emotional support from this friend?'
Anchor: 1 ---- 2 ---- 3 ----- 4 ---- 5
Daily
Weekly
Monthly

211

APPENDIX D: STATA codes for this study
The followings are the STATA codes used in this dissertation. Please note that the
specific commands are italicized. Explanations are with **. The listed variables and file
names are examples.

1) Multilevel Influence Model (Study I)
-

To generate ‘Exposure’

use influence **Selecting a specific data file ‘influence’ when all files are in a same
directory. The file contains nominees’ data as well as nominators’ and nominees’
identification.
gen exposureAll_gpa=acadinter*gpa **Generating a variable of ‘exposureAll_gpa’ by
nominees’ GPA times amount of interaction with the specific nominees.
collapse (mean) exposureAll_gpa, by (nominator) ** Obtaining a mean of all exposures
to nominees for each nominator. (sum) can be used instead of mean.
merge 1:1 nominator using T1 ** Merging nominators’ Time1 data from T1 (file name).
Both files, influence and T1, should have a same variable name for nominators’ id to
merge successfully. It creates a variable ‘_merge’.
to drop if _merge==2 ** Eliminating cases that don’t have nominators’ data
drop _merge **Deleting a variable ‘_merge’ so that another merging can be performed.
merge 1:1 nominator using T2 ** Merging nominators’ Time-2 data from a saved file of
T2. Both files, influence and T2, should have a same variable name for nominators id to
merge successfully.
drop if _merge==2 **Eliminating cases that don’t have nominators’ data
drop _merge ** Deleting a variable ‘_merge’ so that another merging can be
performed.
save influence_gpa ** Saving it into a different file name ‘influence_gpa’
use influence_gpa ** Using the saved file ‘influence_gpa’
drop if exposureAll_gpa==. ** Eliminating cases that have no exposure-data.
regress gpa2 gpaN exposureAll_gpa A B, beta ** Performing the basic influence model
at single level. gpa2 is the dependent variable (nominators’ Time 2 variable). gpaN is
nominators’ Time-1 variable; exposureAll_gpa is an exposure variable; A and B is
control variables from nominators if necessary. beta is a command for standardized
coefficient.
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xtmixed gpa2 || team:, covariance(unstructured) reml ** unconditional multilevel
modeling for a dependent variable ‘gpa2’ by a group variable ‘team’
xtmixed gpa2 gpaN exposureAll_gpa || team: exposureAll_gpa,
covariance(unstructured) reml ** Adding covariate at level-1 ‘gpaN’

2) Multilevel Selection Model (Study II)
To prepare data files, three different files should be properly made. ‘Nominator’ file
contains only a list of nominators, and ‘Nominee’ file contains only a list of nominees.
Their response data should be saved in a different file ‘T1’ for nominators and ‘T1-2’ for
nominees.
-

Creating a file with all possible pairs between nominators and nominees

use nominator ** to open a base file ‘nominator’
cross using nominee to create all possible pairs of nominators and nominees
gen pair=10000*nominator+nominee ** to generate a variable ‘pair’ for an unique
identification of the each pairs
duplicates drop pair, force ** to eliminate a variable ‘ pairs’
drop if nominator==nominee
drop if nominee==.
drop if nominator==.

** to eliminate unnecessary pairs

save nominator, replace
-

Merging networks between nominators and nominees, and their variables

use nominator ** to use ‘nominator’ with all pairs
merge 1:1 pair using network ** to merge if pair is same in the file ‘network’
gen tie=1 if _merge==3
replace tie=0 if _merge==1 | _merge==2 ** to code 1 if the merge variable is 3 (same
pairs), and 0 otherwise.
drop _merge ** To eliminate the variable
merge m:1 nominator using T1, keepusing( a list of variables) ** To merge the
nominators’ variables from a file ‘T1’
drop _merge ** To eliminate the variable

213

merge m:1 nominee using T1-2, keepusing( a list of variables) ** To merge the
nominees’ variable a file ‘T1-2’

-

Generating variables for difference score of variables between nominators and
nominee, and dummy code for same trait.

gen Dgrade2=abs(grade-grade2) ** To create a variable for the difference of grade
between nominator (grade1) and nominee (grade2)
gen samegender=1 if gender==gender2
recode samegender .=0 ** To create dummy variable ‘samegender’. 1 is given if their
gender is same.

-

Running logistic regression and multilevel logistic model

logistic tie samegender Dgrade2 ** To run logistic regression with tie as a
dichotomous, dependent variable ‘tie’.
xtmelogit tie samegender Dgrade2 || nominator: samegender Dgrade || team:,
covariance(unstructured) mle variance ** To run the three level logistic regression with
the level two (nominator) and level three (team)

3) Multilevel Polytomous IRT Model (Study III). For more details, see (Bacci &
Caviezel, 2011; Zheng & Rabe-Hesketh, 2007)
-

Data preparation

replace nominee=_n ** not to have multiple nominees in the variable
reshape long ta, i(nominee) j(item) **to stack item response into one response vector
(ta), so that we obtain one record for each item response-nominee-nominator
combination
drop if ta==. **to eliminate missing data
gen obs=_n ** to identify each item-nominee-nominator combination
expand 5

**to be expanded to have one row for each response category

sort nominator nominee item obs ** to sort by nominator and nominee
-

Generating the variable ‘x’ to contain all possible score for each item-nomineenominator combination. The variable ‘chosen’ specifies the response category.

by obs, sort: gen x=_n-1
gen chosen = ta==x

214

tab item, gen(it)
-

The design matrix for the multilevel RSM

gen step1 = -1*(x>=1)
gen step2 = -1*(x>=2)
gen step3 = -1*(x>=3)
gen step4 = -1*(x>=4)
foreach var of varlist it* {
gen n`var' = -1*`var'*x
}
-

Defining the vectors of discriminant parameters

sort course stud item x
eq slope1: x
eq slope2: x
-

Estimating the multilevel RSM model

gllamm x nit1-nit5 step1 step2 step3 step4, i(stud course) eqs(slope1 slope2)
link(mlogit) expand(obs chosen o) adapt nocons

-

Estimating the second and third level residuals

gllapred res, u
estat ic
-

The design matrix for the Multilevel PCM

forvalues i=1/5 {
forvalues g=1/4 {
gen d`i'_`g' = -1*it`i'*(x>=`g')
}
}
sort course stud item x
-

Defining the vectors of discriminant parameters

eq slope1:x
eq slope2:x

215

-

Estimating the multilevel PCM

gllamm x d1_1-d5_4, i(stud course) eqs(slope1 slope2) link(mlogit) expand(obs chosen
o) adapt nocons
-

Estimating the second and third level residuals

gllapred res, u
estat ic

-

The design matrix for the multilevel 2PL-PCM

forvalues i=1/5 {
forvalues g=1/4 {
gen d`i'_`g' = -1*it`i'*(x>=`g')
}
}
sort course stud item x

-

Defining the vectors of discriminant parameters

eq load1:x_it1-x_it5
eq load2:x_it1-x_it5

-

Estimating the multilevel 2PL-PCM

gllamm x d1_1-d5_4, i(stud course) eqs(load1 load2) link(mlogit) expand(obs chosen o)
adapt nocons

-

Estimating the second and third level residuals

gllapred res, u
estat ic

216