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THE EXPLORATION AND DEVELOPMENT OF A
CAUSAL MODEL FOR ASTHMA MORBIDITY BY
CONFIRMATORY FACTOR ANALYSIS AND PATH
ANALYSIS UTILIZING COMMON CLINICAL
VARIABLES

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Thomas Paul Miller

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5/08 K:IProj/Acc&Pres/ClRCIDateDue.indd

THE EXPLORATION AND DEVELOPMENT OF A CAUSAL MODEL FOR
ASTHMA MORBIDITY BY CONFIRMATORY FACTOR ANALYSIS AND
PATH ANALYSIS UTILIZING COMMON CLINICAL VARIABLES
By

Thomas Paul Miller

A THESIS

Submitted to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of

MASTER OF SCIENCE
Department of Epidemiology

2007

ABSTRACT
THE EXPLORATION AND DEVELOPMENT OF A CAUSAL MODEL FOR
ASTHMA MORBIDITY BY CONFIRMATORY FACTOR ANALYSIS AND PATH
ANALYSIS UTILIZING COMMON CLINICAL VARIABLES
By
Thomas Paul Miller
The current study is an attempt to develop a causal model for asthma morbidity
incorporating current symptom severity, quality of care indicators, and previous severe
disease as explanatory variables. The study population consists of children who
presented to an emergency department for asthma. Data was obtained from four survey
instruments. The data included demographic information, as well as information
regarding asthma history, current symptoms and treatment, medical management, as well
as healthcare seeking behaviors and asthma care since the index visit including urgent
care. All observed variables were assigned to one of the latent variable categories and
then subjected to conﬁrmatory factor analysis (CFA) and path analysis (PA) to develop
the causal model. The presence of severe current symptoms and previous severe disease

were signiﬁcantly related to high quality of care, however, the only factor (latent

variable) that was signiﬁcantly related to six month morbidity was prior severe disease.

TABLE OF CONTENTS

LIST OF TABLES ..................................................................... iv
LIST OF FIGURES .................................................................... v
KEY TO ABBREVIATIONS ...................................................... vi
CHAPTER 1: BACKGROUND ..................................................... 1
CHAPTER 2: METHODS .......................................................... 23
CHAPTER 3: RESULTS ............................................................ 32
CHAPTER 4: DISCUSSION ...................................................... 37
APPENDIX A: TABLES AND FIGURES ....................................... 47
APPENDIX B: SURVEY INSTRUMENTS ..................................... 57
APPENDIX C: SAS CODE AND OUTPUT .................................... 76
REFERENCES ..................................................................... 148

iii

LIST OF TABLES

Table 1: Demographic Characteristics ............................................ 49
Table 2: Latent Variable Deﬁnitions .............................................. 50
Table 3: Variable Description and Frequency Distribution .................... 52
Table 4: Correlation Matrix ......................................................... 53
Table 5: Measurement Model and Structural Model Fit lndices ............... 54
Table 6: Initial and Modiﬁed Measurement and Structural Models .......... 55

iv

LIST OF FIGURES

Figure 1. Proposed causal model ............................................. 47
Figure 2. Conﬁrmatory Factor Analysis ..................................... 48
Figure 3. Path Analysis Model ................................................ 56

KEY TO ABBREVIATIONS

ACT: Asthma control test

AD: Age at diagnosis

AS: Asthma specialist

ASTHED: Asthma education

CDF: Clinical data form

CFA: Conﬁrmatory factor analysis

CFI: Comparative ﬁt index

df: Degrees of freedom

ECRHS: European Community respiratory Health Study
ED: Emergency department

EDE: ED visit ever

FAL: Frequency of activity limitation

FDS: Frequency of daytime symptoms

FEVI: Forced expiratory volume in 1 second

FNS: Frequency of nocturnal symptoms

FVC: Forced vital capacity

GINA: Global Initiative for Asthma

HE: Hospitalization ever

HEDIS: Health Plan Employer Data and Information Set
HRQOL: Health related quality of life

ICS: Inhaled corticosteroids

vi

NAEPP: National Asthma Education and Prevention Program
NCQA: National Committee for Quality Assurance
NHIS: National Health Interview Survey

NNFI: Non-normed ﬁt index

PA: Path analysis

PCP: Primary care physician

PEF: Peak expiratory ﬂow

PFMTR: Peak ﬂow meter

QOL: Quality of life

RMSEA: Root mean square error of approximation
SEM: Structural equation modeling

SMED: Six month emergency department visit
SMF: Six month follow up form

SMH: Six month hospitalization

SMUC: Six month urgent care visit

TCRS: Tucson Children’s Respiratory Study

TWF : Two week follow up form

UK: United Kingdom

SF: Severe ﬂare

SE: Oral or injectable steroids ever

SES: Socioeconomic status

SP: Spacer

WAP: Written action plan

vii

Chaﬁpter 1: Background

Introduction

One of the most common goals in the treatment of most diseases is to prevent
future morbidity. In general this is done by ﬁrst determining the relative stage or
severity of the disease and then outlining a treatment strategy that is expected to
decrease disease activity and future morbidity. The effectiveness of the treatment
strategy is dependent upon many factors; some of which are disease speciﬁc while
others are not. Factors that are disease speciﬁc for asthma could include the degree of
airﬂow obstruction, allergic phenotype, or the relative responsiveness to steroids.
Factors that are not disease speciﬁc could include socioeconomic status or psychosocial
factors that may impact adherence. All of these factors together form the context of
disease. It is desirable to attempt to incorporate the entire context of disease in analyses
to determine how these various factors interrelate as well as cause speciﬁc outcomes.
By doing this, we will not only have a better understanding of the disease itself, but
also develop a more accurate causal model for morbidity. Most risk models tend to be
reductionistic in philosophy i.e. what are the fewest observed variables that are
associated most strongly with the outcome of interest? This can be very beneﬁcial if
we wish to identify a few easily determined risk factors which if modiﬁed can alter
future risk (ex. cholesterol level or tobacco use). With this type of approach, however,
we will never truly be able to develop causal models that explain the complex interplay
between genetic predisposition, environmental exposures, host responses, disease

development, and disease progression. It will only be when we incorporate the entire

context of disease that the complex clinical reality will begin to be deﬁned.
Incorporating the entire context of disease, however, is difﬁcult because of the
potentially inﬁnite number of variables that could impact disease control or future
morbidity. The potential for collinear associations between variables also complicates
the analysis. It is desirable to categorize observed variables into groupings of like
variables for analysis purposes, yet include variables from the major clinically relevant
categories. Thus, this type of approach can be thought of as expansive, in that it is an
attempt to incorporate the entire context of disease, yet reductionistic in the sense that
these variables will be grouped into like groupings that likely represent underlying
constructs. Only by describing clinical disease in this way will we begin to develop
models that reﬂect the entirety of the patient, disease experience.

The current study is an attempt to develop a causal model for asthma morbidity
using conﬁrmatory factor analysis (CFA) followed by path analysis (PA) that
incorporates major elements of the context of disease applied to a clinical data set.
Relevant components of the context of disease will be identiﬁed from the asthma
morbidity risk, assessment literature. They will be organized into categories that likely
represent the underlying theoretic constructs (latent variables) that lead to the variables
that we Observe. The clinical data set will then be analyzed by assigning the observed
variables from the data set to corresponding latent variable categories. The application
of this approach to a clinical data set will allow the development of a model that
reﬂects the clinical reality of asthma morbidity risk assessment that is employed in
clinics and ofﬁces. This approach will also lessen some of the statistical challenges

dealing with collinearity that can be a problem with multivariable analysis. The current

study, by utilizing longitudinal data from an emergency department (ED) cohort of
asthmatic patients, will determine the latent variable model by using conﬁrmatory
factor analysis and will develop a causal model for asthma morbidity by using path
analysis. The model will consist of four latent variables (see ﬁgure 1) including current
symptom severity, quality of care indicators, and previous severe disease, which are
regarded as explanatory variables, and six month morbidity which is the composite

outcome or dependent variable.

What is a latent variable?

In their text Generalized Latent Variable Modeling: multilevel, longitudinal,
and structural equation models, Skrondal and Rabe-Hesketh deﬁne a latent variable “as
a random variable whose realizations are hidden from us...in contrast to manifest
variables where the realizations are observed.” Though latent variable modeling is
perhaps most commonly applied in the ﬁelds of psychology and the social sciences,
Skrondal and Rabe-Hesketh note that latent variables pervade modern statistics and are
also being applied in areas of medicine, economics, engineering, marketing, and
biology. Though their deﬁnition of latent variables may seem simple, the application of
the concept is not. Skrondal and Rabe-Hesketh go on to describe the use of latent
variables to represent a variety of different concepts including the measurement of a
‘true’ variable measured with error, hypothetical constructs, unobserved heterogeneity,
missing data, or other phenomena. In this study, latent variables are considered as the
underlying constructs whose manifestations are the observed variables that can be

measured.

Asthma is a complex syndrome with many clinical presentations in adults and
children. The cardinal characteristics of asthma include airway inﬂammation, a
variable degree of airﬂow obstruction, and bronchial hyperresponsiveness (l). The
Expert Panel Report responsible for setting clinical guidelines (2) deﬁned asthma as a
chronic inﬂammatory disorder of the airways in which many cells and cellular elements
play a role, in particular, mast cells, eosinophils, T lymphocytes, neutrophils, and
epithelial cells. In susceptible individuals, this inﬂammation causes recurrent episodes
of wheezing, breathlessness, chest tightness, and cough, particularly at night and in the
early morning. These episodes are usually associated with widespread but variable
airﬂow obstruction that is often reversible either spontaneously or with treatment. The
airway inﬂammation results in an increase in the existing bronchial
hyperresponsiveness to a variety of stimuli. This deﬁnition of asthma was reafﬁrmed
in the 2002 Expert Panel Report Update, though the concept of asthma was expanded to
include airway remodeling (irreversible obstruction) in some patients (3). Besides the
themes of airﬂow obstruction, airway inﬂammation and hyperresponsiveness, these
deﬁnitions emphasize the variable nature of asthma, which may be a reﬂection of the
various etiologic factors that can contribute to asthma. Asthma is frequently a
manifestation of allergic disease, thus the development of asthma is closely linked to
the development of allergic sensitization.

Asthma prevalence in the United States has been tracked by the National Health
Interview Survey (NHIS). From 1980 until 1996 the NHIS determined asthma
prevalence rates based on a self-reported asthma episode in the preceding 12 months.

Starting in 1997 a second question reﬂecting lifetime prevalence was added (though

this question is termed ‘current asthma’). Prevalence increased through much of the
1980’s and early 1990’s, (4) however, these prevalence rates (asthma episode in the
preceding 12 months) have been fairly constant since 1997 ranging from 3.9% (1999)
to 4.3% (2002) with the most recent ﬁgure of 4.2% in 2005 (5). The asthma episode
prevalence rate in young children is higher than older age groups; in 2005 the rate
among children aged 0-14 years was 5.4% (6.4% in males and 4.3% in females),
compared to 4.1% in those aged 15-34 years (2.8% in males and 5.5% in females), and
3.8% in those over 34 years (2.5% in males and 5.0% in females).

Prevalence differences by race were also observed. Asthma episodes in the last
12 months and current asthma prevalence rates in the 0-14 year age group were highest
in non-Hispanic Black children (6.7%, 13.6% respectively), compared to Hispanic
children (5.4%, 9.2%) and White non—Hispanic children (4.8%, 7.5%). Current asthma
prevalence in the 15 years and over age group was highest in non-Hispanic Black
individuals (8.4%), compared to non-Hispanic White (7.7%) and Hispanic (5.3%)
individuals. In the 15 years and over, age group, for an asthma episode in the last 12
months, the highest rate was observed in the non-Hispanic White group (4.1%)
compared to non-Hispanic Black (3.7%) and Hispanic (3.0%) groups.

Asthma morbidity, as measured by healthcare utilization, in children is
substantial. In 2003 there were 4.6 million ambulatory visits to ofﬁce-based physicians
or hospital clinics for asthma in children aged 3 — 17 years in the United States. During
the same year there were 475,000 ED visits and 132,000 hospitalizations for asthma in
the same age group. Just as prevalence rates are highest in the younger age groups,

hospitalization rates are also higher. Even though the younger group (aged 3-10 years)

made up approximately 50% of the individuals in the 3-17 years age group,
approximately 70% of the hospitalizations for asthma occurred in this younger age
group (6).

Simplistically, the development of asthma can be conceptualized as occurring in
a genetically susceptible individual after sufﬁcient environmental exposures. However,
the reality of this simplistic concept is extremely complex. Twin studies have
demonstrated the importance of genetic factors (7-9). There have been hundreds of
genetic association studies evaluating asthma related phenotypes in various populations
(10). The results of these studies suggest that there is no single “asthma gene” and the
high level of heterogeneity at a genetic level plays a signiﬁcant role in the
heterogeneity observed clinically.

The complexity of gene-environment interactions is also implicated by the
heterogeneity of exposures that play a role in the development of asthma. Studies of
early childhood exposures have led to the “hygiene hypothesis” which has suggested
that a cleaner early childhood environment including less exposure to other children
and fewer infections has led to an increase in the incidence of allergic diseases and
asthma. The association between increased infections and decreased risk for allergic
rhinitis, eczema, and elevated circulating IgE levels has been demonstrated, however,
the association with asthma is less clear (1 1-14).

The natural history of asthma has been observed in a few well-designed
longitudinal studies. Perhaps the most widely recognized is the Tucson Children’s

Respiratory Study (TCRS) which began is 1980 with a birth cohort and continues today

(15). In this cohort approximately one third of the children experienced wheezing

 

during a lower respiratory tract infection at some point during the ﬁrst year of life. This
risk declined in subsequent years, however, approximately 41% of children who
wheeze with infections during the ﬁrst few years of life will develop persistent
wheezing (wheezing at age 6 years). This risk of developing persistent wheezing, is
increased if the children have a family history of asthma or have evidence of allergic
disease (examples include atopic dermatitis, eosinophilia, or high IgE levels). The risk
of transient and persistent wheezing is increased with environmental tobacco smoke
expOsure as well.

The diagnosis of asthma typically includes three components: the presence of
episodic symptoms reﬂective of airﬂow obstruction, demonstration of airﬂow
obstruction that is at least partially reversible, and exclusion of alternative diagnoses
(2). The goal of pharrnacologic therapy is to prevent or control asthma symptoms,
reduce the frequency and severity of exacerbations, and decrease airﬂow obstruction.
This is done by utilizing long-tenn control medications on a daily basis and utilizing
symptom relief medications (beta agonsits) as needed. The most effective long-term
control medications are the inhaled steroids as they are able to decrease airway
inﬂammation better than any other single medication. Asthma treatment requires a
comprehensive approach that involves determining the severity of disease, adjusting the
type, number and dose of medications accordingly, and developing a partnership with
patients to promote education and patient self-management. Even with our increasing
knowledge of asthma pathophysiology and pharmacology, asthma education and self
monitoring techniques, asthma patients continue to experience severe exacerbations

resulting in urgent care visits, emergency department (ED) visits, hospitalizations, or

even death. There is a large literature devoted to the exploration of risk factors for

asthma morbidity and mortality.

Proposed theoretical model

There is a large literature that has identiﬁed individual factors that are
associated with an increased risk for asthma morbidity (16-61). These observed
variables likely represent the underlying latent variables mentioned above (current
disease control, quality of care, and previous severe disease). The following is a
description of the literature supporting these proposed latent variable groupings. These
descriptions are of those variables that could be included in each speciﬁc group,
however, not all these variables were available from the data we utilized in this study.
Observed variables reﬂecting socioeconomic status or psychosocial factors were not
adequately represented in the data set. These factors will therefore not be included in
the model; however, these factors should be included in future models. These factors
are mentioned below because the literature supports including them in risk models.
This will be discussed in the discussion section.
1. Current symptom severity. Deﬁning asthma severity has been the subject of much
discussion over the last few years (16-25). The distinction between severity and control
is at times ill-deﬁned. The National Asthma Education and Prevention Program
(N AEPP) guidelines were ﬁrst published in 1991 (26) with a second expert panel report
published in 1997 (2). These guidelines suggested a severity based classiﬁcation
system (i.e., mild intermittent, mild persistent, moderate persistent, and severe

persistent) for asthma with stepwise treatment recommendations based on the given

severity level. This severity classiﬁcation was based on the presence and frequency of
current symptoms, exercise intolerance, nocturnal symptoms, as well as measures of
pulmonary function (peak expiratory ﬂow or forced expiratory volume in 1 second).
This severity classiﬁcation system should be determined based on clinical features
before treatment and is therefore difﬁcult to implement, as most patients are receiving
varying levels of therapy. This classiﬁcation system shares many components with
what we now would consider measures of current disease control, which is also based
on current symptoms (27-29). The level of current symptoms is greatly inﬂuenced by
both the underlying disease severity as well as the level of medication utilized. For
example, a given patient with severe disease may require very high levels .of inhaled
steroids in combination with a long acting bronchodilator. This patient may in fact
have very good disease control with this aggressive regimen; however, this masks the
fact that this individual has severe asthma. Because of the overlap between the
concepts of disease severity and disease control we included both in one latent variable
category. Speciﬁcally, in this category we will include level and frequency of current
symptoms, level of pulmonary function, and current medication requirements. The
literature supporting the association between increased disease severity or decreased
disease control and increased risk for future asthma morbidity is well established (30-
32) and includes factors such as increased symptom severity, frequency (30-32),
decreased FEVI (33,34), increased B agonist use (31,35,36), or the use of oral steroids
(33-35,37).

2. Quality of care indicators. The following quality of care indicators are based on our

interpretation of the NAEPP Expert Panel Report 2 (2). These quality indicators

include: (1) at least two scheduled appointments with an asthma care provider in the
last year, (2) access to and use of a spacer if age appropriate, (3) access to and use of a
peak ﬂow meter if age appropriate, (4) presence of a long term control medicine for
persistent asthmatics, (5) access to and use of a written asthma action plan, (6) asthma
education regarding self—management, (7) referral to an asthma specialist for moderate
to severe persistent asthrha, and (8) timely follow-up with an asthma care provider after
ED visit. The literature supporting the association between poorer quality of care and
increased asthma morbidity includes not having a personal physician (35), no action
plan (31,36,37), not using a controller such as cromolyn (35,38,40) or an inhaled
steroid (38,41-43) low ICS to B agonist ratio (44), or having a large number of
prescribers (35). We include these measures as indicators of the quality of care even
though, as pointed out in the 2002 Expert Panel Report Update (3), data are insufﬁcient
to support or refute some of these speciﬁc interventions (ex. peak ﬂow versus symptom
monitoring Only).

3. Previous severe disease. Previous healthcare utilization will be included and
deﬁned as an ED visit or hospitalization (with or without intensive care unit care).
Previous utilization has been one of the most consistent risk factors for future
morbidity. This includes previous ED visits (30,31,35,36,46,47), previous
hospitalizations (34,35,37,48-50), recent outpatient asthma visits (30,32,50), including
unscheduled asthma visits (30). Since the presence of asthma at a younger age has
been shown to reﬂect increased severity of disease as deﬁned by increased
hospitalization rates or ED visits (30,35,44), age at diagnosis will be included in this

category. As the need for oral or injectable steroids reﬂects a more severe asthma ﬂair,

10

the presence of the previous need for oral or injectable steroids will also be included in
this category.

Socioeconomic status and psychosocial functioning represents a separate
category. This category is broad and may contain the most diverse group of factors,
however, for some individuals, these factors may be the most important. This category
includes demographic factors shown to be associated with increased asthma morbidity,
such as gender (51-53) and ethnicity (44,54-56). Socioeconomic factors such as
income or poverty status (31,44,54), educational level (44,54), insurance status (48,57)
are included. Behavioral issues whether smoking (58), illicit drug use (59), psychiatric
factors (42,60), lack of social support (32), crowding (54) or language barrier (61) have

also been associated with increased asthma morbidity.

Current Risk Models

There is overlap in the concepts of severity assessment, determination of disease
control, and morbidity risk stratiﬁcation. As mentioned above, the NAEPP
recommendations for severity classiﬁcation are more consistent with what we would
now consider measures of disease control (based on current daytime and nighttime
symptoms, as well as current pulmonary ﬁmction). The Global Initiative for Asthma
(GINA) was launched in 1993 by worldwide leaders in asthma care in collaboration
with the National Heart, Lung, and Blood Institute, National Institutes of Health, USA,
and the World Health Organization. GINA guidelines (62) suggest current medications
be considered along with current symptoms and pulmonary function to determine

severity. A more formal tool used to determine current disease control is the Asthma

11

Control Test (ACT) (63). This 5-question survey determines the frequency during the
past 4 weeks of shortness of breath, nighttime awakenings, beta agonist use, and
activity limitation. The last question regards self-rated asthma control (How would you
rate your asthma control in the last 4 weeks?) The ACT, like the NAEPP and GINA
severity classiﬁcation guidelines, is mainly inﬂuenced by the level of current
symptoms. The only difference is that the ACT asks about self-rated control, whereas
NAEPP and GINA incorporate pulmonary function, and GINA considers current
.medications. These tools can essentially be considered as clinical risk stratiﬁcation
instruments as they identify patients who are judged to have more severe disease
(NAEPP and GINA) or poor disease control (ACT) in whom increased therapy is
expected to decrease disease activity and future morbidity.

Various other risk assessment models have been proposed that incorporate
additional information (33-35,46,49,50,64-69). These models may be based on clinical
information obtained from patients, administrative data obtained from a computer
database, or a combination, and typically include data on demographics, socioeconomic
status, asthma symptoms, past healthcare resource utilization, medication usage,
elements of the treatment program (ex. asthma education), or comorbid conditions. A
variety of analytic techniques are used to identify risk factors or high risk groups,
including multivariate regression techniques, factor analysis, or recursive partitioning
(classiﬁcation tree) techniques, although most commonly univariate analysis followed
by multivariable logistic regression is used. Our latent variable model and casual path
analysis differs from these risk stratiﬁcation tools or risk assessment models in that we

are attempting to describe the underlying constructs and not the observed variables

12

themselves, and determine how these factors (constructs) interrelate and lead to
increased morbidity as opposed to develop a clinical classiﬁcation system based on the
observed variables and applied to individual patients. Risk assessments models may
reveal if a given factor is associated with an outcome, however, it does not reveal how
or why the factor is associated with increased risk. Reviewing existing risk assessment
models in addition to the clinical measures of severity or control mentioned above, can
offer insight into the types of observed variables that should be included in the latent
variable structure of our study.

Risk assessment models were evaluated as background, for the latent variable
structure of this study that incorporated a divergent group of independent variables in
an attempt to predict future morbidity. An example of a clinical risk assessment model
is one developed by Li et a1 (34) who incorporated historical information as well as
clinical measures of current disease control into a risk stratiﬁcation model to predict
hospitalization. Stepwise logistic regression and recursive partitioning were employed
for model determination. The authors found an increased risk of subsequent
hospitalization was associated with a hospitalization in the last year, moderate to severe
respiratory impairment based on spirometry, severe disease based on medication
regimen, the need for systemic steroids in the prior year, overnight PEF variability >
40%, or evening PEF value < 60%.

An example of utilizing electronic information in an attempt to assess risk of
future morbidity involves the use of the Health Plan Employer Data and Information
Set (HEDIS). This data set was developed by the National Committee for Quality

Assurance (NCQA) to evaluate health plans. Based on electronic claims, this data set

13

tracks the proportion of persistent asthmatic patients who ﬁll long-term controller
prescriptions. This information was recently used to predict asthma related utilization
outcomes (70). The researchers found that patients with low adherence to controller
medication had the highest risk of ED visit or hospitalization. In an effort to increase
the clinical application of risk assessment strategies utilizing information from an
electronic database, Schatz et al (64) developed a clinical prediction rule. The
researchers utilized an administrative database to develop a clinically useful prediction
rule to identify patients who were at risk of subsequent hospitalization. Logistic
regression modeling revealed that independent predictors of subsequent asthma
hospitalizations in children included younger age, increased number of prior year
hospitalizations, the number of beta agonist dispensings, and increased number of
prescribing providers. The "authors found that increased anti-inﬂammatory treatment
was associated with a decreased risk of hospitalization. The model was able to identify
about half the patients who required a hospitalization and was most useful in
identifying subjects who were at low risk. Some authors have added generic and
disease speciﬁc measures of health related quality of life (HRQOL) to the models or
psychometric instruments (66,71,72). Though adding these dimensions likely more
accurately reﬂected what patients were experiencing, the relative predictive value was
similar to previous studies.

The current study, attempting to develop a causal model for asthma morbidity,
may seem similar to previous asthma morbidity risk assessment models or analyses that
utilize factor analysis (reviewed below). The most important distinction is the use of a

latent variable framework. To our knowledge the use of conﬁrmatory factor analysis to

14

establish the measurement model (deﬁne the ﬁt of the latent variable model to the data),
followed by path analysis to suggest a causal model for asthma morbidity has never
been done previously. The fact that the latent variable groupings are an attempt to
reﬂect the entire context of disease is also novel. Reviewing current asthma risk
models as well as uses of factor analysis in asthma are appropriate background

information for our approach.

What is factor analysis?

Factor analysis techniques, such as used in this study, can be confusing for the
average clinician. Factor analysis techniques have been used for many years in the
development and evaluation of psychological measures (73). These techniques are
being increasingly applied to other areas of clinical medicine. Factor analysis can be
divided into exploratory or conﬁrmatory techniques depending on the extent of
knowledge that currently exists regarding underlying causes or constructs.
Conﬁrmatory factor analysis is a distinct technique, which was used in this analysis. In
factor analysis the covariance of the observed variables is assumed to be due to the
causal inﬂuence of underlying latent variables (or factors) on the observed variables.
This assumption is not made in a related statistical technique termed principle
component analysis, which simply reduces the number of variables into components
that explain most of the observed variance. Therefore, to identify the factor structure
(latent constructs) underlying a data set, exploratory factor analysis would be
employed, whereas, to simply reduce the data to the fewest components that explain

most of the observed variance, principle component analysis would be employed

15

 

(though exploratory factor analysis will also reduce the number of variables).
Exploratory'factor analysis is used if the investigator desires to deﬁne the number and
nature of the underlying latent variables, but has no previous knowledge (based on
research or theory) as to what these underlying latent variables (constructs) should
consist of. If there is a basis for suspecting what the underlying latent variables might
consist of, then conﬁrmatory factor analysis can be utilized (74). Conﬁrmatory factor
analysis is used to develop a measurement model which describes the relationships
between the latent variables and the observed variables. This measurement model
consists of the theoretic underlying latent variables and the observed variables that are
presumed manifestations of the speciﬁc latent variable. Testing the measurement
model will determine whether the observed (indicator) variables are truly measuring the
underlying latent variable (construct) of interest, and whether the measurement model
has an acceptable ﬁt to the data. With conﬁrmatory factor analysis all the latent
variables are allowed to covary with each other, so no causal assumptions can be made.
However, once the measurement model has been demonstrated to have an acceptable ﬁt
to the data, then a path analysis can be pursued to demonstrate the presence of causal
relationships between latent variables. Path analysis is the technique utilized in the
development of the structural model that speciﬁes the causal relationships between the
latent constructs themselves. This is done by specifying causal relationships between
the latent variables that were signiﬁcantly associated with each other in the
measurement model, and consistent with postulated causal relationships (as opposed to
conﬁrmatory factor analysis in which all latent variables are allowed to covary in the

measurement model and no causal relationships are postulated). Other names for path

16

analysis modeling could include structural equation modeling, covariance structure
modeling or latent variable modeling. This two-step approach of conﬁrmatory factor

analysis followed by path analysis was the approach taken in the current study.

Factor Analysis in Asthma Research

Factor analysis techniques have been employed with increasing frequency in
asthma research over the last decade. In general, these techniques are employed to
validate survey instruments, determine whether a speciﬁc underlying construct is
associated with a speciﬁc outcome, or determine the factor structure or common source
of variance for observed variables. However, none have attempted to account for the
entire context of disease and determine a causal model for asthma morbidity as we are
doing.

Factor analysis is perhaps most commonly used in asthma research to determine
the underlying factor structure or source of common variance for various observed
variables. Rosi et al (75) sought to determine the separate dimensions of chronic
asthma in clinically stable patients. Factor analysis was applied to various measures of
airway obstruction, bronchial hyperreactivity, sputum eosinophils and eosinophilic
cationic protein. The analysis yielded 3 independent factors representing airway
function, bronchial hyperreactivity, and sputum results. Grazzini et al (76) utilizing
similar methods sought to determine whether measures of lung function, sensation of
dyspnea, respiratory muscle strength, and exertional capacity would reduce to similar or
different factors. The authors found that 3 factors accounted for 78% of the observed

variance. Measures of airway obstruction (FEVl, F VC) loaded on factor 1, respiratory

17

muscle strength, FRC, and exertional capacity loaded on factor 2, and dyspnea loaded
on factor 3. Juniper et al (72) determined the factor structure underlying overall asthma
health status which included measures of quality of life (QOL) and conventional
clinical measures. The authors found that overall asthma health status consisted of 4
components: asthma speciﬁc QOL, airway caliber, daytime symptoms and beta agonist
use, and nighttime symptoms and beta agonist use. Leung et al (77) sought to
determine whether lung function parameters, atopy, exhaled nitric oxide, and airway
inﬂammatory markers represent separate dimensions by principle component analysis
in chronic stable pediatric asthmatic patients. The authors found that atopy and airway
inﬂammatory indices are separate dimensions in assessment of chronic asthma.
Interestingly, they also found that inﬂammatory markers in peripheral blood and
exhaled breath condensate are non-overlapping factors. Schatz et al (66) sought to
evaluate the relationships between various validated survey instruments measuring
QOL, asthma control, symptom severity, self described severity, control and course
over time, and history of acute exacerbations. Principle component analysis resulted in
a 5 factor model which explained 59% of the observed variance. The authors, however,
were unable to identify distinct constructs reﬂecting severity versus control.

The validation of asthma-related survey instruments has been a common area
for the use of factor analysis. Sunyer et al (78) determined the cross-cultural validity of
the European Community Respiratory Health Study (ECRHS) despite the fact that it
was translated into multiple languages and applied in various countries and cultures.
They initially identiﬁed the factor structure using exploratory factor analysis of

questionnaire data collected in the United Kingdom (UK). Using this factor structure, a

18

conﬁrmatory factor analysis was obtained using data from the other countries and
languages to see if the factor structure identiﬁed in the UK was replicated by the data
from the other countries. The authors found a high degree of internal consistency
suggesting that the cross-cultural variations in reporting of symptoms had minimal
impact. Schatz et a1 (79) used factor analysis to validate an asthma control scale based
on beta agonist usage during the previous 12 months. The asthma control scale was
signiﬁcantly associated with validated measures of asthma symptom and control scales.
Factor analysis was employed to determine construct validity, by showing that the
asthma control scale loaded on the symptom and control factor.

Factor analysis can also be employed to determine whether an underlying
construct is associated with a speciﬁc outcome. Fiese et a1 (80) initially determined the
common source of variance of various surveys measuring asthma management routines,
adherence, and quality of life by principle component analysis. The analysis revealed'2
dimensions, which the authors described as medication routines and routine burden.
The medication routines dimension was signiﬁcantly related to adherence and
healthcare utilization, while the routine burden was signiﬁcantly related to quality of
life. Grus et a1 (81) sought to evaluate the association between parental self-efﬁcacy
and asthma morbidity. Parents completed a survey, which measured self-efﬁcacy.
Factor analysis of this instrument yielded 2 factors, learned helplessness and self-
efﬁcacy. The authors found that learned helplessness correlated with multiple
measures of increased morbidity, whereas self-efﬁcacy was associated with missed
school only, suggesting that targeting parents who are experiencing high levels of

perceived helplessness may be more helpful in an intervention program.

19

Fisher et a1 (82) utilized structural equation modeling (SEM) to determine
whether a community-based intervention could improve asthma management practices
and reduce the need for acute care. SEM was used to analyze the role of participation
in the asthma coalition intervention within the context of other factors related to
changes in acute care rates. The authors found that a high participation level in the
intervention program was associated with a decline in acute care rates. The advantage
of SEM was that the authors were able to determine the various relationships
represented by the observed variables followed in the study.

Though most of these studies utilized an exploratory form of factor analysis and
determined the speciﬁc relationship between an underlying construct and a speciﬁc
outcome or determined the factor structure or common source of variance for observed
variables, they have all been fairly narrow in focus. None has sought to categorize the
entire context of disease to deﬁne how speciﬁc observed variables covary or group
together to account for the entire context of disease.

If one summarizes the speciﬁc observed variables that were associated with
increased morbidity from the risk assessment models, it is apparent that they seem to
group in categories similar to those outlined above in the asthma risk literature.
Grouping of risk factors is implied in treatment guidelines (2). In the initial diagnosis
of asthma it is recommended that clinicians ask about symptoms in the last 12 months
and also the last 4 weeks (thus categorizing chronic and recent symptoms). These
recommendations also deﬁne asthma severity by current symptom and activity
restriction, nighttime symptoms, and lung function thus categorizing severity

assessment. Researchers reviewing the asthma risk literature have grouped observed

20

variables into many categories such as age/gender, race/ethnicity, socioeconomic,
clinical, utilization, medication, and social/environmental (14) or few including history
of previous severe attack, poor current disease control, and psychosocial factors
compromising disease management (83). The current literature reﬂecting the
application of factor analysis techniques to asthma does little to conﬁrm or refute this
type of organization. It is important, however, that like variables be grouped together
for analysis purposes. The difﬁculties in dealing with large numbers of presumably
independent variables in epidemiologic studies have been reviewed, with speciﬁc
reference to the problem of collinearity (84). Thus, the categories deﬁned by the
clinical risk literature are supported by the risk assessment model literature. These
categories reﬂect clinically relevant groupings of observed variables that are likely
collinear. By grouping them together, the statistical problems associated with
collinearity will be lessened (85,86). Therefore, since there is a theoretic basis for these
latent variable groupings as discussed above as well as precedence for these groupings
in previous risk models, conﬁrmatory factor analysis can be appropriately utilized in
this analysis. As the perspective of conﬁrmatory factor analysis is theory driven, these
groupings will serve as the basis for the latent variable model, which will then be tested

to see if this theoretic model ﬁts the data.
Prespeciﬁed hypothesis

Asthma risk stratiﬁcation is a complex undertaking that will only be partially

accurate until the entire context of disease is incorporated into the risk models. An

21

approach utilizing latent variables has the potential to incorporate the multiple

dimensions that impact asthma morbidity.

Speciﬁc Aims

1. Use conﬁrmatory factor analysis to apply a latent variable approach to risk
stratiﬁcation of asthma patients that incorporates a broader context of asthma.

2. Use path analysis modeling of the latent variables deﬁned above to explore the
magnitude and statistical signiﬁcance of causal relationships between these latent
variables.

3. Apply these techniques in a longitudinal cohort of asthmatic patients that will

demonstrate a method that could be applied to other populations and different diseases.

22

Ma 2: Methods
Study population

The study population consists of children who presented to 1 of 3 emergency
departments for the evaluation and treatment of asthma during 2001. The original
study was designed as a prospective cohort enrolling children aged 2-17 years who
presented to an ED for evaluation and treatment of asthma at one of three western
Michigan hospitals. The three hospitals represented urban, suburban, and rural
locations. Children were eligible if they presented with signs and symptoms
compatible with an acute asthma exacerbation (shortness of breath, coughing,
wheezing, or chest tightness) and had a discharge diagnosis of asthma or had a previous
diagnosis of asthma, reactive airways disease, or had ﬁlled a prescription for a
bronchodilator in the past year. Patients were excluded if they had other signiﬁcant
illnesses or were hospitalized at the index visit. Children were enrolled by either
trained research personnel or by respiratory therapists working at the rural hospital. The
enrolled subjects represented a convenience sample of all asthma visits. Demographic
characteristics are displayed in table 1 in the results section. More complete details of
the child cohort patient population have been published elsewhere (87). In the original
publication only two week follow up information was analyzed. In the current study

six month follow up information was analyzed.
Data Collection

Data was obtained in the form of four survey instruments: clinical data form

(CDF), child cohort visit form (CVF), two week follow-up form (TWF), and six month

23

follow-up form (SMF). Information for the CDF was obtained at the index visit from
the medical record. The CDF contained information regarding the patient’s initial
presenting signs and symptoms as well as information regarding the evaluation and
treatment received in the ED. Information for the CVF was obtained by a face to face
interview with the parent or guardian at the index visit. The CVF contained
demographic information, as well as information regarding asthma history, current
symptoms and treatment, medical management, as well as healthcare seeking
behaviors. Information for the two follow up forms was obtained by telephone
interview with the parent or guardian. The follow-up forms contained information
regarding asthma care since the index visit (including usual and urgent care, medical
care, and current symptoms). The parent or guardian was asked whether urgent
medical treatment had been required since the last information was obtained. They
were asked where this urgent care was obtained, whether the child needed to be
transferred to an ED or hospital, and whether the child was admitted to the hospital
over night. These questions were the basis for determining whether the children needed
urgent care, were seen in an ED, or were hospitalized. These forms are included in the
appendix. In an effort to be inclusive, any observed variable (question) that reﬂected
information that could be a component of the theoretic latent variable categories, as
outlined above, was included unless the speciﬁc variable (or logical grouping of
variables) was missing in 15% or more of the subjects. Subjects whose 6 month
follow-up information was missing because of loss-to-follow-up (n = 31) were also
eliminated from analysis leaving 166 subjects. Since the purpose of this study is to be

clinically relevant all variables were characterized as to what would be considered high

24

risk or low risk. Most variables were dichotomous, however, the few that were not
were converted to dichotomous at clinically relevant cut-off points if possible. These
observed variables that were organized into the latent variables categories described in
Chapter 1 (i.e., six month morbidity, current symptom severity, previous severe disease,
and quality of care indicators). The latent variable representing the dependent or
outcome variable in this study was six month morbidity. The independent (explanatory
or exposure) variables in this study included the 3 latent variables labeled as current

symptom severity, prior severe disease, and quality of care indicators.

Outcome and exposure variables (See table 2 for deﬁnitions of the observed variables
in their latent variable categories and table 3 for description and distribution of all
variables)

1. Six month morbidity. Three observed variables collected in the 6-month F U survey
were used to deﬁne this latent variable. These three variables included urgent care
visits (SMUC), ED visits (SMED), and hospitalizations (SMH) during the six month
follow up. To increase the discrimination of this outcome these dichotomous variables
were combined into one three level variable, which corresponded to no urgent care
visits, one or more asthma-related urgent care visits that did not involve an ED visit or
hospitalization (i.e., an unscheduled visit to a physician ofﬁce), or one or more asthma-
related ED visit or hospitalization during the 6 month follow-up.

2. Current symptom severity. The following observed variables were utilized as
surrogates for the latent variable current symptoms. These variables were

dichotomized into higher risk and lower risk. The cut-off values were chosen for these

25

variables based on the distinction between mild persistent and moderate persistent
asthma as deﬁned in the Expert Panel Report (2). Frequency of daytime symptoms
(FDS), higher risk category was 23 times per week. Frequency of nocturnal symptoms
(FNS), higher risk category was 33 times in the last 4 weeks. Frequency of activity
limitation (FAL) higher risk category was _>_3 times in the last 4 weeks. Severe ﬂare
(SF) was deﬁned as an asthma attack during the previous 4 weeks of sufﬁcient severity
where the child was only able to speak 1 or 2 words between breaths.

3. Previous severe disease. The following observed variables were utilized as
surrogates for the latent variable previous severe disease. Age at diagnosis (AD) was
considered higher risk if initial diagnosis of asthma was at 5 years of age or younger.
Having received oral or injectable steroids ever (SE) resulted in a higher risk
classiﬁcation for this observed variable. Having an ED visit ever (EDE) or
hospitalization ever (HE) resulted in a higher risk classiﬁcation for these observed
variables (EDE and HE). This grouping is utilized because previous severe disease is
frequently the strongest predictor of future exacerbations (34,64).

4. Quality of care. The following observed variables were utilized as surrogates for
the latent variable quality of care. Not utilizing an inhaled steroid (ICS), never having
seen an asthma specialist (AS), never receiving a spacer (SP) or a peak ﬂow meter
(PFMTR), not having a written action plan (WAP) or receiving asthma education
(ASTHED) were considered higher risk. These quality of care indicators are reﬂective
of recommendations from the Expert Panel Report (2). They are included in this
category even though it is likely that some individuals may have only been identiﬁed as

being candidates for these interventions at the ED visit itself.

26

Statistics

Conﬁrmatory factor analysis of the theoretically based latent variables (as
deﬁned above) is ﬁrst used to develop a measurement model that demonstrates an
acceptable ﬁt to the data. Conﬁrmatory factor analysis starts with theory to develop the
model and then utilizes data to test the model, as opposed to exploratory factor analysis,
which starts with data to develop the model, which is then used to develop the theory.
More detailed discussions of the techniques employed in this study are available in
references (73,74) or structural equation modeling textbooks (88). The measurement
model is then modiﬁed to become the structural (causal) model by path analysis. This
structural model is then tested and modiﬁed if necessary until it is theoretically
meaningful and statistically acceptable. Correlations with standard deviations between
all manifest (observed) variables are ﬁrst determined using the SAS correlation (proc
corr) procedure. The covariance structure model is analyzed with conﬁrmatory factor
analysis and then path analysis using the SAS CALIS (proc calis) procedure. Latent
variables are indicated by at least three manifest variables. The two step approach is
based in part on a method recommended by Anderson and Gerbing (89). The speciﬁc
steps used to evaluate the measurement and structural model performance are explained

below:

1. General ﬁt of the model to the data. The measurement model describes the

relationships between the latent variables themselves as well as the observed (manifest

or indicator) variables that measure these latent variables. In the current study the

27

model consisted of four latent variables (or factors): current symptom severity (F2),
quality of care indicators (F4), previous severe disease (F3), and six-month morbidity
(Fl). An overall model chi square value is determined for the initial measurement
model using the maximal likelihood method. The null hypothesis is that the model ﬁts
the data. Because the chi square test is excessively sensitive, a chi square divided by
the model degrees of freedom value is calculated and should be < 2, indicating the
model may ﬁt the data. Other ﬁt indices are also reviewed including the non-normed
ﬁt index (NNFI) (90), the comparative ﬁt index (CFI) (91) and root mean square error
of approximation (RMSEA). These measure overall goodness of ﬁt and are included in
the SAS output though their derivation reﬂects a different perspective. Acceptable
values for NNFI and CFI are > 0.95. The NNFI can be viewed simplistically as
indicating the amount of covariance that is explained by the model compared to a
model with no interrelationships between any of the variables. The RMSEA and CFI
can be considered alternative ﬁt indices as they operate on the perspective of the extent
to which the model fails to ﬁt the data (called the “noncentrality parameter”). A
RMSEA value <0.05 can be considered as indicative of the model being a reasonable
approximation to the analyzed data. The CFI can be thought of as a ratio of the
improvement (or change) in noncentrality when moving from the null model (high
noncentrality) to the proposed model (low noncentrality), over the null model (high
noncentrality), therefore a high CFI (>0.95) is good while a low RMSEA (<0.0S) is
good even though both indices share the perspective of noncentrality (88). If these

indices reveal that the model does not ﬁt the data, then the next step would be

28

reviewing the speciﬁc factor loadings and the residual covariance matrix to determine
why the ﬁt is not good.

2. Review of speciﬁc variable or factor loadings and residual covariance matrix.
When evaluating the speciﬁc factor loadings a non-signiﬁcant factor loading indicates
that the speciﬁc indicator (observed) variable is not doing a good job of measuring the
underlying factor and perhaps should be reassigned to a different factor or dropped. In
general factor loadings can be viewed as an indication of how much of the observed
variance is caused by the underlying factor. Under certain conditions these loadings
can be viewed as similar to regression or correlation coefﬁcients. We ﬁrst verify that
there are no near zero standard errors. We then evaluate the t test results. The large
sample t test of the null hypothesis, that the factor loadings are zero in the general
population is used. A non-signiﬁcant t test suggests that these variables could perhaps
be dropped. The residual covariance represents the discrepancy between the predicted
covariances based on the model and the actual observed covariances based on the data.
We ﬁrst observe the distribution of normalized residuals. A good ﬁt results in a
distribution that is centered on zero, symmetrical and contains no or few (<2) large
residuals. Standardized residuals can be roughly interpreted as a z score, i.e. a value >
1.96 (or > 2.58) would correspond to a p value < 0.05 (or < 0.01). A large residual
suggests that there is a large discrepancy between the predicted covariance between
speciﬁc variables and the actual observed covariance between these variables. If the
predicted covariance is much smaller than the actual covariance (yielding a positive
standardized residual value), this suggests that the model underestimates the strength of

the relationship between the variables. This usually (though not always) occurs when

29

the variables covary (are associated with each other) yet are modeled to represent
different latent variables. A large negative standardized residual value suggests that the
variables covary less than the model is predicting (the model overestimates the
covariance). The rank order of the ten largest standardized residuals is displayed in the
SAS output. Dropping any of these variables, with large residuals, from the
measurement model would increase the ﬁt of the model to the data, however, dropping
as few as possible increases the construct validity and external validity of the model. It
is also important to have at least three observed variables measuring each latent
variable.

3. Modiﬁcation indices. The Wald test, which is part of the standard SAS output
indicates which variables, if dropped from the model would improve the ﬁt the most
(i.e. the Wald test simply lists which parameters if ﬁxed to zero would increase the
model ﬁt the most). The Lagrange Multiplier test, which is also part of the standard
SAS output, describes which variables or paths could be reassigned or added to
improve the model ﬁt (i.e. the LaGrange Multiplier test results in a list of parameters or
pathways that, if added, would increase the model ﬁt the most). It is important to be
sure that alterations in the model recommended by the Wald or Lagrange Multiplier
tests are theory driven and not strictly data driven.

The preceding three steps are applicable for conﬁrmatory factor analysis as well
as path analysis; however, there are differences in the initial assumptions for the
models. Conﬁrmatory factor analysis is done by allowing all the factors to covary.
Path analysis, however, speciﬁes a directionality in the relationships between the

factors (latent variables), thus allowing a causal model to be theorized. This

30

directionality can be suggested by the results of the stepwise multivariate Wald test
from the modiﬁed measurement model but should be consistent with clinical
observations. The Wald test suggests not only individual variables that can be dropped
from the model to improve ﬁt, as mentioned above, but also suggests factor covariances
that could be dropped to improve ﬁt (such as if speciﬁc latent variables do not covary).
Assuming that the model ﬁts the data, the path equations are evaluated utilizing the
factor loadings, standard error and t tests. This reveals the strength and impact of the
speciﬁc factors. The R2 value in path analysis is calculated for any endogenous
(dependent) factor (latent variable). The R2 value indicates the percent of the variance
for that factor that is accounted for by those factors that are directly antecedent to them.
This value is derived from the sum of the squares of the path loadings (correlations) for
all paths that lead to a given factor.

Figures 2 and 3 depict the proposed causal model and the modiﬁed
measurement model respectively. In these models observed (or manifest) variables are
represented by rectangles and factors (latent variables) are represented by ovals. A
straight, single-headed arrow represents a unidirectional causal path, whereas a curved,
double-headed arrow represents correlation or covariance between the two variables.
Figure 3 includes the speciﬁc factor loading values for the observed variables as well as

disturbance (error) terms, as well as correlations between factors.

31

garner 3: Results

Of 197 children enrolled in the original study, 6-month follow-up information
was available in 166. Of these, 115 (69.8%) were enrolled at the urban site, 30 (18.1%)
at the suburban site and 21 (12.7%) at the rural site. See table 1 for the demographic
characteristics of the population. Table 2 displays the speciﬁc variables that correspond
the each latent variable, as well as the criteria used to determine high risk or low risk
with each variable. Table 3 displays the frequency distribution for these same
variables. Table 4 is the correlation matrix of all the observed variables. The
intersection of one variable with another displays the correlation between these two
variables. It is Of note that, in general, the variables that were grouped together on
theoretical grounds have higher correlations with each other.

The initial measurement model did not ﬁt the data well. After modiﬁcation,
however, the ﬁt was good. The structural model improved with modiﬁcations as well,
resulting in a good ﬁt to the data allowing speciﬁc relationships between the latent
variables to be determined. See table 4 for the ﬁt indices for the initial and modiﬁed

measurement model, and initial and modiﬁed structural (path analysis) model.

Initial Measurement Model

The initial measurement model, which describes the relationships between the
latent variables, was estimated using the maximum likelihood method, which resulted
in a chi square value of 134.9 with a p = 0.0005 (df = 85 n = 164, see table 5). The

degrees of freedom are calculated by subtracting the total number of parameters in the

32

model from the number of nonredundent elements. The number of nonredundent
elements is determined by multiplying the number of observed variables times the
number of observed variables plus 1, all divided by 2. As the chi square value is large
(and the p value highly signiﬁcant) we would normally conclude that the null
hypothesis (that the model ﬁts the data) is rejected. However, because the chi square
test is known to be excessively sensitive (74), a modiﬁed test calculated as a chi square
divided by the degrees of freedom was calculated and this was < 2 (1.61) indicating the
model may still ﬁt the data. However, the NNFI and the CFI were both < 0.9 (0.86,
0.89 respectively), and the RMSEA was 0.06 indicating an unacceptable level of ﬁt.
Therefore the unadjusted (unmodiﬁed) measurement model does not ﬁt the data very
well.

The speciﬁc factor loadings were evaluated next. We ﬁrst verify that there are
no near zero standard errors; all are > 0.01. We then evaluate the t test results. This
null hypothesis is rejected for all variables, at a level of p <0.05 meaning that the
speciﬁc observed variable is signiﬁcantly associated with the underlying factor.
Evaluating the residual covariance matrix revealed that the highest residuals were
between variables 10 (receiving asthma education) and 2 (frequency of nocturnal
symptoms), between variables 7 (receiving a spacer) and 6 (asthma specialist), and
between variables 9 (having a written asthma action plan) and 1 (frequency of daytime
symptoms). The large residuals between these variables were negative numbers
suggesting that the model overestimated the association observed between these

variables.

33

Dropping these variables from the measurement model would increase the ﬁt of
the model to the data. After reviewing all the above information and theory driven
decision making employed, it was decided to drop variables 10 (asthma education), 9
(having a written asthma action plan), and 7 (spacer). Even though it may seem that
some of these variables would be important to include, it is likely that the remaining
variables represent the underlying latent variable adequately without the additional
information provided by these dropped variables. For example, in the unadjusted
measurement model it was proposed that the latent variable “quality of care indicators”
would be represented by variables 5 (inhaled corticosteroids), 6 (having seen an asthma
specialist), 7 (having a spacer), 8 (having a peak ﬂow meter), 9 (having a written action
plan), and 10 (receiving asthma education). The model ﬁts the data better without
variables 7, 9, and 10 being included. Therefore it seems apparent that the latent
variable “quality of care indicators” is adequately measured by variables 5 (inhaled
steroids), 6 (asthma specialist), and 8 (peak ﬂow meter) alone. At this point there were
still two variables associated with high residuals. Variable 2 (nocturnal symptoms) had
a high positive residual with variable 1 (daytime symptoms) suggesting that these
variables may be measuring the same thing. Variable 2 also had a high negative
residual with variable 3 (activity limitation) suggesting that the model overestimates the
covariance. Variable 14 (previous hospitalization) had high positive residuals with
variables 5 (inhaled steroids) and 13 (previous ED visit), and a high negative residual
value with variable 12 (oral or injectable steroids ever). This would suggest that
variable 13 (previous ED visits) and variable 14 (previous hospitalizations) might be

measuring the same thing. The fact that variable 14 (previous hospitalizations) and

34

variables 5 (inhaled steroids) had a high positive residual suggests that they are
associated to a greater extent than would be explained by the model (which grouped
them into different latent variable categories). A high negative residual value between
variable 14 (previous hospitalizations) and variable 12 (oral or injectable steroids ever)
suggests that the model overestimates the covariance between these two variables.
Variables 2 (nocturnal symptoms) and variable 14 (previous hospitalizations) were
eliminated. These modiﬁcations resulted in high overall goodness of ﬁt indices. This
modiﬁed model was then used to construct the path analysis. Table 6 includes the
individual variable standardized loadings and t values for all variables included in the
initial and modiﬁed measurement models, (as well as unmodiﬁed and modiﬁed
structural models). All variable loadings are signiﬁcant (a t value > 1.96 corresponds to
p < 0.05 and is considered signiﬁcant) suggesting that the observed variables are
signiﬁcantly associated with the underlying factors. After these modiﬁcations were
made the ﬁt of the modiﬁed model improved, chi square p=0.39, NNFI = 0.99,

RMSEA = 0.02, CFI = 0.99 indicating a good level of ﬁt.

Structural Model

The Wald test in the modiﬁed measurement model suggested that, based on the
data, the covariance pathway between the following factors were not statistically
signiﬁcant and could be eliminated: the path between F3 (current symptom severity)
and F 1 (six-month morbidity), as well as the path between F4 (previous severe disease)
and F3 (current symptom severity) (Figure 2). The results of the path analysis of the

structural (causal) model reveal that it has a good ﬁt to the data. The chi square value is

35

34.41 (df = 32 p = 0.35), the NNFI and CFI are both above 0.9 (0.99 and 0.99
respectively) and the RMSEA = 0.02. (Table 5) These measures suggesta good ﬁt of
the model to the data and all individual variable loadings are signiﬁcant (t > 1.96
corresponding to p < 0.05). The path from F2 (quality of care indicators) to F1 (six
month morbidity) (PF1F2) was nonsigniﬁcant with a factor loading of 0.03 and a t
value of 0.20, suggesting that the factors do not covary and the path likely does not
represent a causal pathway. Thus the path from F2 (quality of care indicators) to F1
(six month morbidity) was eliminated. This modiﬁcation resulted in the ﬁnal structural
model which revealed a gOod ﬁt to the data (chi square p=0.40, NNFI = 0.99, RMSEA
= 0.02, CFI = 0.99, see table 5). The Paths PF1F4 which represents the impact of
previous severe disease (F4) on six month morbidity (F1) (factor loading 0.25, p <
0.01), PF2F3 which reﬂects the impact of current symptom severity (F3) on quality of
care (F2) (factor loading 0.52, p < 0.001), and PF2F4 which reﬂects the impact of
previous severe disease (F4) on quality of care (F2)

(factor loading 0.62, p < 0.001) (see ﬁgure 3). The signiﬁcant factor loadings reveal
that the antecedent factors are signiﬁcantly inﬂuencing the subsequent factors. The R2
values quantify the amount of variance for a factor that is explained by the antecedent
factors. The R2 value for F 1 (six month morbidity) and F2 (quality of care) were 0.06
and 0.66 respectively (also displayed in ﬁgure 3). This suggests that only 6% of the
variance of F1 (six month morbidity) is explained by F4 (previous severe disease) and
66% of the variance of F2 (quality of care) is explained by F3 (current symptom

severity) and F4 (previous severe disease).

36

Chapmar 4: Discussion

 

Causal Model

We have identiﬁed relationships between the latent variables as a part of a
causal model for asthma morbidity by using path analysis. Signiﬁcant relationships
were identiﬁed between previous severe disease and 6 month morbidity, quality of care
indicatOrs and current symptoms, and previous severe disease. The association between
previous severe disease and future morbidity is a well established risk factor and this
relationship was conﬁrmed in our study. Signiﬁcant associations were noted reﬂecting
the impact of current symptoms and previous severe disease on quality of care. The
positive association between current symptoms and quality of care meant that high
symptom level was associated with a high level of care. High previous severe disease
was also associated with high quality care, however there was no signiﬁcant
relationship between current symptoms and previous severe disease or between quality
of care and 6 month morbidity. The relationships between current symptoms or
previous severe disease and quality of care could be the result of the fact that patients
who were at increased risk for future morbidity were identiﬁed and interventions were
implemented more oﬁen is this group than for lower risk individuals thus increasing the
quality of care. It is plausible that once patients were identiﬁed as being at increased
risk because of previous severe disease, the quality of care improved (thus the
statistically signiﬁcant association). This makes sense clinically as individuals
identiﬁed as having increased symptoms or previous severe disease would be more apt

to be given inhaled steroids or a peak ﬂow meter, or be referred to a specialist. These

37

clinical interventions that likely occurred in these patients may have decreased their
risk of morbidity perhaps explaining the non-signiﬁcant association between quality of
care and six-month morbidity.

Despite increasing knowledge of asthma and advances in treatment options the
frequency of healthcare utilization continues to be a problem. This fact is observed
clinically and corroborated by the fact that asthma risk models have a low positive
predictive value. This study utilizes variables that are standard clinical questions used
by healthcare providers in an attempt to gauge the risk of future morbidity, thus the
variables are reﬂective of what is happening clinically even though the construct
validity of these observed variables is not established. It is of interest to review the R2
values for six month morbidity and quality of care. The R2 value, indicating the percent
of variance accounted for by antecedent factors as discussed above, is calculated for
any endogenous (dependent) factor (latent variable). Figure 3 displays the path
loadings and the p values for each pathway as well as the R2 value for F1 (6-month
morbidity) and F2 (quality of care). The path from previous severe disease to 6 month
morbidity (PF 1F4) was signiﬁcant (P <0.01), however, the R2 value for six month
morbidity was only 0.06, suggesting that previous morbidity accounted for only 6% of
the variance observed in six month morbidity. Obviously, this suggests that the current
model does not provide an adequate explanation of the factors that determine asthma
morbidity. This is a reﬂection of what is occurring clinically. We try to identify high
risk individuals and improve the quality of care. Despite these efforts asthma morbidity
continues. The fact that the R2 value for the quality of care latent variable was 0.66,

suggested that 66% of the variance in quality of care indicators is accounted for by

38

current symptom severity and previous severe disease. This is corroborated by the
signiﬁcant path loadings for both factors. It is recognized that various triggers
including viral infections, allergens or irritants may precipitate an asthma attack. These
unpredictable exposures likely play a role in the lack of stronger path factor loadings
for 6 month morbidity. However, it is also possible that other factors such as intrinsic
steroid sensitivity, degree of pulmonary deterioration in the presence of a viral
infection, perception of airﬂow obstruction, or other disease speciﬁc factors may be
operative. It is also possible that 6-month morbidity may be a reﬂection of social
circumstances, learned behaviors, insurance or medical system access which were not
addressed in this investigation.

The good news of this study is that we seem to be identifying patients at high
risk because of severe symptoms or previous morbidity and increasing their quality of
care. The negative conclusion, however, is that we are doing a poor job predicting who
is at increased risk for future morbidity. This suggests that we need to better
understand the predictors of ED, hospital and urgent care visits by expanding our scope
of investigation to include both disease speciﬁc factors as well as those that are not

disease speciﬁc.

Limitations and Implications for the Future

We have demonstrated a methodology of risk stratiﬁcation modeling utilizing a
latent variable approach that includes various dimensions of asthma morbidity risk.
The model is valid to the extent that the latent variable groupings are based on

established risk factors. The validity of the model would have been improved if the

39

latent variables had been deﬁned by instruments with established construct validity,
rather than being deﬁned accOrding to recognized clinical variables. The latent variable
categories of current symptom severity and previous severe disease are likely valid
measures of the underlying constructs since they have obvious face validity and are
similar to groupings in the literature. The observed variables that deﬁned current
symptom severity (i.e., symptom frequency, recent exacerbations, and activity
limitations) are similar to those included in several validated measures of current
disease control (for example, the ACT). The construct of previous severe disease is
relatively uncomplicated being based on prior utilization (hospitalization and/or ED
visits), early age of asthma diagnosis (as younger age is associated with increased
utilization) (30,35,44) and past oral steroid use. The construct of quality of care
indicators is taken directly from national treatment guidelines (2,3). The fact that the
model ﬁt better, with some of these commonly accepted clinical variables eliminated
(ex. previous hospitalization), suggests that the underlying constructs are more complex
than is reﬂected by current clinical practice. It also suggests that the observed variables
exhibit associations with other observed variables and latent factors that go beyond
those deﬁned in the model.

The construct of socioeconomic or psychosocial factors is more difﬁcult to
deﬁne however; previous researchers have included variables related to behavioral,
psychological, and social factors. This construct was not adequately represented by the
observed variables in the data set; therefore it was not included in the model. In the
asthma morbidity risk models reviewed in the background section (33-35,46,49,50,64-

69), it is notable that the independent variables included in these models included few

40

variables that would be considered measures of socioeconomic or psychosocial risk
factors. This is surprising given that individual factors have been associated with
increased asthma morbidity including factors such as gender (51-53), ethnicity (44,54-
56), income or poverty status (31,44,54), educational level (44,54), insurance status
(48,57), smoking (58), illicit drug use (59), psychiatric factors (42,60), lack of social
support (32), crowding (54) or language barrier (61). The most common factors
incorporated into the risk models included age, sex and ﬁnancial implications of access
to healthcare or medications (i.e. insurance type, co-payments for ofﬁce visits or
prescriptions). A few factors reﬂected the access or assumed continuity of care by
determining whether a PCP was listed on a computer database, or whether multiple
providers had written prescriptions for the individual. Only two models included
educational attainment and household income. These factors may reﬂect
socioeconomic status (SES) that may be playing a role, but they are likely a poor
reﬂection of the role of psychological stress, which is likely contributing to the
increased risk associated with poor psychosocial functioning.

These factors likely reﬂect different constructs and are categorized in various
ways in the literature. Socioeconomic or demographic factors are fairly
straightforward; however there is more variability in how psychosocial factors are
deﬁned. Some authors use the terms ‘psychosocial’ and ‘psychological’
interchangeably either explicitly or in practice. To investigate the association between
‘psychosocial’ factors and the development of symptoms suggestive of asthma, Calam
et a1 (92) deﬁned psychosocial factors as child behavior problems (deﬁned by the

Eyberg Child Behavior Inventory), family relationships (deﬁned by the Family

41

Relationships Index), and parental mental health (deﬁned by the Hospital Anxiety and
Depression Scale and the General Health Questionnaire). In a review detailing the
childhood asthma disparities of the inner-city poor, Federico and Liu (93), deﬁne
psychosocial stress as the psychologic stresses of inner-city living including concerns
regarding safety and poverty, which may lead to stress-related behaviors in the
caregiver. There has been a recent review detailing the health effects of neighborhood
violence on urban asthma control (94). In another review focusing on asthma in urban
children Eggleston (95) includes stress related to poverty as well as speciﬁc
psychological functioning and potential drinking problems under the category of
psychosocial stress. In a study to determine whether psychosocial factors and health
behaviors were important in asthma deaths (96), 533 cases and 533 controls were
evaluated in regard to various measures of behavioral, psychological, and social factors.
The social factors evaluated included sexual problems, bereavement, marital
breakdown or family problems, domestic abuse, isolation, housing, ﬁnancial, or
employment problems, drug or alcohol abuse, or criminal record. These social factors
likely have signiﬁcant psychiatric implications however; they were distinguished from
more formal psychiatric diagnoses, use of psychiatric medications, or mental healthcare
utilization.

More extensive hypothesized frameworks for psychosocial factors have been
utilized by Adams et a1 (97) and proposed by Wade et al (98). In a study to evaluate
‘ whether better asthma management (as deﬁned by the use of a written asthma action
plan and increased inhaled steroid usage) prevented asthma related ED visits or

hospitalizations, Adams et a1 incorporated individual characteristics such as coping

42

styles and attitudes toward asthma management into the evaluation. They deﬁned
psychosocial factors as including personal coping styles (avoidance coping, active
coping, and denial), attitudes and behaviors regarding asthma medication (including
self-reported adherence), as well as preferences regarding decision making autonomy
(asthma autonomy preference index), level of conﬁdence (self-efﬁcacy) in managing
asthma, indicators of perceived emotional social support and participation. During the
12 month follow up, those who had an asthma related hospital admission were more apt
to use avoidance coping and have lower autonomy preferences in moderate attacks, as
well as have more severe disease, have previous hospitalizations as well as no written
action plan. Individuals who had two or more ED visits for asthma were found to have
a greater dislike of asthma medications, as well as increased severity of disease, regular
use of oral steroids, previous hospitalization, and no written action plan. Barton et a1
(99) have suggested that coping, as opposed to a component of psychosocial
functioning should be viewed as a mediator of the psychosocial impediments of asthma
control.

The most extensive proposed model deﬁning psychosocial characteristics was
proposed by Wade et al. The most proximal factors included aspects of the asthma
management. This included caretaker’s attitudes and beliefs, knowledge, problem
solving and responsibility for tasks. Less proximate to asthma management, the model
included three adjustment factors including caretaker adjustment (screening for
alcoholism and psychological symptoms), family adjustment (evaluating the family
environment and parenting practices), and child adjustment (including behavior

problems, cognitive competence, and self-competence). The most distal elements Of

43

the model incorporated a measure of stressful life events and degree of social support.
This model is based on the asthma literature; however, it has not been validated yet.

In addition to measures of current symptom severity, previous disease severity,
and quality of care, it is clear that incorporating measures of socioeconomic and
psychosocial functioning will be important to more accurately include the entire context
of disease. Chen et a1 recently demonstrated an association between SES,
psychological stress, and immune pathways that play a role in asthma (100). It is clear
that psychosocial factors are much more complex and extensive than is reﬂected in
previous risk models or by the observed variables that were present in the data set used
in this investigation. It is likely that exploratory techniques are the best current
approach to clarify this construct because of the variable nature of socioeconomic and
psychosocial risk factors and the lack of clarity as to what factors are most Operative in
increasing morbidity risk in asthmatic patients. Based on the results of the study by
Adams et a1 it seems reasonable to not only include suggestions for self-monitoring
including a written action plan, but also asking about areas of concern (dislike)
regarding asthma medications, as well as conﬁdence issues in managing attacks.

The current model is likely an oversimpliﬁcation of the reality of clinical
medicine, however as it is a reﬂection of what is occurring in clinics it likely suggests
that our approach to asthma care is an oversimpliﬁcation and does not account for all
the operative elements. Our treatments will not be speciﬁcally directed at the area of
need for the individual patient until we are able to deveIOp a risk model that moves

beyond simple associations to a multi-dimensional causal model, thus identifying the

44

needed intervention for a given patient. The current study is a ﬁrst step in this
direction.

Further efforts to augment this model and identify limitations will likely include
further clariﬁcation of the underlying factors (constructs) that impact asthma morbidity.
This is reﬂected by the fact that the R2 for 6 month morbidity was so low. The current
model clearly did not identify the factors that were playing a role in 6 month morbidity.
This could be because the observed variables were a poor reﬂection of the underlying
construct or it could be a reﬂection that the hypothesized factors are really not the most
signiﬁcant factors causing asthma morbidity. The answer to this question has
tremendous clinical application. If the lack of associations with 6 month morbidity
were because of poor construct validity of the model, then the solution would be to
utilize reliable and validated measures of these underlying constructs leaving the model
relatively unchanged, however, if the lack of associations reﬂects the impact of, as of
yet unidentiﬁed factors, then this suggests that our current clinical approach needs to be
reassessed in addition to this model. We have also not begun to explore the inﬂuence
of mediators and moderators, which are not included in the model. Future directions
could include utilizing reliable and valid instruments to measure the underlying
constructs as well as reassessing the model itself. These issues should be pursued prior
to the application of these methods to other asthmatic populations. However, in the
future applying these methods to other populations will be important as the same
factors and factor relationships may be different in other asthmatic populations.

In summary, quality of care is high in response to high current symptoms or

previous severe disease. Six month morbidity was related to previous severe disease,

45

albeit only modestly. The lack of other associations could be the result of low model
sensitivity, lack of construct validity of the observed variables, or the impact of yet
unidentiﬁed latent variables. The fact that the latent variables were represented by
single clinical questions and not instruments with established construct validity, though
a limitation from a research standpoint, likely increased the reﬂection of what is
actually occurring in clinics. Therefore these results might be as much a critique of
clinical practice patterns as the inadequacy of the current model. This is consistent with
the fact that current clinical risk models for asthma morbidity have low positive
predictive values, as outlined in the background section. Further research is needed to
deﬁne the characteristics and impact of SES and psychosocial functioning on asthma
risk. Only with these factors better deﬁned and included in future models will the

predictive accuracy improve.

46

APPENDIX A: TABLES AND FIGURES

>®O

ﬁgure 1: Proposed causal model. The following factors (latent variables) are
represented by ovals; F 1: 6 month morbidity, F2: quality of care indicators, F3:
current symptom severity, F4: previous severe disease. A straight, single-headed
arrow represents a unidirectional causal path.

47

 

 

e 0 Morbidity composite

 

  

Fl: 6 month

 

 

morbidity

   

 

 

e 0 33 Inhaled steroids

 

 

 

0 88 Peak ﬂow meter

  

F 2: quality
of care

0.48

 

 

   

 

indicators

   

 

 

6 0,90 Asthma specialist

 

 

 

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severity

 

   

 

 

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0.63 Steroids ever

 

F4: Previous

   

 

 

   

severe

 

     

disease

 

6 .933, ED visit ever

 

0.47

 

 

//

 

 

F_igure 2: Conﬁrmatorv Factor Analysis: modiﬁed measurement model. Observed
(or manifest) variables are represented by rectangles and factors (latent variables) are
represented by ovals. A straight, single-headed arrow represents a unidirectional
causal path, whereas a curved, double-headed arrow represents correlation or
covariance between the two variables.

48

Table 1: Demographic Characteristics

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Variable % (n)
Age Mean age 8.1 years Range 1 —
17years
Hospital Urban 69.3 (115)
location Suburban 18.1 (30)
Rural 12.7 (21)
Gender Female 38.6 (64)
Male 61.5 (102)
Race Caucasion/white 71.7 (119)
(survey African American 30.1 (50)
instructions: Hispanic 15.7 (26)
“select one or American Indian or 4.2 (7)
more” Alaska Native
Asian 1.2 (2)
other 1.2 (2)
Parental Less than high school 13.9 (23)
education level High school or GED 31.3 (52)
1-3 years of college 33.1 (55)
4 years of college or 21.1 (35)

 

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51

Table 3: Variable Description and Frequency Distribution

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Latent Observed Low risk % (11) High risk % (n)
Variable Variable
Abbreviation
(and #)
6 month SMUC (15) 3 level composite outcome
morbidity SMED (15) 1) no urgent care 78.3 (130)
(F1) SMH (15) 2) urgent care (no ED/hosp) 13.9 (23)
3) ED or hospitalization 7.8 (13)
Quality of ICS (5) Y 52.4 (87) N 47.6 (79)
care (F2) AS (6) Y 27.7 (46) N 72.3 (120)
SP (7) Y 65.7(109) N 34.3 (57)
PFMTR (8) Y 43.4 (72) N 56.6 (94)
WAP (9) Y 45.8 (76) N 54.2 (90)
ASTHED Y 71.1 (118) N 28.9 (48)
(10)
Current FDS (l) _<_2x/wk 74.1 (123) 33x/wk 25.9 (43)
symptoms FNS (2) 52x/4wk 74.1 (123) 33x/4wk 25.9 (43)
(F 3) FAL (3) 52x/last 4 weeks 33x/last 4 weeks
75.9 (126) 24.1 (40)
SF (4) N 82.5 (137) Y 17.5 (29)
Prior AD (1 l) > 5 years 31.3 (52) < 5 years 68.7 (114)
morbidity SE (12) N 22.3 Q6) Y 77.7 (129)
(F4) EDE (13) N 16.3 (27) Y 83.7 (139)
HE (l4) N488 (81) Y 51.2 (85)

 

 

 

 

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56

APPENDIX B: SURVEY INTRUMENTS

CHILD COHORT VISIT FORM
Emergency Department (CIRCLE ONE):

Gerber Blodgett Butterworth

ED visit date (mm/dd/yr) _/ _/

ED triage time (hhzmm) _/

Insurance Company

 

Presenting complaint -

 

PLEASE ANSWER EVERY QUESTION. IF PARENT DOES NOT KNOW AN
ANSWER PLEASE WRITE IN ‘DK’ (DON’T KNOW). RECORD ONLY ONE
ANSWER TO EACH QUESTION UNLESS SPECIFICALLY INSTRUCTED TO
‘CHECK ALL THAT APPLY’.

A. DEMOGRAPHIC INFORMATION

1. Date of child’s birth (mm/dd/yr) _ / _/

 

2. Sex: ................................................................................................. Male
...................................................................................................... Female
3. Is your child Spanish, Hispanic or Latino?
No ......................................................................................................... 01
Yes ....................................................................................................... 02
4. What race is your child? (SELECT ONE QR MORE)
White or Caucasian .............................................................................. 01
Black or African-American .................................................................. 02
Asian .................................................................................................... 03
American Indian or Alaska Native ...................................................... 04
Native Hawaiian or Paciﬁc Islander .................................................... 05
Other race, please specify: ............................ O6
5. How much schooling have mg (parent or guardian) completed?
Less than high school ........................................................................... 01
Graduated high school or got GED ...................................................... 02
1-3 years of college .............................................................................. 03
4-year college degree or more .............................................................. O4

57

B. ASTHMA HISTORY

6. Has a doctor ever told you that your child has asthma?
No ......................................................................................................... 01
Yes ....................................................................................................... 02
If Yes, 6a. How old was your child when a doctor ﬁrst diagnosed him/her with asthma?
< 2 years old ......................................................................................... 01
2 - 5 years ............................................................................................. 02
5 — 9 years ............................................................................................. 03
10 - 14 years ......................................................................................... 04
15 - 18 years ......................................................................................... 05

The following questions are about your child’s asthma symptoms over the last 4 weeks
that is from to (but do not refer to this current episode)

 

 

7. How often in the last 4 weeks has your child had asthma symptoms during the
day? (i.e., wheezing, a dry cough, shortness of breath, and/or chest tightness)

Never .................................................................................................... 01
Less than once a week .......................................................................... 02
l or 2 times a week ......... O3
3 to 6 times a week ............................................................................... 04
Every day ............................................................................................. 05
Continually (all the time) ..................................................................... O6 .
8. How many times over the last 4 weeks did your child wake up at night because

of asthma symptoms? (i. e., wheezing, a dry cough, shortness of breath, and/or chest
tightness)

Never .................................................................................................... 01
1 or 2 times .......................................................................................... 02
3 to 4 times .......................................................................................... 03
5 to 9 times .......................................................................................... O4
10 or more times .................................................................................. 05
9. How many times over the last 4 weeks has your child’s activities been affected or

restricted by his/her asthma symptoms?

Never .................................................................................................... 01
1 or 2 times ........................................................................................... 02
3 to 4 times ........................................................................................... 03
5 or more times .................................................................................... 04
All the time .......................................................................................... 05

10. In the last 4 weeks has your child’s asthma symptoms ever been severe enough to
limit your child’s speech to only 1 or 2 words at a time between breaths?

No ......................................................................................................... 01

Yes ....................................................................................................... 02

58

If Yes, 10a. How many times has this occurred in the last 4 weeks?

 

C. USUAL SOURCE OF ASTHMA CARE

11. Does your child have a “primary care provider” or other regular source of medical
care (such as a family doctor, pediatric nurse practitioner or medical clinic)?

No (IF NO, SKIP TO QUESTION 13) .......................................... 01
Yes ....................................................................................................... 02

12. Does this doctor/provider/clinic take primary responsibility for your child’s
regular asthma care? (i.e., directs your child’s asthma care and writes most of your
prescriptions) [= REGULAR ASTHMA CARE PROVIDER]

No ......................................................................................................... 01
Yes (IF YES, SKIP TO QUESTION 14) ........................................ 02

13. What type of doctor/provider/clinic takes primary responsibility for your regular
asthma care? (i.e., directs your child’s asthma care and writes most of your
prescriptions) [= REGULAR ASTHMA CARE PROVIDER]

 

 

 

 

Emergency Department (specify: ) ........ 01
Med center (= urgent care center) (specify: ) ..... 02
An asthma specialist (specify pulmonologist, allergist,

or asthma clinic ) ................................... 03
Other provider/site (specify: ) ...... 04
No regular asthma care provider (SKIP TO QUESTION 16) ............. 05

14. How many times in the last 12 months did your child visit m1}:
(doctor/provider/clinic) for a regularly scheduled appointment for asthma care?

[SCHEDULED APPT. = REGULAR OR ROUTINE VISIT TO DISCUSS
ASTHMA]

times or Never

 

15. How many months ago was the last regularly scheduled appointment for asthma
care with this doctor/provider/clinic?

S 1 month ago ...................................................................................... 01

1 - 3 months ago .................................................................................. 02

4 - 6 months ago ................................................................................... O3

7 — 12 months ago ................................................................................ 04

> 12 months ago ................................................................................... 05

59

16. In the last 12 months, has your child visited an asthma specialist (e.g.,

pulmonologist, allergist, asthma clinic or other specialist)? (LEAVE BLANK IF

SPECIALIST IS REGULAR ASTHMA CARE PROVIDER AS DEFINED IN

QUESTION 13).

Nn
Yes

01
(Y)

D. CURRENT ASTHMA TREATMENT, MANAGEMENT AND CONTROL

17. RECORD ALL PRESCRIPTION AND NON-PRESCRIPTION ASTHMA
RELATED MEDICATIONS USED IN THE LAST 4 WEEKS IN THE FOLLOWING

TABLE (EXCEPT SYSTEMIC STEROIDS — SEE QUESTION 18)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Medicatio Frequency Doctor Current Frequency of Route Has Rx Used in
(name) Rx’d Use Run Out? last four
weeks?
Daily QOD weekly Daily QOD PO Inh Yes No Yes No
PRN Weekly PRN Neb
Daily QOD weekly Daily QOD PO Inh Yes No Yes No
PRN Weekly PRN Neb
Daily QOD weekly Daily QOD PO Inh Yes No Yes No
PRN Weekly PRN Neb
Daily QOD weekly Daily QOD PO Inh Yes No Yes No
PRN Weekly PRN Neb
Daily QOD weekly Daily QOD PO Inh Yes No Yes No
PRN Weekly PRN Neb
Daily QOD weekly Daily QOD PO Inh Yes No Yes No
PRN Weekly PRN Neb
Daily QOD weekly Daily QOD PO Inh Yes No Yes No
PRN Weekly PRN Neb
18. Has your child ever taken steroids orally or by injection for a severe asthma
attack?
No 01
Yes ()7

 

60

If Yes, 18a. Over the past 4 weeks, has child taken any steroids orally or by injection for
asthma? (CHECK ORAL AND INJECTION IF HAVE TAKEN BOTH)

 

No ......................................................................................................... 01

Yes — Injection ..................................................................................... 02

Yes - Oral ............................................................................................ 03
If Yes - Oral,

18b. How many days in the past 4 weeks did child take oral steroids? days
18c. How many days ago did child last take oral steroids? days

IF CHILD NOT CURRENTLY USING INHALED CORTICOSTEROIDS:
19. Has child eye; used an inhaled steroid for asthma?

 

No ......................................................................................................... 01
Yes ....................................................................................................... 02
If Yes,
19a. Names (5)

 

19b. For how long did child take an inhaled steroid for asthma?
weeks / months / years.

19c. When did child last use an inhaled steroid for asthma?
months / years ago.

20. Are you usually able to get your asthma prescriptions ﬁlled?
No ......................................................................................................... 01
Yes ....................................................................................................... 02

If No, 20a. Why not? Specify main reason

 

21. A spacer is a device that you put between the mouth and inhaler to make it easier
to breathe medicine into the lungs. Does your child have a spacer?

No ......................................................................................................... 01
Yes ....................................................................................................... 02
If Yes, 21a. How often does child use the spacer when using the inhaler?
Never .................................................................................................... 01
Rarely ................................................................................................... 02
Occasionally ......................................................................................... 03
Usually ................................................................................................. O4
Always ................................................................................................. 05

61

22. A peak ﬂow meter measures how hard you can blow air out of the lungs. Does
your child have a peak ﬂow meter?

No ......................................................................................................... 01
Yes ....................................................................................................... 02
If Yes, 223. On average, how often does your child use the peak ﬂow meter?
Rarely ................................................................................................... 01
< 1/week ............................................................................................... 02
1-3/week ............................................................................................... 03
4-6/week ............................................................................................... 04
Daily ..................................................................................................... 05
Only during exacerbations ................................................................... O6

23.Has a doctor or a nurse ever given you a written plan for you to treat your child’s
asthma? [= ASTHMA ACTION PLAN]

No ......................................................................................................... 01

Yes ....................................................................................................... 02

24. Have you or your child ever received education about asthma control and
treatment from a health professional?
No ......................................................................................................... 01
Yes ....................................................................................................... 02

If Yes, 24a. What did you learn about (CIRCLE YES OR NO FOR EACH ITEM):

 

Things that can trigger your asthma? YES NO
Medications and treatments? YES NO
How to use an inhaler or nebulizer? YES NO
How to use a peak ﬂow meter? YES NO
What to do during an asthma attack? YES NO
How to use a written action plan? YES NO

E. EMERGENCY ASTHMA CARE

[THE FOLLOWING ANSWERS SHOULD NOT INCLUDE THE CURRENT
EPISODE]

25. Has your child ever been hospitalized overnight for treatment of asthma

symptoms [i.e., wheezing, dry cough, shortness of breath, and/or chest tightness]?
No ......................................................................................................... 01
Yes ....................................................................................................... 02

If Yes, 25a. How many times in the last 12 months, did your child stay over night in the
hospital for treatment of asthma symptoms? ......................... times

62

26. Excluding today, has your child ever previously gone to an emergency room for
urgent treatment of asthma symptoms?

No ......................................................................................................... 01

Yes ....................................................................................................... 02

If Yes, 26a. How many times in the last 12 months, did your child visit an emergency
room for urgent treatment of asthma symptoms?
times

 

26b. Which emergency rooms did your child visit?

 

26c. How long ago was the last visit? days / weeks / months ago

 

27. When your child is having problems with asthma symptoms that requires urgent
treatment - that is, treatment needed within 24 hours of recognizing a problem, where do
you usually end up taking him/her?

Regular asthma care provider (as deﬁned previously)

 

 

 

 

 

SKIP TO QUESTION 28 ..................................................................... 01
Emergency Department (if after hours or RACP is NA) ..................... 02
......................................... (specify: )
Emergency department (ALL times) Specify: ) .03
Med care center (specify: ) ........................ 04
An asthma specialist (specify pulmonologist, allergist,
or asthma clinic: ) ................................. 05
Other provider/site (specify: ) .................... 06
No speciﬁc location/provider ............................................................... 07

If answer is NOT regular asthma care provider then:

27a. Why do you use this particular place for asthma care? (CHECK ALL THAT
APPLY) '

 

 

No regular asthma care provider .......................................................... 01
Regular asthma care provider not available ......................................... 02
Insurance company dictates ................................................................. 03
No insurance ........................................................................................ 04
Other cost issues (specify: ) ................................. 05
Transport issues (specify: ) ................................ O6
Convenience ......................................................................................... 07
Best medical care ................................................................................. 08
Past experience/comfort with people/place ......................................... 09
Other (specify: ) ................................... 10

 

28. How many times in the last 12 months did your child visit a doctor’s Ofﬁce or clinic
for urgent treatment of asthma symptoms? [URGENT VISIT = NOT SCHEDULED OR
SCHEDULED < 24 HRS AHEAD OF TIME. DO NOT INCLUDE ED OR HOSPITAL
VISITS] times or Never

 

63

F. ASTHMA AWARENESS OF PARENT

Please tell us if the following statements are true of false.

29. Most people with asthma can become free of symptoms with proper treatment
True ...................................................................................................... 01
False ..................................................................................................... 02

30. Asthma is characterized by inﬂammation of the airways, which if controlled can
greatly reduce symptoms »

True ...................................................................................................... 01

False ..................................................................................................... 02

31. If someone with asthma feels well, it is Okay to stop taking his or her
medications?
True ...................................................................................................... 01
False ..................................................................................................... 02

Parent Name

That’s it! Do you have any questions or comments? As you know, we’re going to call you in 2
weeks to see how [child] is doing.

What’s the best number to reach you? D Home( )_ _ _-
D Work( )-_____- ______

Other(specify)(___)_________-_____________

When is the best time to call: Between and AM PM

Is it okay to leave a message on the answering machine? YES NO

If you are not available when we call, is there another family member who we could talk to that is
familiar enough with [child’s] asthma care?
(name)

 

(relationship)

 

64

6-MONTH CHILD COHORT FOLLOW-UP FORM

l_.\.S l \-'l.Sl l R|i\’llz\\'

 

 

 

 

 

 

 

 

 

 

 

 

    

     

 

 

Emergency Department 0 1. GERBER o 2. BLODGETT o 3. BUTTERWORTH
(check one)
ED Visit Date (mm/dd) l | l / l l l
Subsequent relapse O O. No 0 1- Yes (SPCCifY date (mm/dd)l | l / l l I
ED/l—Iosp visits?
0 2. Yes (specify date (mm/dd)| l l / | l l
o 3. Yes (specify date (mm/dd)! | 1/1 ' | |
Date 2-wk FU call completed Who was interviewed? Name and Relationship?
(mm/dd) | HI | I
Date Time Caller initials Comment
_ _ / _ _ _ _ __ _ _ _
/

 

 

 

 

 

 

INII R\|l \\ .SI \11 .S

O l. Agreed to o 2. refused O 3. unreachable x 8 O 4 Other (specify)
participate f/u interview (over at least 10 days)

( \l l l\(i St lxll’l

 

 

 

 

Phonel:

PhoneIL

Hello. May I speak with ‘ ? My name is __
and I work for the MSU/Grand Rapids Asthma Project.

On (date) you took [child] to the

 

 

(hospital) emergency dept for an asthma attack.

We are calling to learn how [child] has been doing over the last 6 months.
Is this a good time to talk for 5 minutes?

NO: When would be a better time to contact you?

 

YES: Great. Please remember that all of your answers will be kept conﬁdential,
and will be used for asthma research only.

 

 

 

65

 

I 1. Date Interview Completed? (mm/dd) | l |/ l l |

 

2. Who was 0 1. Mother 0 2. Father 0 3. Grandparent 0 4- Other (313305”:
interviewed?

 

2a. Name

 

SECTION A: EMERGENCY ASTHMA VISITS

 

FIRST CONFIRM INFORMATION COLLECTED AT 2-WEEK FU CALL

Your [child] was ﬁrst enrolled in this study when he/she visited ED
on _/ / . We conducted our ﬁrst follow-up call with you about X weeks

later on _/_/ . At this call we determined that since leaving the
ED/Hospital the [child] had:

 

- visited the ED or Urgent Care center for an asthma problem on __ occasions,
- and- had been hospitalized overnight on _ occasions. OK?

During this ﬁrst call we also conﬁrmed that the doctor/provider/clinic that takes
primary responsibility for your child’s asthma was
Is this still correct?

 

Now we would like to ask you about your child’s asthma experience
since the time we last talked to you on _/__/ and today. OK?

 

 

 

1. Is the above information correct?

 

 

NO (What data is incorrect?: Ol ..................... RACPTrue

Yes 02 .................................................................................... RACPTrue
2. Since we last talked to you on I | I / | | | , has he/she had a worsening of his/her
asthma that led you to take him/her for urgent medical treatment?

No 01 .............................................................................. :> SKIP TO 8

Yes 02 ................................................................................................ UV

3. How many times has this happened since we last talked to you?
(times) |___|_| ........................................................................... UVCnt

4. Thinking about the ﬁrst time this happened since we last talked to you. When did
you take [child] for urgent medical treatment for his/her asthma?
(mm/dd) I l I / | | I ..................................................... UVDate

 

66

5. Where did you f1r_st take [child] for this urgent asthma visit?

 

 

 

 

 

 

Regular asthma care provider (as deﬁned above) 01 ..... => SKIP TO 6
Hospital ED (specify: 02 ......................... UVWhen2
Med care center (specify: 03 .......................... UVWhen3
An asthma specialist: pulmonologist ................................................... 04
An asthma specialist: allergist ............................................................. 05
An asthma specialist: asthma clinic ..................................................... 06
Other provider/site (specify: 07 .................. UVWhen7
No speciﬁc location/provider 08 .............................................. UVWhen
5a. Why did you use this particular place for asthma care?
(CHECK ALL THAT APPLY)
No regular asthma care provider .......................................................... 01
Regular asthma care provider not available ......................................... 02
Insurance company dictates ................................................................. 03
No insurance ........................................................................................ 04
Other cost issues (specify: 05 UVPlaceS
Transport issues (specify: 06 ..UVPLace6
Convenience ......................................................................................... 07
Best medical care ................................................................................. 08
Past experience/comfort with people/place ......................................... 09
Other (specify: 10 UVPlacelO
Severity of episode — EMERGENCY! 11 ................................ UVPlace

6. At this visit did the doctor change [child]’s asthma medicines or make any other
changes in the management of his/her asthma? (PROMPT — FOR EXAMPLE, GIVE
YOU A NEW MEDICATION, OR CHANGE THE WAY YOU USE YOUR
EXISITING MEDICATIONS, OR CHANGE THE WAY YOU MONITOR OR

MANAGE YOUR ASTHMA)
No asthma treatment given (including no inhaled B-agonist) ................. 01
Given inhaled B-agonist treatment but no new asthma Rx .................... 02
Change in treatment plan (specify below) ....... 03 Chnng
Details

 

ChnRxTxt

 

7. Did this visit result in child being transferred to an emergency department or
hospital?

 

No 01 ............................................................................................ TransZ

Yes (Specify ED: 02 ................................ Trans
If Yes, 7a. Was [child] then admitted to the hospital overnight?

No ......................................................................................................... 01

Yes (Specify hospital: 02 ........................ TransNit

 

67

IF Q3 = MORE THAN ONE “RELAPSE” VISIT — REPEAT QUESTIONS FOR
SECOND VISIT SINCE 2-WEEK F U CALL COMPLETED. AT END OF THIS
SECTION CONFIRM SINCE 2-WEEK FU CALL:

Total (cumulative) number of ED/Urgent Care visits l___|___| ......... EDUCCnt

Total (cumulative) number of overnight hospitalizations |_|___| ..... NightCnt

SECTION B: ROUTINE ASTHMA VISITS

 

FIRST CONFIRM INFORMATION COLLECTED AT 2-WEEK FU CALL
(SPECIFICALLY Q.8A)

At the time that we ﬁrst contacted you on / , we determined that since leaving the

hospital/ED that the child HAD / HAD NOT seen the child’s regular asthma care

provider
(RA CP) for a follow-up asthma check-up. OK?

 

 

 

IF CHILD HAD NOT YET SEEN RACP AT 2-WEEK FU CALL FOR F OLLOW-

 

 

UP VISIT
8. When did [child] ﬁ_rs_t see this doctor/nurse/clinic (RA CP) for a follow-up asthma
check-up?
(mm/dd) l l | / | | l .................................................... Cthate
or number of days after ED visit (days) I l l | .............. Cthays

 

 

Now again we would like to ask you about your child’s experience
since the time we last talked to you on _____/____

 

 

 

8a. Since we last talked to you, has the child seen his/her regular asthma care provider
(RACP) for a routine asthma check up?
No 01 .............................................................................. 2 SKIP TO 9
Yes 02 ..................................................................................... RACPApt

8b. How many routine asthma cheglp—ups has child had with this doctor/nurse/ clinic
(RA CP) since we last talked to you?
(number of checkups) |__|___| .................................................. ChkCnt

8c. As a result of this visit (these visits), did the doctor change [child]’s asthma
medicines or make any other changes in the management of his/her asthma? (PROMPT —

68

NEW MEDS?, OR CHANGE EXISITING MEDS?, OR CHANGE IN MANAGEMENT

OF ASTHMA?)
No ......................................................................................................... 01
Yes 02 ......................................................................................... Newa
Describe:

 

NewaTxt

 

9. Has child had any other doctor visits speciﬁcally related to his/her asthma care and
treatment since we last talked to you on __ / __ ? (i.e., NOT WITH RACP, e.g.,

ASTHMA SPECIALISTS)
No .......................................................... 01 :> SKIP TO 10
Yes ..................................................................... 02 .ODV

9a. When did [child] f1_rs_t see ANOTHER doctor/nurse/clinic (NOT RACP) for an
asthma related visit?

 

 

(mm/dd) l l | / | | | .................................................. ODVDate
or number of days after ED visit (days) | l l | ............ ODVDays
NOT APPLICABLE (ﬁrst visit recorded at 2-WK F U call) ............... 99

9b. How many asthma related visits has child had with ANOTHER doctor/nurse/clinic
(NOT RACP) since we last talked to you?
(number of visits) |_|___| ........ g .............................................. ARVCnt

90. Where did the visit take place and who was it with? (CHECK MORE THAN ONE
RESPONSE IF VISITS TO MORE THAN ONE SPECIALIST)

 

 

Asthma specialist (specify type: 01 ........... ARVLocl
Specialty Asthma Clinic ...................................................................... 02
Other primary care type doctor/clinic .................................................. 03
Other (specify: 04 .................... ARVLoc2
ARVLoc
Name & location ARVLocNL

 

9d. What was the primary purpose of this (these) visit(s)?

Describe:

 

ARVWhy

 

9e. As a result of this (these) visit(s), did the doctor change [childJ’s asthma
medicines or make any other changes in the management of his/her asthma? (PROMPT —

69

NEW MEDS?, OR CHANGE EXISITING MEDS?, OR CHANGE IN MANAGEMENT

 

 

 

 

OF ASTHMA?)
NO 01
Yes 02 ARVNewa
Describe:
ARVNTxt
10. Has child had any other doctor visits for health problems not related to asthma since
we last talked to you on _/_? (# visits) |___|_| ................................... NonARV
If Yes,
10a. What was visit for? NonARVTx

 

C. CURRENT ASTHMA RELATED MEDICATIONS

11. RECORD ALL PRESCRIPTION AND NON-PRESCRIPTION ASTHMA
RELATED MEDICATIONS USED IN THE LAST 6 MONTHS IN THE FOLLOWING
TABLE (EXCEPT SYSTEMIC STEROIDS — SEE QUESTION 11a)

 

 

 

 

 

 

 

 

 

Medication Frequency Docto Current Frequency of Route Time period of
(name) Rx’d Use use (months)
(-) most recent)
PO Inh
Daily QOD Daily QOD Week Neb 1 2 3 4 5 6
weekly PRN PRN
PO Inh
Daily QOD Daily QOD Week Neb 1 2 3 4 5 6
weekly PRN PRN
PO Inh
Daily QOD Daily QOD Week Neb 1 2 3 4 5 6
weekly PRN PRN
PO Inh
Daily QOD Daily QOD Week Neb 1 2 3 4 5 6
weekly PRN PRN
PO Inh
Daily QOD Daily QOD Week Neb l 2 3 4 5 6
weekly PRN PRN
PO Inh
Daily QOD Daily QOD Week Neb 1 2 3 4 5 6
weekly PRN PRN
PO Inh
Daily QOD Daily QOD Week Neb 1 2 3 4 5 6
weekly PRN PRN

 

 

 

 

 

 

COMMENTS:

 

7O

11a. Over the past 6 months, has child taken any steroids orally or by injection for
asthma? (CHECK ORAL AND INJECTION IF HAVE TAKEN BOTH)

No ......................................................................................................... 01

Yes — Injection ..................................................................................... 02

Yes — Oral ............................................................................................ 03
If Yes - Oral,

11b. How many rounds Of oral steroids has child taken over the last 6 months?
rounds

11c. How long ago was the last round of oral steroids? days / weeks ago
D. CURRENT SYMPTOMS, CONTROL AND QUALITY OF LIFE

12. How often in the last 4 weeks has your child had asthma symptoms during the day?
(i.e., wheezing, a dry cough, shortness of breath, and/or chest tightness)

 

Never .................................................................................................... 01
Less than once a week .......................................................................... O2
1 or 2 times a week .............................................................................. O3
3 to 6 times a week ............................................................................... 04
Every day ............................................................................................. 05
Continually (all the time) ...................................... 06 ..SympDay

13. How many times over the last 4 weeks did your child wake up at night because of
asthma symptoms? (i.e., wheezing, a dry cough, shortness of breath, and/or chest
tightness)

 

Never .................................................................................................... 01
l or 2 times.................. ......................................................................... 02
3 to 4 times ........................................................................................... 03
S to 9 times ........................................................................................... 04
10 or more times ................................................. 05 .SympNit

14. How many times over the last 4 weeks has your child’s activities been affected or
restricted by his/her asthma symptoms?

Never .................................................................................................... 01
l or 2 times ........................................................................................... 02
3 to 4 times ........................................................................................... O3
5 or more times .................................................................................... 04
All the time ......................................................... 05 Restrict

15. Over the past 4 weeks has your child’s asthma symptoms been severe enough to limit
your child’s speech to only 1 or 2 words at a time between breaths?

No .............................................................................. 01

Yes .................................................................... 02 Speech

71

If Yes,
15a. How many times has this occurred in the last 4 weeks? I__I__ISpeecht

16. Over the past 4 weeks how many days has your child had to use his/her quick relief
medicine. (i.e., short acting bronchodilator or rescue medicine)

(days) I_I_| ........................................................................ QuicDays

17. Over the past 4 weeks, how much discomfort or distress has [child] felt because of
asthma symptoms? Would you say...

None ..................................................................................................... 01
Mild ...................................................................................................... 02
Moderate .............................................................................................. O3
Severe ............................................................... O4.Distress

18. How would you rate [child]’s asthma condition now compared to around the time
period when he/she went to the emergency department on _ / _?

Much worse .......................................................................................... 01
A little worse ........................................................................................ 02
About the same .................................................................................... 03
A little better ........................................................................................ 04
Much better ...................................................... 05 CondNow

IF CHILD IS 7 YEARS OF AGE OR OLDER:

19. Over the past 4 weeks how often did your child use his/her peak ﬂow meter?

 

 

 

None ........................................................ 01=> SKIP TO 20
< l/week ............................................................................................... 02
l-3/week ............................................................................................... 03
4-6/week ............................................................................................... 04
Daily ..................................................................................................... 05
Only during exacerbations ................................................................... 06
Doesn’t have a PFM ..................................... 07 :> SKIP TO 20
PeakFreq
19a. What is the child’s personal best peak ﬂow reading? (liters/minute)
I | I I

19b. Over the past 4 weeks, what were the highest and lowest peak ﬂow readings?
Highest reading (liters/minute) I I I I ......................... PeakHigh
Lowest reading (liters/minute) I I I I ........................... PeakLow

19c. Over the past 4 weeks, has the peak flow dropped below 80% of [child’s]

personnel best?
No .............................................................................. 01
Yes ................................................................. 02 PeakDrop

72

If Yes,
19d. What did you do when this occurred?

Details: PkDropDo
ALL AGES:
20. A spacer is a device that you put between the mouth and inhaler to make it easier

to breathe medicine into the lungs. Does your child have a spacer?

If Yes,

20a. Over the past 4 weeks, how often has your child used the spacer when using the
inhaler?

Never .................................................................................................... 01
Rarely ................................................................................................... 02
Occasionally ......................................................................................... 03
Usually ................................................................................................. O4
Always ................................................................................................. 05
21. Have you and your child received asthma education since your initial ED visit?
No ........................................................................................................ 01'
Yes ....................................................................................................... 02
If Yes
21a. What was the source of this education? — that is, who provided it?
Your regular asthma care provider ...................................................... 01
Asthma specialist (allergist, or pulmonologist) ................................... 02
ED or Urgent Care Center .................................................................... O3
Asthma Coalition ................................................................................. 04
Other health professional (Specify ) ...... 05

 

[SPECIFY TYPE OF PROFESSIONAL AND ORGANIZATION
e.g., RN-SCHOOL, RN-COMMUNTY)

21b. What did you learn about? (Circle Yes or No for each item)

Things that can trigger your asthma? YES NO
Medications and treatments? YES NO
How to use an inhaler or nebulizer? YES NO
How to use a peak ﬂow meter? YES NO
What to do during an asthma attack? YES NO
How to use a written action plan? YES NO

22. Did you have an asthma management plan at the time of the initial ED visit?
No ........................................................................................................ 01
Yes ....................................................................................................... 02

73

If No,
22a. Do you have an asthma management plan now?
No ........................................................................................................ 01
Yes ....................................................................................................... 02

23. How conﬁdent do you feel about your ability to:

23a. Manage your child’s asthma on a day-to-day basis?

 

 

(READ and CIRCLE ONE)
Very unsure Somewhat unsure Somewhat conﬁdent Very conﬁdent Don’t know
1 2 3 4 5
23b. Manage or control an asthma attack or exacerbation?
(READ and CIRCLE ONE)
Very unsure Somewhat unsure Somewhat conﬁdent Very conﬁdent Don’t kﬂw
1 2 3 4 5

24. If your child had an asthma attack today, how likely are you to do the following?

24a. Measure the asthma severity using a PFM (READ and CIRCLE ONE)
Deﬁnitely Yes Probably Yes Probably Not Deﬁnitely NOT Don’t Know N/A (< 7 yrs)

 

1 2 3 4 5 6
24b. Increase the amount of rescue medication (albuterol) (either dose or freq) (READ
and CIRCLE ONE)

Deﬁnitely Yes Probably Yes Probably Not Deﬁnitely NOT Don’inow

1 2 3 4 5

24c. Wait to see if the symptoms subside after using the medication before calling your
doctor or going to the ED (READ and CIRCLE ONE)
Deﬁnitely Yes Probably Yes Probably Not Deﬁnitely NOT Don’t know

1 2 3 4 5

25. If the symptoms continued to persist what action would you take next?

Call PCP ............................................................................................... 01
Go directly to ED/Urgent Care - always .............................................. 02
Go directly to ED/Urgent Care - if after hours and PCP N/A ............. 03
Continue with treatment ....................................................................... 04
Not sure ................................................................................................ 05
Other (Specify) .............. 05

 

26. What other actions or steps do you think would help you better control and manage
your child’s asthma?

74

 

 

 

That’s it! Do you have any questions or comments? [pause] This is the last time we need
to call you. Thank you for your help with this asthma study.

 

COMMENTS:Comments

75

 

APPENDIX C: SAS CODE AND OUTPUT

libname cohort "F :\";
data test;
set cohort.PedsFudeleted;
IF AgeDg in (01,02)
then AD = 02;
IF AgeDg = > 03
then AD = 01;
IF SympDay in (01,02,03)
then FDS = 01;
IF SympDay in (04,05,06)
then FDS = 02;
IF SympDay = 999
then FDS = .;
IF SympNgt in (01,02)
then FN S = 01;
IF SympNgt in (03,04,05)
then FNS = 02;
IF SympNgt = 999
then FNS = .;
IF ActRstr in (01,02)
then FAL = 01;
IF ActRstr in (03,04,05)
then F AL = 02;
IF ActRstr = 999
then F AL = .;
IF AAka = 01
then SF = 01;
IF AAttack = 02
then SF = 02;
IF AAttack = 999
then SF = .;
IF CDF64 = 01
THEN ICS = 02;
IF CDF64 = 02
THEN ICS = 01;
IF CDF 64 = 999
THEN ICS = 01;
IF AsthSpec = 01
then AS = 01;
IF AsthSpec = 02
then AS = 02;
IF AsthSpec = 999
then AS = 01;
IF Spacer = 01

76

then SP = 01;

IF Spacer = 02
then SP = 02;

IF Spacer = 999
then SP = .;

IF PF M = 01
then PFMTR = 01;

IF PFM = 02
then PF MTR = 02;

IF PF M = 999
then PF MTR = .;

IF ActPlan = 01
then WAP = 01;

IF ActPlan = 02
then WAP = 02;

IF ActPlan = 999
then WAP = .;

IF AsthEdu = 01
then ASTHED = 01;

IF AsthEdu = 02
then ASTHED = 02;

IF AsthEdu = 999
then ASTHED = .;

IF WhereGo in (3,4)
then US = 02;

else US = 01;

IF EverSOI = 01
then SE = 01;

IF EverSOI = 02
then SE = 02;

IF EverSOI = 999
then SE = .;

IF EverEr = 01
then EDE = 01;

IF EverEr = 02
then EDE = 02;

IF EverEr = 999
then EDE = .;

IF EverHosp = 01
then HE = 01;

IF EverHosp = 02
then HE = 02;

IF EverHosp = 999
then HE = .;

IF EDE = 01
then PM = 01;

77

IF (EDE = 02 and HE = 01)
then PM = 02;
IF HE = 02
then PM = 03;
IF PCP = 1
then PCP_TM = 02;
IF PCP = 2
then PCP_TM = 01;
IF PCP = 999
then PCP_TM = .;
IF (Hispanic = 02 or Race02 = 1 or Race04 = 1)
then RaceRsk = 02;
else RaceRsk = 01;
IF Educate in (01,02)
then PEL = 02;
IF Educate in (03,04)
then PEL = 01;
IF Educate = 999
then PEL = .;
IF Prescrpt = 01
then F P = 02;
IF Prescrpt = 02
then FP = 01;
IF Prescrpt = 999
then F P = .;
IF RACPApt_2 = 01
then FUA = 02;
IF RACPApt_2 == 02
then FUA = 01;
IF RACPApt_2 = 999
then FUA = 01;
IF C2 = 01
then SMUC = 01;
IF C2 = 02
then SMUC = 02;
IF C2 = 999
then SMUC = 01;
IF C7 = 01
then SMED = 01;
IF C7 = 02
then SMED = 02;
IF C7 = 999
then SMED = 01;
IF C7a = 01
then SMH = 01;
IF C7a = 02

78

then SMH = 02;

IF C7a = 999
then SMH = 01;

IF SMUC in (01,999)
then SMM = 01;

IF (SMUC = 02 and SMED = 01)
then SMM = 02;

IF (SMED = 02 or SMH = 02)
then SMM = 03;

run;

PROC CORR DATA=TEST;
TITLE 'CORRELATION MATRIX'; .
VAR FDS FNS FAL SF ICS AS SP PFMTR WAP ASTHED AD SE EDE HE SMM;

RUN;
CORRELATION MATRIX 09:40 Tuesday, March 6, 2007 237
The CORR Procedure
15 Variables: FDS FNS FAL SF ICS AS SP PFMTR WAP
ASTHED AD SE EDE HE SMM

Simple Statistics

Variable N Mean Std Dev Sum Minimum Maximum
F DS 166 1.25904 0.43943 209.00000 1.00000 2.00000
FNS 166 1.25904 0.43 943 209.00000 1.00000 2.00000
FAL 166 1 .24096 0.42896 206.00000 1 .00000 2.00000
SF 166 1.17470 0.38086 195.00000 1.00000 2.00000
ICS 165 1.52727 0.50078 252.00000 1.00000 2.00000
AS 166 1 . 17470 0.38086 195.00000 1.00000 2.00000
SP 166 1.65663 0.47627 275.00000 1.00000 2.00000
PFMTR 166 1.43373 0.49709 238.00000 1.00000 . 2.00000
WAP 164 1 .46341 0.50019 240.00000 1 .00000 2.00000
ASTHED 166 1 .71084 0.45474 284.00000 1.00000 2.00000
AD 166 1.68675 0.46522 280.00000 1.00000 2.00000
SE 165 1.78182 0.41427 294.00000 1.00000 2.00000
EDE 166 1.83735 0.37016 305.00000 1.00000 2.00000
HE 166 1.51205 0.50137 251 .00000 1.00000 2.00000
SMM 166 1.29518 0.60571 215.00000 1.00000 3.00000

79

Pearson Correlation COefﬁcients
Prob > IrI under H0: Rho=0
Number of Observations

FDS FNS FAL SF ICS AS SP PF MTR

FDS 1.00000 0.49783 0.53496 0.41601 0.16315 0.12631 0.16695
0.17617
<.0001 <.0001 <.0001 0.0363 0.1049 0.0316. 0.0232
166 166 I66 166 165 166 166 166

FNS 0.49783 1.00000 0.40635 0.34359 0.23029 0.09010 0.13799
0.17617
<.0001 <.0001 <.0001 0.0029 0.2483 0.0762 0.0232
166 166 166 166 165 166 166 166

FAL 0.53496 0.40635 1.00000 0.51980 0.28069 0.22303 -0.03753
0.24587
<.0001 <.0001 <.0001 0.0003 0.0039 0.6312 0.0014
166 166 166 166 I65 166 166 166

SF 0.41601 0.34359 0.51980 1.00000 0.24587 0.12258 -0.00141
0.07752
<.0001 <.0001 <.0001 0.0015 0.1156 0.9856 0.3208
166 166 166 166 165 166 166 166

ICS 0.16315 0.23029 0.28069 0.24587 1.00000 0.29870 0.12904
0.22119
0.0363 0.0029 0.0003 0.0015 <.0001 0.0986 0.0043
165 165 165 165 165 165 165 165

AS 0.12631 0.09010 0.22303 0.12258 0.29870 1.00000 -0.00141
0.23759
0.1049 0.2483 0.0039 0.1156 <.0001 0.9856 0.0021
166 I66 166 166 165 166 166 166

SP 0.16695 0.13799 -0.03753 -0.00141 0.12904 -0.00141 1.00000

0.30010
0.0316 0.0762 0.6312 0.9856 0.0986 0.9856 <.0001
166 166 166 166 165 166 166 166

PFMTR 0.17617 0.17617 0.24587 0.07752 0.22119 0.23759 0.30010

1.00000
0.0232 0.0232 0.0014 0.3208 0.0043 0.0021 <.0001
166 166 166 166 165 166 I66 166

80

WAP -0.02824 0.07106 0.09825 0.06579 0.32910 0.30643 0.17925
0.37259
0.7196 0.3659 0.2107 0.4026 <.0001 <.0001 0.0216 <.0001
164 164 164 164 163 164 164 164

ASTHED -0.01717 -0.07783 0.01759 0.08348 0.26309 0.18846 0.26635
0.26327
0.8262 0.3189 0.8220 0.2849 0.0006 0.0150 0.0005 0.0006
166 166 166 166 165 166 166 166

AD 0.13251 0.07322 -0.04464 -0.06553 0.08932 0.10550 0.27748
0.19798
0.0888 0.3485 0.5679 0.4016 0.2539 0.1761 0.0003 0.0106
166 166 166 166 165 166 166 166

SE 0.07962 0.07962 0.09339 0.12828 0.32757 0.16683 0.29513
0.28728
0.3093 0.3093 0.2328 0.1006 <.0001 0.0322 0.0001 0.0002
165 165 I65 165 164 165 165 165

EDE 0.07429 -0.00022 -0.05702 -0.01217 0.10620 0.03082 0.26570

0.18810
0.3415 0.9977 0.4656 0.8763 0.1746 0.6935 0.0005 0.0152
166 166 I66 166 165 166 166 166

HE 0.08203 0.05452 0.07096 0.10000 0.33289 0.03652 0.20779

0.17345
0.2934 0.4854 0.3636 0.1999 <.0001 0.6404 0.0072 0.0254
166 166 166 166 165 166 166 166

SMM -0.08408 0.00700 0.00450 0.01155 0.12362 0.14291 -0.00367

0.05529
0.2815 0.9287 0.9542 0.8826 0.1137 0.0662 0.9626 0.4792
166 166 166 166 165 166 166 166

81

CORRELATION MATRIX 09:40 Tuesday, March 6, 2007
239

The CORR Procedure

Pearson Correlation Coefﬁcients
Prob > |r| under H0: Rho=0
Number of Observations

WAP ASTHED AD SE EDE HE SMM

FDS -0.02824 -0.01717 0.13251 0.07962 0.07429 0.08203 -0.08408
0.7196 0.8262 0.0888 0.3093 0.3415 0.2934 0.2815
164 166 166 165 166 166 166

FNS 0.07106 -0.07783 0.07322 0.07962 -0.00022 0.05452 0.00700
0.3659 0.3189 0.3485 0.3093 0.9977 0.4854 0.9287
164 166 166 165 166 166 166

FAL 0.09825 0.01759 -0.04464 0.09339 -0.05702 0.07096 0.00450
0.2107 0.8220 0.5679 0.2328 0.4656 0.3636 0.9542
164 I66 166 I65 166 I66 166

SF 0.06579 0.08348 -0.06553 0.12828 -0.01217 0.10000 0.01155
0.4026 0.2849 0.4016 0.1006 0.8763 0.1999 0.8826
164 166 166 165 166 166 166

ICS 0.32910 0.26309 0.08932 0.32757 0.10620 0.33289 0.12362
<.0001 0.0006 0.2539 <.0001 0.1746 <.0001 0.1137
163 165 165 164 165 165 165

AS 0.30643 0.18846 0.10550 0.16683 0.03082 0.03652 0.14291
<.0001 0.0150 0.1761 0.0322 0.6935 0.6404 0.0662
164 166 166 165 166 166 166

SP 0.17925 0.26635 0.27748 0.29513 0.26570 0.20779 -0.00367
0.0216 0.0005 0.0003 0.0001 0.0005 0.0072 0.9626
164 166 166 165 166 166 166

PFMTR 0.37259 0.26327 0.19798 0.28728 0.18810 0.17345 0.05529
<.0001 0.0006 0.0106 0.0002 0.0152 0.0254 0.4792
164 166 166 165 166 166 166

WAP 1.00000 0.41692 0.13734 0.20116 0.10207 0.21070 0.00590
<.0001 0.0795 0.0100 0.1934 0.0068 0.9402

82

164 164 164 163 164 164 164

ASTHED 0.41692 1.00000 0.11356 0.27551 0.25897 0.17487 0.15773
<.0001 0.1452 0.0003 0.0008 0.0242 0.0424
164 166 166 165 166 166 166

AD 0.13734 0.11356 1.00000 0.36812 0.26544 0.27612 0.11505
0.0795 0.1452 <.0001 0.0005 0.0003 0.1399
164 166 166 165 166 166 166

SE 0.20116 0.27551 0.36812 1.00000 0.36132 0.30963 0.15746
0.0100 0.0003 <.0001 <.0001 <.0001 0.0434
163 165 165 165 165 165 165

EDE 0.10207 0.25897 0.26544 0.36132 1.00000 0.38617 0.13434
0.1934 0.0008 0.0005 <.0001 <.0001 0.0844
164 166 I66 165 166 166 166

HE 0.21070 0.17487 0.27612 0.30963 0.38617 1.00000 0.13790
0.0068 0.0242 0.0003 <.0001 <.0001 0.0764
164 166 166 165 166 166 166

SMM 0.00590 0.15773 0.11505 0.15746 0.13434 0.13790 1.00000

0.9402 0.0424 0.1399 0.0434 0.0844 0.0764
164 166 166 165 166 166 166

83

DATA PATH (type=corr);

INPUT _TYPE_ $ _NAME_ 15 V1-V15;

DATALINES;

N.166166166166165166166166164166166165166166166

STD . 0.43943 0.43943 0.42896 0.38086 0.50078 0.38086 0.47627 0.49709 0.50019
0.45474 0.46522 0.41427 0.37016 0.50137 0.60571

CORR V1 1.00000 ..............

CORR V2 0.49783 1.00000 .............

CORR V3 0.53496 0.40635 1.00000 ............

CORR V4 0.41601 0.34359 0.51980 1.00000 ...........

CORR V5 0.16315 0.23029 0.28069 0.24587 1.00000 ..........

CORR V6 0.12631 0.09010 0.22303 0.12258 0.29870 1.00000 .........

CORR V7 0.16695 0.13799 -0.03753 -0.00141 0.12904 -0.00141 1.00000 ........
CORR V8 0.17617 0.17617 0.24587 0.07752 0.22119 0.23759 0.30010 1.00000 .......
CORR V9 -0.02824 0.07106 0.09825 0.06579 0.32910 0.30643 0.17925 0.37259
1.00000 ......

CORR V10 -0.01717 -0.07783 0.01759 0.08348 0.26309 0.18846 0.26635 0.26327
0.41692 1.00000 .....

CORR V11 0.13251 0. 07322 -0. 04464 —0. 06553 0. 08932 0.10550 0. 27748 0.19798
0.13734 0.11356 1.00000.

CORR V12 0. 07962 0. 07962 0. 09339 0. 12828 0. 32757 0.16683 0. 29513 0. 28728
0.20116 0.27551 0.36812 1.00000 . . .

CORR V13 0.07429 -0.00022 -0.05702 -0.01217 0.10620 0.03082 0.26570 0.18810
0.10207 0.25897 0.26544 0.36132 1.00000 . .

CORR V14 0.08203 0.05452 0.07096 0.10000 0.33289 0.03652 0.20779 0.17345
0.21070 0.17487 0.27612 0.30963 0.38617 1.00000 .

CORR V15 -0.08408 0.00700 0.00450 0.01155 0.12362 0.14291 -0.00367 0.05529
0.00590 0.15773 0.11505 0.15746 0.13434 0.13790 1.00000

PROC CALIS COVARIANCE CORR RESIDUAL MODIFICATION;
LINEQS

VI = LV1F3 F3 + E1,

V2 = LV2F3 F3 + E2,

V3 = LV3F3 F3 + E3,
V4 = LV4F 3 F3 + E4,
V5 = LV5F2 F2 + E5,
V6 = LV6F2 F2 + E6,
V7 = LV7F2 F2 + E7,
V8 = LV8F2 F2 + E8,

V9 = LV9F2 F2+E9,
V10=LV10F2 F2 +E10,
V11=LV11F4F4+E11,
V12=LV12F4 F4+E12,
V13 =LV13F4 F4+E13,
V14=LV14F4 F4+E14,
V15 =F1+E15;

84

STD

F1 =1,

F2 =1,

F3 =1,

F4 =1,

E1-E15 =VAREl-VARE15;
COV

F1 F2 = CF1F2,
F1 F3 = CF1F3,
F1 F4 = CF1F4,
F2 F3 = CF2F3,
F2 F4 = CF2F4,
F3 F4 = CF3F4;
VAR V1-V15;
RUN;

CORRELATION MATRIX 09:40 Tuesday, March 6, 2007 300

The CALIS Procedure
Covariance Structure Analysis: Pattern and Initial Values
LIN EQS Model Statement
Matrix Rows Columns ------ Matrix Type -------
Term 1 1 _SEL_ 15 34 SELECTION

2 _BETA_ 34 34 EQSBETA IMINUSINV

3 _GAMMA_ 34 19 EQSGAMMA
4 _PHI_ I9 19 SYMMETRIC

The 15 Endogenous Variables

Manifest V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11

V12 V13 V14 V15

Latent
The 19 Exogenous Variables
Manifest
Latent F3 F2 F4 F1
Error El E2 E3 E4 E5 E6 E7 E8 E9 E10 E11

E12 E13 E14 E15

85

CORRELATION MATRIX 09:40 Tuesday, March 6, 2007
The CALIS Procedure
Covariance Structure Analysis: Pattern and Initial Values

Manifest Variable Equations with Initial Estimates

Vl = .*F3 + 1.0000 El
LV1F3

V2 = .*F3 + 1.0000 E2
LV2F3

V3 = .*F3 + 1.0000 E3
LV3F3

V4 = .*F3 + 1.0000 E4
LV4F3

V5 = .*F2 + 1.0000 E5
LV5F2

V6 = .*F2 + 1.0000 E6
LV6F2

V7 = .*F2 + 1.0000 E7
LV7F2

V8 = .*F2 + 1.0000 E8
LV8F2

V9 = .*F2 + 1.0000 E9
LV9F2

V10 = .*F2 + 1.0000 E10
LV10F2

V11 = .*F4 + 1.0000 E11
LV11F4

V12 = .*F4 + 1.0000 E12
LV12F4

V13 = .*F4 + 1.0000 E13
LV13F4

V14 = .*F4 + 1.0000 E14
LV14F4

V15 = 1.0000 Fl + 1.0000 E15

86

Variances of Exogenous Variables

Variable Parameter Estimate

F3 1 .00000
F2 1 .00000
F4 1 .00000
F 1 1.00000
E1 VAREI

E2 VARE2

E3 VARE3

E4 VARE4

E5 VARES

E6 VARE6

E7 VARE7

E8 VARE8

E9 VARE9

E10 VARE 1 0

El 1 VAREl 1

E12 VARE12

E1 3 VARE] 3

E14 VARE14

E 1 5 VARE] 5

Covariances Among Exogenous Variables
Varl Var2 Parameter Estimate

F3 F2 CF2F3
F3 F4 CF3F4
F2 F4 CF2F4
F3 F1 CF1F3
F2 F1 CF1F2
F4 F1 CF1F4

87

CORRELATION MATRIX
The CALIS Procedure

09:40 Tuesday, March 6, 2007

Covariance Structure Analysis: Maximum Likelihood Estimation

Observations 164 Model Terms 1
Variables 15 Model Matrices 4
Informations 120 Parameters 35
Variable Mean Std Dev
V1 0 0.43943
V2 0 0.43943
V3 0 0.42896
V4 0 0.38086
V5 0 0.50078
V6 0 0.38086
V7 0 0.47627
V8 0 0.49709
V9 0 0.50019
V10 0 0.45474
V11 0 0.46522
V12 0 0.41427
V13 0 0.37016
V14 0 0.50137
V15 0 0.60571
Covariances
V1 V2 V3 V4 V5
V1 0.1930987249 0.0961303382 0.1008388327 0.0696239785
0.0359024228
V2 0.0961303382 0.1930987249 0.0765961187 0.0575036724
0.0506771005
V3 0.1008388327 0.0765961187 0.1840066816 0.0849216522
0.0602963069
V4 0.0696239785 0.0575036724 0.0849216522 0.1450543396
0.0468940649
V5 0.0359024228 0.0506771005 0.0602963069 0.0468940649
0.2507806084
V6 0.0211394070 0.0150792540 0.0364372376 0.0177807609
0.0569701760
V7 0.0349405191 0.0288795581 -.0076674082 -.0002557630
00307768775

88

V8 0.0384819157 0.0384819157 0.0524272846 0.0146762180
0.0550614306
V9 -.0062071094 0.0156188808 0.0210806676 0.0125331505
0.0824346623
V10 -.0034310193 -.0155524886 0.0034311981 0.0144580912
0.0599120906
V11 0.0270892346 0.0149684836 -.0089083928 -.0116108472
0.0208091369
V12 0.0144942371 0.0144942371 0.0165958942 0.0202398737
0.0679570598
V13 0.0120839675 -.0000357851 -.0090538542 -.0017157161
0.0196861586
V14 0.0180726051 0.0120116839 0.0152612022 0.0190951778
0.0835807125
V15 -.0223793336 0.0018631700 0.0011692141 0.0026644777
0.0374973398

Covariances
V6 V7 V8 V9 V10
V1 0.0211394070 0.0349405191 0.0384819157 -.0062071094
.0034310193
V2 0.0150792540 0.0288795581 0.0384819157 0.0156188808
.0155524886
V3 0.0364372376 -.0076674082 0.0524272846 0.0210806676
0.0034311981
V4 0.0177807609 -.0002557630 0.0146762180 0.0125331505
0.0144580912

V5 0.0569701760 0.0307768775 0.0550614306 0.0824346623
0.0599120906
V6 0.1450543396 -.0002557630 0.0449809421 0.0583756392
0.0326398164
V7 -.0002557630 0.2268331129 0.0710483912 0.0427019193
0.0576858219
V8 0.0449809421 0.0710483912 0.2470984681 0.0926405716
0.0595113164
V9 0.0583756392 0.0427019193 0.0926405716 0.2501900361

0.0948311225
V10 0.0326398164 0.0576858219 0.0595113164 0.0948311225
0.2067884676
V11 0.0186928792 0.0614813350 0.0457841044 0.0319587971
0.0240240885

V12 0.0263222492 0.0582304396 0.0591594194 0.0416831102
0.0519019899

89

V13 0.0043449770 0.0468418746
0.0435915288
V14 0.0069735589 00496176525
00398691348
V15 00329680095 -.0010587271
00434452404
Covariances
V11 V12 V13
V1 00270892346 00144942371
.0223793336
V2 00149684836 0.0144942371
00018631700
V3 -.0089083928 00165958942
00011692141
V4 -.0116108472 00202398737
00026644777
V5 00208091369 00679570598
00374973398
V6 00186928792 00263222492
0.0329680095
V7 00614813350 00582304396
.0010587271
V8 00457841044 00591594194
00166473979
V9 00319587971 00416831102
00017875235
V10 00240240885 00519019899
0.0434452404
V11 02164296484 00709465489
00324197561
V12 0.0709465489 01716196329
0.0395110413
V13 00457103169 00554070429
00301203195
V14 00644042587 00643109405
00418781371
V15 0.0324197561 00395110413
03668846041

Determinant 1 .74698E- 12 Ln

00346109332

00432282520

0.01 66473 979

V14

00120839675

-.0000357851

-.0090538542

-.0017157161

0.0196861586

00043449770

0.0468418746

0.0346109332

00188982942

00435915288

0.0457103169

0.05 54070429

0.1370184256

0.0716681778

0.0301203195

0.0188982942

00528394008

0.0017875235

V15

0.0180726051

0.0120116839

00152612022

0.0190951778

00835807125

00069735589

00496176525

0.0432282520

0.0528394008

0.0398691348

0.06440425 87

0.0643109405

0.0716681778

0.2513718769

0.0418781371

-27.073133

NOTE: Some initial estimates computed by instrumental variable method.

90

wwwwwwNNNNNNNNNNH—H—‘H—t—b—w—
LII-kUJNF‘OSOWQQMAWN—iocmqamgwwﬂcooo\IONKI’I~15me

CORRELATION MATRIX

09:40 Tuesday, March 6, 2007

The CALIS Procedure
Covariance Structure Analysis: Maximum Likelihood Estimation

Vector of Initial Estimates

Parameter

LV1F3
LV2F3
LV3F3
LV4F3
LV5F2
LV6F2
LV7F2
LV8F2
LV9F2
LV10F2
LV1 1F4
LV12F4
LV13F4
LV14F4
CF2F3
CF3F4
CF2F4
CF1F3
CF1F2
CF1F4
VARE]
VARE2
VARE3
VARE4
VARES
VARE6
VARE7
VARE8
VARE9
VAREIO
VAREI 1
VARE12
VARE13
VARE14
VAREIS

Estimate

0.37713
0.29026
0.35410
0.27046
0.431 13
0.16263
0.20893
0.33922
0.30125
0.20595
0.30554
0.36084
0.25400
0.30337
0.26043
0.10316
0.45210
-0.02628
0.11932
0.19336
0.05087
0.10885
0.05862
0.07190
0.06490
0.11861
0.18318
0.13202
0.15944
0.16437
0.12307
0.04141
0.07250
0.15934
0.15546

Type

Matrix Entry: _GAMMA_[I :1]
Matrix Entry: _GAMMA_[2: 1]
Matrix Entry: _GAMMA_[3: 1]
Matrix Entry: _GAMMA_[4: 1]
Matrix Entry: _GAMMA_[5:2]
Matrix Entry: _GAMMA_[6:2]
Matrix Entry: _GAMMA_[722]
Matrix Entry: _GAMMA_[8z2]
Matrix Entry: _GAMMA_[922]
Matrix Entry: _GAMMA_[1022]
Matrix Entry: _GAMMA_[I 1:3]
Matrix Entry: _GAMMA_[1223]
Matrix Entry: _GAMMA_[I 3:3]
Matrix Entry: _GAMMA_[14:3]
Matrix Entry: _PHI_[2z1]
Matrix Entry: _PHI_[3z1]
Matrix Entry: _PHI;[3:2] .
Matrix Entry: _PHI_[4:1]
Matrix Entry: _PHI_[4:2]
Matrix Entry: _PHI_[4:3]
Matrix Entry: _PHI_[5:5]
Matrix Entry: _PHI_[6z6]
Matrix Entry: _PHI_[727]
Matrix Entry: _PHI_[8z8]
Matrix Entry: _PHI_[9:9]
Matrix Entry: _PHI_[10210]
Matrix Entry: _PHI_[11:11]
Matrix Entry: _PHI_[12: 12]
Matrix Entry: _PHI_[13zl3]
Matrix Entry: _PHI_[14:14]
Matrix Entry: _PHI_[15:15]
Matrix Entry: _PHI_[162 16]
Matrix Entry: _PHI_[17z 17]
Matrix Entry: _PHI_[18: 18]
Matrix Entry: _PHI_[19:19]

91

CORRELATION MATRIX 09:40 Tuesday, March 6, 2007
306

The CALIS Procedure
Covariance Structure Analysis: Maximum Likelihood Estimation

Levenberg-Marquardt Optimization
Scaling Update of More (1978)

Parameter Estimates 35
Functions (Observations) 120

Optimization Start

Active Constraints 0 Objective Function 2.1923056363
Max Abs Gradient Element 8.3496409147 Radius 179.97629786

Ratio
Between
Actual
Objective Max Abs and
Function Active Objective Function Gradient Predicted
Iter Restarts Calls Constraints Function Change Element Lambda Change

1 0 2 0 0.85709 1.3352 0.6541 0 0.847
2 0 3 0 0.82946 0.0276 0.0862 0 0.928
3 0 4 0 0.82789 0.00157 0.0353 0 0.746
4 0 5 0 0.82771 0.000188 0.0119 0 0.693
5 0 6 0 0.82768 0.000026 0.00537 0 0.675
6 0 7 0 0.82768 3.693E-6 0.00179 0 0.663
7 0 8 0 0.82768 5.434E-7 0.000792 0 0.659
8 0 9 0 0.82768 8.076E-8 0.000268 0 0.656
9 0 10 0 0.82768 1.21E-8 0.000117 0 0.655
10 0 11 0 0.82768 1.821E-9 0.000040 0 0.656
Optimization Results

Iterations 10 Function Calls 12

Jacobian Calls 11 Active Constraints 0

Objective Function 08276760975 Max Abs Gradient Element

0000040333

Lambda 0 Actual Over Pred Change 0655586944

Radius 0.0003017209

GCONV convergence criterion satisﬁed.

92

CORRELATION MATRIX 09:40 Tuesday, March 6, 2007
The CALIS Procedure
Covariance Structure Analysis: Maximum Likelihood Estimation

Predicted Model Matrix
V1 V2 V3 V4 V5
V1 0.1930987249 0.0827791594 0.1027940973 0.0756139626

00259725872
V2 00827791594 01930987249 0.0846892491 00622962785

00213981052

V3 01027940973 00846892491 01840066816 00773587188
00265718923

V4 00756139626 0.0622962785 0.0773587188 01450543396
00195459284

V5 0.0259725872 0.0213981052 0.0265718923 0.0195459284
02507806085 '

V6 00148880317 00122658427 00152315659 00112041361
0.0411075376

V7 00185273832 00152642050 00189548937 00139429662
0.0511561983

V8 00273550847 00225371071 00279862902 00205863406
00755304796

V9 00291086937 00239818577 00297803630 00219060365
00803723923

V10 00240596000 00198220473 00246147638 00181062909
0.0664312741

V11 00099708004 00082146701 00102008718 00075036248
00406534788

V12 00119064538 00098094021 00121811896 00089603201
00485456283

V13 00088289979 00072739703 00090327229 00066443501
00359980611

V14 00118931385 00097984319 00121675670 00089502995
0.0484913382

V15 -.0053271258 -.0043888734 -.0054500467 -.0040089814
00241002562

Predicted Model Matrix
V6 V7 V8 V9 V 1 0

V1 0.0148880317 0.0185273832 0.0273550847 0.0291086937
0.0240596000

93

V2 0.0122658427 0.0152642050 0.0225371071
0.0198220473
V3 0.0152315659 0.0189548937 0.0279862902
00246147638
V4 0.0112041361 0.0139429662 0.0205863406
0.0181062909
V5 00411075376 00511561983 0.0755304796
0.0664312741
V6 0.1450543396 00293238057 00432956549
00380797995
V7 0.0293238057 02268331129 00538791967
00473883352
V8 00432956549 0.0538791967 02470984682
0.0699673 510
V9 00460711408 00573331450 00846505424
00744526371
V10 0.0380797995 0.0473883352 00699673510
02067884676
V11 00233034266 00289999057 00428174269
00376591839
V12 00278273722 00346297213 00511296684
00449700443
V13 00206348435 00256789924 00379142054
00333466567
V14 00277962520 00345909938 00510724885
00449197529
V15 00138147723 00171917675 00253830912
00223251738
Predicted Model Matrix

V11 V12 V13 V14
V1 0.0099708004 0.0119064538 0.0088289979
.0053271258
V2 0.0082146701 0.0098094021 0.0072739703
.0043888734
V3 0.0102008718 0.0121811896 0.0090327229
.0054500467
V4 0.0075036248 0.0089603201 0.0066443501
.0040089814
V5 0.0406534788 0.0485456283 0.0359980611
00241002562
V6 0.0233034266 0.0278273722 0.0206348435
0.0138147723

94

0.0239818577

0.0297803630

0.0219060365

0.0803723923

0.0460711408

0.0573331450

0.0846505424

02501900362

0.0744526371

00455622558

00544073570

0.0403447113

00543465116

00270102848

V15

0.0118931385

0.0097984319

0.0121675670

0.0089502995

00484913382

00277962520

V7 00289999057
0.0171917675
V8 0.0428174269
0.0253830912
V9 00455622558
0.0270102848
V10 0.0376591839
0.0223251738
V11 02164296484
00336200295
V12 00645506933
00401467599
V13 00478663040
00297700445
V14 00644785043
00401018626
V15 0.0336200295
0.3668846041

Determinant 3.997082E-12 Ln

0.0346297213

0.051 1296684

0.0544073570

0.0449700443

0.0645506933

0.1716196329

0.0571586951

00769958585

00401467599

95

0.0256789924 0.0345909938
0.0379142054 0.0510724885
0.0403447113 0.05434651 16
0.0333466567 0.0449197529
0.0478663040 0.0644785043
00571586951 0.0769958585
01370184256 00570947728
0.0570947728 02513718769
0.0297700445 0.0401018626
-26.245457

CORRELATION MATRIX 09:40 Tuesday, March 6, 2007

309
The CALIS Procedure

Covariance Structure Analysis: Maximum Likelihood Estimation
Fit Function 0.8277
Goodness of Fit Index (GFI) 0.8968
GFI Adjusted for Degrees of Freedom (AGFI) 0.8543
Root Mean Square Residual (RMR) 0.0144
Parsimonious GFI (Mulaik, 1989) 0.7260
Chi-Square 134.91 12
Chi-Square DF 85
Pr > Chi-Square 0.0005
Independence Model Chi-Square 544.34
Independence Model Chi-Square UP 105
RMSEA Estimate 0.0600
RMSEA 90% Lower Conﬁdence Limit 0.0400
RMSEA 90% Upper Conﬁdence Limit 0.0786
ECVI Estimate 1.3039
ECVI 90% Lower Conﬁdence Limit 1.1316
ECVI 90% Upper Conﬁdence Limit 1.5307
Probability of Close Fit 0.1888
Bentler's Comparative Fit Index 0.8864
Normal Theory Reweighted LS Chi-Square 140.7284
Akaike's Information Criterion -35.0888
Bozdogan's (1987) CAIC -383.5774
Schwarz's Bayesian Criterion ~298.5774
McDonald's (1989) Centrality 0.8588
Bentler & Bonett's (1980) Non-normed Index 0.8597
Bentler & Bonett's (1980) NFI 0.7522
James, Mulaik, & Brett (1982) Parsimonious NFI 0.6089
Z-Test of Wilson & Hilferty (1931) 3.3070
Bollen (1986) Normed Index Rhol 0.6938
Bollen (1988) Non-normed Index Delta2 0.8913
Hoelter's (1983) Critical N 131

WARNING: The central parameter matrix _PHI_ has probably 1 negative eigenvalue(s).

96

310

CORRELATION MATRIX 09:40 Tuesday, March 6, 2007

The CALIS Procedure
Covariance Structure Analysis: Maximum Likelihood Estimation

Raw Residual Matrix
V1 V2 V3 V4 V5

V1 00000000000 00133511788 -.0019552646 -.0059899841 00099298356
V2 0.0133511788 00000000000 -.0080931304 -.0047926060 00292789953
V3 -.0019552646 -.0080931304 00000000000 00075629334 00337244146
V4 -.0059899841 -.0047926060 0.0075629334 00000000000 00273481365
V5 0.0099298356 0.0292789953 0.0337244146 0.0273481365 00000000000
V6 00062513754 00028134114 00212056716 00065766249 00158626384
V7 00164131359 00136153532 -.0266223020 -.0141987292 -.0203793208
V8 00111268310 00159448086 00244409943 -.0059101226 -.0204690490
V9 -.0353158031 -.0083629769 -.0086996954 -.0093728860 00020622700
V10 -.0274906193 -.0353745359 -.0211835657 -.0036481997 -.0065191835
V11 00171184342 00067538135 -.0191092647 -.0191144720 -.0198443419
V12 00025877832 00046848350 00044147046 00112795537 00194114316
V13 00032549695 -.0073097553 -.0180865771 -.0083600662 -.0163119025
V14 00061794666 00022132519 00030936352 00101448783 00350893743
V15 -.0170522078 00062520434 00066192608 0.0066734591 00133970836

Raw Residual Matrix
V6 V7 V8 V9 V10

V1 0.0062513754 0.0164131359 0.0111268310 -.0353158031 -.0274906193
V2 0.0028134114 0.0136153532 0.0159448086 -.0083629769 -.0353745359
V3 0.0212056716 -.0266223020 00244409943 -.0086996954 -.0211835657

V4 0.0065766249 -.0141987292 -.0059101226 -.0093728860 -.0036481997

V5 0.0158626384 -.0203793208 -.0204690490 0.0020622700 -.006519l835

V6 00000000000 -.0295795687 00016852872 00123044984 -.0054399830
V7 -.0295795687 00000000000 00171691945 -.0146312257 00102974867
V8 0.0016852872 00171691945 00000000000 00079900292 -.0104560345
V9 0.0123044984 -.0146312257 0.0079900292 00000000000 00203784855
V10 -.0054399830 0.0102974867 -.0104560345 0.0203784855 00000000000
V11 -.0046105474 00324814293 00029666775 -.0136034587 -.0136350955
V12 -.0015051230 00236007183 00080297510 -.0127242468 00069319456
V13 -.0162898665 00211628822 -.0033032723 -.0214464171 00102448721
V14 -.0208226931 00150266587 -.0078442365 -.0015071107 -.0050506l81

V15 00191532372 -.0182504946 -.0087356933 -.0252227613 00211200665

97

V1
V2
V3
V4
V5
V6
V7
V8
V9

V10 -.0136350955 0.0069319456 00102448721 -.0050506l81
00000000000 00063958556 -.0021559871 -.0000742456
0.0063958556 00000000000 —.0017516522 -.0126849180
-.0021559871 -.0017516522 00000000000 0014573405]
-.0000742456 -.0126849180 00145734051 00000000000
-.0012002733 —.0006357187 00003502750 00017762745

V11
V12
V13
V14
V15

Raw Residual Matrix

V11

V12

V13

V15

0.0171184342 0.0025877832 0.0032549695 0.0061794666 -.0170522078
0.0067538135 0.0046848350 -.0073097553 0.0022132519 0.0062520434
-.0191092647 0.0044147046 -.0180865771 0.0030936352 0.0066192608
-.0191144720 0.0112795537 -.0083600662 0.0101448783 00066734591
-.0198443419 0.0194114316 -.0163119025 0.0350893743 00133970836
-.0046105474 -.0015051230 -.0162898665 -.0208226931 0.0191532372

0.0324814293 0.0236007183 0.0211628822 0.0150266587 -.0182504946
0.0029666775 0.0080297510 -.0033032723 -.0078442365 -.0087356933
-.0136034587 -.0127242468 -.0214464171 -.0015071107 -.0252227613

Average Absolute Residual

Average Off-diagonal Absolute Residual

Rank Order of the 10 Largest Raw Residuals

Row

V10
V9
V14
V5
V11
V7
V5
V10
V5
V7

Column

V2
V1
V5
V3
V7
V6
V2
V1
V4
V3

Residual

-003537
-0.03532
0.03509
0.03372
0.03248
-0.02958
0.02928
-0.02749
0.02735
-0.02662

98

0.021 1200665
-.0012002733
-.0006357187
00003502750
0.0017762745
00000000000

CORRELATION MATRIX 09:40 Tuesday, March 6. 2007
The CALIS Procedure
Covariance Structure Analysis: Maximum Likelihood Estimation

Asymptotically Standardized Residual Matrix
V1 V2 V3 V4 V5

V1 0000000000 2.491948433 —0730421402 -1.428714411 0705372318
V2 2.491948433 0000000000 -1.798711902 -0760994209 1.944313334
V3 -0730421402 -1.798711902 0000000000 2.163378833 2.509259611
V4 -1.4287l4411 -0760994209 2.163378833 0000000000 2.126951751
V5 0.705372318 1.944313334 2.509259611 2.126951751 0000000000
V6 0539238923 0233336312 1.897393727 0634958512 1.576203978
V7 1.131104986 0902443297 -1.902879833 -1.095478132 -1.616650933
V8 0817004524 1.083901984 1.886391405 -0471484367 -1.912982436
V9 -2.651937405 -0574931607 -0689569221 -0757924805 0203987057
V10 -2.168172475 -2.600207996 -1.751908982 -0314263552 -0641863938
V11 1.242324867 0465203807 -1.445145026 -1.537012628 -l.369756294
V12 0245937839 0396237072 0448145808 1.128517896 1.728238103
V13 0309400490 -0648897327 -1.801957718 -0869360726 -1.471554123
V14 0432612504 0144844447 0226921809 0777581269 2.331744746
V15 -1.412952867 0404965738 0626192853 0523105863 0748761805

Asymptotically Standardized Residual Matrix
V6 V7 V8 V9 V 1 0

V1 0.539238923 1.131104986 0.817004524 -2.651937405 -2.168172475
V2 0233336312 0.902443297 1.083901984 -0574931607 -2.600207996 .
V3 1.897393727 -1.902879833 1.886391405 ~0689569221 -1.751908982
V4 0.634958512 -l.095478132 -0471484367 -0757924805 -0314263552
V5 1.576203978 -1.6l6650933 -1.9l2982436 0.203987057 -0641863938
V6 0000000000 -2.696957870 0176833592 1.355524365 -0604121034
V7 -2.696957870 0000000000 1.438142061 -1.2866l9660 0912932048
V8 0.176833592 1.438142061 0000000000 0844883512 -1.095237407
V9 1.355524365 -1.286619660 0.844883512 0000000000 2.261362286
V10 -0604121034 0.912932048 -l.095237407 2.261362286 0000000000
V11 -0389594778 2.193004262 0211038562 -0986085356 -1.043991665
V12 -0158516765 1.985238319 0745984756 -1.222242393 0687255830
V13 —1.782174624 1.849721500 -0308131306 -2.046307371 1.026268675
V14 -1.678995911 0968002863 -0538875605 -0105878187 -0.372653705
V15 1.231329614 -0.936852516 -0.515403147 -1.562105430 1.319082608

99

Asymptotically Standardized Residual Matrix
V11 V12 V13 V14 V15

V1 1.242324867 0.245937839 0.309400490 0.432612504 -1.412952867
V2 0.465203807 0.396237072 -0648897327 0144844447 0.404965738
V3 -1.445145026 0.448145808 -l.801957718 0.226921809 0.626192853
V4 -1.537012628 1.128517896 -0869360726 0.777581269 0.523105863
V5 -1.369756294 1.728238103 -1.471554123 2.331744746 0.748761805
V6 -0389594778 -0158516765 —1.782174624 -1.678995911 1.231329614
V7 2.193004262 1.985238319 1.849721500 0.968002863 -0.936852516
V8 0.211038562 0.745984756 -0.308131306 -0538875605 -0515403147
V9 -0.986085356 -1.222242393 -2.046307371 -0105878187 -1.562105430
V10 -1.043991665 0.687255830 1.026268675 -0372653705 1319082608
V11 0000000000 0993503089 -0.281883109 -0.007126977 ~0071965585
V12 0.993503089 0000000000 -0.389449095 -2.065647786 -0059529577
V13 -0281883109 -0389449095 0000000000 1.943050976 0028559789
V14 -0.007126977 -2.065647786 1943050976 0000000000 0106413470
V15 -0.071965585 -0.059529577 0.028559789 0.106413470 0000000000

Average Standardized Residual 0.949484
Average Off-diagonal Standardized Residual 1.085125

Rank Order of the 10 Largest Asymptotically Standardized Residuals

Row Column Residual
V7 V6 -2.69696
V9 V1 -2.65194
V10 V2 -2.60021
V5 V3 2.50926
V2 V1 2.49195
V14 V5 2.33174
V10 V9 2.26136
V11 V7 2.19300
V10 V1 -2.16817
V4 V3 2.16338

100

CORRELATION MATRIX
The CALIS Procedure

09:40 Tuesday, March 6, 2007

Covariance Structure Analysis: Maximum Likelihood Estimation

Distribution of Asymptotically Standardized Residuals

Each * Represents 1 Residuals

101

---------- Range--------- Freq Percent
-2.75000 -2.50000 3 2.50 ***
-2.50000 -2.25000 0 0.00
-2.25000 -2.00000 3 2.50 ***
-2.00000 -1.75000 6 5.00 ******
-1.75000 -l.50000 4 3.33 ****
-1.50000 -1.25000 6 5.00 ******
-1.25000 -1.00000 4 3.33 ****
-1.00000 -0.75000 5 4.17 * ** **
-0.75000 -0.50000 8 6.67 ********
-050000 -025000 7 5.83 *******
-025000 0 5 4.17 *****

0 025000 24 20.00 ************************
0.25000 0.50000 6 5.00 ******
0.50000 0.75000 8 6.67 ********
0.75000 1.00000 7 5.83 *******
1.00000 1.25000 6 5.00 ******
1.25000 1.50000 3 2.50 ***
1.50000 1.75000 2 1.67 **
1.75000 2.00000 6 5.00 ******
2.00000 2.25000 3 2.50 ***
2.25000 2.50000 3 2.50 ***
2.50000 2.75000 1 0.83 *

CORRELATION MATRIX 09:40 Tuesday, March 6, 2007
The CALIS Procedure

Covariance Structure Analysis: Maximum Likelihood Estimation
Manifest Variable Equations with Estimates

VI = 03170*F3 + 1.0000 El
Std Err 0.0343 LV1F3
t Value 9.2449
V2 = 0.2612*F3 + 1.0000 E2
Std Err 0.0354 LV2F3
t Value 7.3762
V3 = 0.3243*F3 + 1.0000 E3
Std Err 0.0332 LV3F3
t Value 9.7542
V4 = 0.2385*F3 + 1.0000 E4
Std Err 0.0304 LV4F 3
t Value 7.8471
V5 = 0.2678*F2 + 1.0000 E5
Std Err 0.0428 LV5F2
t Value 6.2526
V6 = 0.1535*F2 + 1.0000 E6
Std Err 0.0335 LV6F2
t Value 4.5826
V7 = 01910*F2 + 1.0000 E7
Std Err 0.0419 LV7F2
t Value 4.5587
V8 = 02820*F2 + 1.0000 E8
Std Err 0.0422 LV8F2
t Value 6.6834
V9 = 03001*F2 + 1.0000 E9
Std Err 0.0422 LV9F2
t Value 7.1186
V10 = 0.2481"‘F2 + 1.0000 E10
Std Err 0.0388 LV10F2
t Value 6.3941
V11 = 02325*F4 + 1.0000 E11
Std Err 0.0408 LV11F4
t Value 5.6946
V12 = 02776*F4 + 1.0000 E12
Std Err 0.0356 LV12F4
t Value 7.8012
V13 = 02059*F4 + 1.0000 E13
Std Err 0.0322 LV13F4
t Value 6.3995
V14 = 02773*F4 + 1.0000 E14
Std Err 0.0436 LV14F4
t Value 6.3614
V15 = 1.0000 F1 + 1.0000 E15

102

CORRELATION MATRIX
The CALIS Procedure
Covariance Structure Analysis: Maximum Likelihood Estimation

09:40 Tuesday, March 6, 2007

Variances of Exogenous Variables

Standard
Variable Parameter Estimate Error t Value
F3 1.00000
F2 1.00000
F4 1.00000
F 1 1.00000
E1 VAREl 0.09262 0.01502 6.17
E2 VARE2 0.12490 0.01635 7.64
E3 VARE3 0.07884 0.01422 5.55
E4 VARE4 0.08815 0.01195 7.38
E5 VARES 0.17907 0.02327 7.70
E6 VARE6 0.12149 0.01448 8.39
E7 VARE7 0.19034 0.02267 8.40
E8 VARE8 0.16755 0.02250 7.45
E9 VARE9 0.1601 1 0.02240 7.15
E10 VAREIO 0.14525 0.01907 7.62
E11 VAREll 0.16237 0.02080 7.81
E12 VARE12 0.09454 0.01576 6.00
E13 VARE13 0.09463 0.01284 7.37
E14 VARE14 0.17446 0.02359 7.40
E15 VARE] 5 -0.63312 0.04064 -15.58

Covariances Among Exogenous Variables

Standard
Varl Var2 Parameter Estimate Error t Value
F3 F2 CF2F3 0.30597 0.09957 3.07
F3 F4 CF3F4 0.13529 0.10676 1.27
F2 F4 CF2F4 0.65294 0.08622 7.57
F3 F1 CF1F3 -0.01681 0.05360 -0.31
F2 F1 CF1F2 0.09000 0.05667 1.59
F4 F1 CF1F4 0.14460 0.05702 2.54

103

maamawN-d

CORRELATION MATRIX

09:40 Tuesday, March 6, 2007

The CALIS Procedure

Covariance Structure Analysis: Maximum Likelihood Estimation
Manifest Variable Equations with Standardized Estimates

Vl =

V2 =

V3 =

V4 =

V5 =

V6 =

V7 =

V8 =

V9 =

V10 =

V11 =

V12 =

V13 =

V14 =

V15 =

Variable
V1
V2
V3
V4
V5
V6
V7

0.7213*F3 + 0.6926 E1
LV1F3

05943*F3 + 0.8042 E2
LV2F3

07560*F3 + 0.6546 E3
LV3F3 '

0.6263*F3 + 0.7796 E4
LV4F3

05348*F2 + 08450 E5
LV5F2

04030*F2 + 0.9152 E6
LV6F2

04011*F2 + 0.9160 E7
LV7F2

0.5674*F2 + 0.8234 E8
LV8F2

06000*F2 + 0.8000 E9
LV9F2

0.5455*F2 + 0.8381 E10
LV10F2

0.4998*F4 + 0.8662 E11
LV11F4

0.6702*F4 + 0.7422 E12
LV12F4

05562*F4 + 0.8311 E13
LV13F4

05531*F4 + 0.8331 E14
LV14F4

1.6510 F1 + 1.0000 E15

Squared Multiple Correlations

Error Total
Variance Variance R-Square
0.09262 0.19310 0.5203
0.12490 ‘ 0.19310 0.3532
0.07884 0.18401 0.5715
0.08815 0.14505 0.3923
0.17907 0.25078 0.2860
0.12149 0.14505 0.1624
0.19034 0.22683 0.1609
0.16755 0.24710 0.3219

V8

104

9 V9 0.16011 0.25019 0.3600

10 V10 0.14525 0.20679 0.2976
11 V11 0.16237 0.21643 0.2498
12 V12 0.09454 0.17162 0.4491
13 V13 0.09463 0.13702 0.3093
14 V14 0.17446 0.25137 0.3060
15 V15 -0.63312 0.36688 2.7257

Correlations Among Exogenous Variables
Varl Var2 Parameter Estimate

F3 F2 CF2F3 0.30597
F3 F4 CF3F4 0.13529
F2 F4 CF2F4 0.65294
F3 F1 CF1F3 -0.0168l
F2 F1 CF1F2 0.09000
F4 F1 CF1F4 0.14460

Stepwise Multivariate Wald Test

------ Cumulative Statistics----- --Univariate Increment--
Parameter Chi-Square DF Pr>ChiSq Chi-Square Pr>ChiSq

CF1F3 0.09831 1 0.7539 0.09831 0.7539

CF3F4 1.93576 2 0.3799 1.83746 0.1752
CF1F2 4.99991 3 0.1718 3.06414 0.0800

105

PROC CALIS COVARIANCE CORR RESIDUAL MODIFICATION;
LINEQS

VI = LV1F3 F3 + E1,

/*V2 = LV2F3 F3 + E2,*/
V3 = LV3F3 F3 + E3,

V4 = LV4F3 F3 + E4,

V5 = LV5F2 F2 + E5,

V6 = LV6F2 F2 + E6,

/*V7 = LV7F2 F2 + E7,*/
V8 = LV8F2 F2 + E8,

/*V9 = LV9F2 F2 + E9,

V10 = LV10F2 F2 + E10,*/
V11 =LV11F4 F4 +E11,
V12 = LV12F4 F4 + E12,

V13 = LV13F4 F4 + E13,
/*V14 = LV14F4 F4 + E14,*/'
V15 = F1 + E15;

STD

F1 =1,

F2 =1,

F3 =1,

F4 =1,

E1 = VAREI,

E3-E6 = VARE3-VARE6,

E8 = VARE8,

Ell-E13 = VARE11-VARE13,
E15 = VARE15;

COV

F1 F2 = CF1F2,

F1 F4 = CF1F4,

F2 F3 = CF2F3,

F2 F4 = CF2F4;

VAR V1 V3-V6 V8 V11-V14 V15;
RUN;

The SAS System 19:38 Thursday, March 8, 2007 141

The CALIS Procedure
Covariance Structure Analysis: Pattern and Initial Values

Automatic Variable Selection, the Following Manifest Variables are not Used in the
Model V14

Using the VAR statement for variable selection could save memory and computing time.

106

LIN EQS Model Statement

Matrix Rows Columns ------ Matrix Type -------

Term] 1 _SEL_ 10 24 SELECTION

2 _BETA_ 24 24 EQSBETA IMINUSINV
3 _GAMMA_ 24 14 EQSGAMMA
4 _PHI_ 14 14 SYMMETRIC

The 10 Endogenous Variables

Manifest V1 V3 V4 V5 V6 V8 V11 V12 V13 V15
Latent

The 14 Exogenous Variables
Manifest
Latent F3 F2 F4 F1
Error E1 E3 E4 E5 E6 E8 E11E12 E13 E15
The SAS System 19:38 Thursday, March 8, 2007 142

The CALIS Procedure
Covariance Structure Analysis: Pattern and Initial Values

Manifest Variable Equations with Initial Estimates

VI = .*F3 + 1.0000 E1
LV1F3

V3 = .*F3 + 1.0000 E3
LV3F3

V4 = .*F3 + 1.0000 E4
LV4F3

V5 = .*F2 + 1.0000 E5
LV5F2

V6 = .*F2 + 1.0000 E6
LV6F2

V8 = .*F2 + 1.0000 E8
LV8F2

V11 = .*F4 + 1.0000 E11
LV11F4

V12 = .*F4 + 1.0000 E12
LV12F4

V13 = .*F4 + 1.0000 E13
LV13F4

V15 = 1.0000 Fl + 1.0000 E15

107

Variances of Exogenous Variables

Variable Parameter Estimate

F3
F2
F4
F1
El
E3
E4
E5
E6
E8
E11
E12
E13
E15

VARE 1
VARE3
VARE4
VARE5
VARE6
VARE8

VAREII
VARE12
VARE13
VAREIS

1 .00000
1 .00000
1 .00000
1 .00000

Covariances Among Exogenous Variables

Varl Var2 Parameter Estimate

F3 F2 CF 2F3
F2 F4 CF 2F4 1
F2 F 1 CF 1F2
F4 F 1 CF1F4
The SAS System 19:38 Thursday, March 8, 2007 144
The CALIS Procedure
Covariance Structure Analysis: Maximum Likelihood Estimation
Observations 165 Model Terms 1
Variables 10 Model Matrices 4
Informations 55 Parameters 23
Variable Mean Std Dev
V1 ' 0 0.43943
V3 0 0.42896
V4 0 0.38086
V5 0 0.50078
V6 0 0.38086
V8 0 0.49709
V11 0 0.46522
V12 0 0.41427
V13 0 0.37016
V15 0 0.60571

108

V1

V1 0.1930987249
0.0211394070
V3 01008388327
00364372376
V4 00696239785
00177807609
V5 00359024228
0.0569701760
V6 0.021 1394070
0.1450543396
V8 00384819157
00449809421
V11 0.0270892346
0.0186928792
V12 0.0144942371
0.0263222492
V13 0.0120839675
00043449770
V15 -.0223793336
0.0329680095

V8

V1 0.0384819157
.0223793336
V3 00524272846
0.0011692141
V4 0.0146762180
0.0026644777
V5 00550614306
0.0374973398
V6 00449809421
0.0329680095
V8 02470984681
0.0 1 66473 979
V11 0.0457841044
0.0324197561
V12 0.0591594194
0.0395110413
V13 0.0346109332
0.0301203195

Covariances
V3

V4
0.1008388327
0.1840066816
00849216522
0.0602963069
0.0364372376
00524272846
a0089083928
0.0165958942
40090538542

0.0011692141

Covariances
V1 1 V12
0.0270892346
-.0089083928
-.0116108472
0.0208091369
0.0186928792
0.0457841044

0.2164296484
0.0709465489

00457103169

109

V5

0.0696239785

0.0849216522

0.1450543396

00468940649

0.0177807609

00146762180

-.0116108472

0.0202398737

-.0017157161

0.0026644777

V13

0.0144942371

0.0165958942

0.0202398737

0.0679570598

0.0263222492

0.0591594194

0.0709465489

0.1716196329

0.05 54070429

V6

0.0359024228

00602963069

0.0468940649

02507806084

00569701760

0.0550614306

0.0208091369

0.0679570598

00196861586

0.0374973 398

V15

0.0120839675

-.0090538542

—.0017157161

0.0196861586

0.0043449770

0.0346109332

0.0457103169

0.0554070429

0.1370184256

V15 0.0166473979 0.0324197561 0.0395110413 0.0301203195
0.3668846041
The SAS System 19:38 Thursday, March 8, 2007 145
The CALIS Procedure

Covariance Structure Analysis: Maximum Likelihood Estimation

Determinant 1.5879961E—8 Ln

-17.958208

NOTE: Some initial estimates computed by instrumental variable method.

NNNNI—il—db—‘h—‘U—ir—II—‘F—‘Hh—l
WN—‘OSOOOQOSMAUJNt—‘oomqo‘m'AWNH

The SAS System

19:38 Thursday, March 8, 2007 146

The CALIS Procedure
Covariance Structure Analysis: Maximum Likelihood Estimation

Vector of Initial Estimates

Parameter

LV1 F3
LV3 F3
LV4F3

LV5 F2
LV6F 2
LV8F2
LV1 1 F4
LV12F4
LV13F4
CF 2F3
CF 2F4
CF 1 F2
CF 1 F4
VAREI
VARE3

Estimate

0.32719

0.40696
0.27066
0.41298
0.20469
0.34526
0.29988
0.39202
0.21570
0.33773
0.35448
0.13929
0.18043

0.08605
0.01839

VARE4
VARE5
VARE6
VARE8
VAREI 1
VARE12
VARE] 3
VAREI 5

0.07180
0.08022
0.10316
0.12790
0.12650
0.01794
0.09049
0.15546

Type

Matrix Entry: _GAMMA_[I :1]
Matrix Entry: _GAMMA_[2:1]
Matrix Entry: _GAMMA_[3:1]
Matrix Entry: _GAMMA_[4:2]
Matrix Entry: _GAMMA_[SzZ]
Matrix Entry: _GAMMA_[6z2]
Matrix Entry: _GAMMA_[723]
Matrix Entry: _GAMMA_[8z3]
Matrix Entry: _GAMMA_[9z3]
Matrix Entry: _PHI_[2:1]
Matrix Entry: _PHI_[3:2]
Matrix Entry: _PHI_[4:2]
Matrix Entry: _PHI_[4:3]
Matrix Entry: _PHI_[5:5]
Matrix Entry: _PHI_[6z6]
Matrix Entry: _PHI_[7:7]
Matrix Entry: _PHI_[8z8]
Matrix Entry: _PHI_[9:9]
Matrix Entry: _PHI_[10:10]
Matrix Entry: _PHI_[] 1 :1 1]
Matrix Entry: _PHI_[12:12]
Matrix Entry: _PHI_[13213]
Matrix Entry: _PHI_[14:14]

110

Predetermined Elements of the Predicted Moment Matrix

V1 V3 V4 V5 V6
V1
V3
V4
V5
V6
V8 . . .
V11 0 0 0
V12 0 0 0
V13 0 0 0
V15 0 0 0

Predetermined Elements of the Predicted Moment Matrix

V8 V11 V12 V13 V15
V1 . 0 0 0 0
V3 . 0 O 0 0
V4 . 0 0 0 0

The SAS System 19:38 Thursday, March 8, 2007 147
The CALIS Procedure
Covariance Structure Analysis: Maximum Likelihood Estimation
Predetermined Elements of the Predicted Moment Matrix

V8 V11 V12 V13 V15
V5
V6
V8
V11
V12
V13
V15

WARNING: The predicted moment matrix has 12 constant elements whose values differ
from those of the observed moment matrix. The sum of squared differences is
00025833963.

NOTE: Only 43 elements of the moment matrix are used in the model speciﬁcation.

111

The SAS System 19:38 Thursday, March 8, 2007 148

The CALIS Procedure
Covariance Structure Analysis: Maximum Likelihood Estimation

Levenberg-Marquardt Optimization

Scaling Update of More (1978)

Parameter Estimates 23
Functions (Observations) 55
Optimization Start
Active Constraints 0 Objective Function 1.3952540646
Max Abs Gradient Element 9.3417130151 Radius
188.87556781
Ratio
Between
Actual
Objective Max Abs and
Function Active Objective Function Gradient Predicted

Iter Restarts Calls Constraints Function Change Element Lambda
Change

1 0 2 0 0.21906 1.1762 0.3211 0 0.948
2 0 3 0 0.20596 0.0131 0.0683 0 1.186
3 0 4 0 0.20529 0.000671 0.0209 0 1.162
4 0 5 0 0.20522 0.000063 0.00405 0 1.101
5 0 6 0 0.20522 6.584E-6 0.00278 0 1.009
6 0 7 0 0.20522 7.628E-7 0.000387 0 0.908
7 0 8 0 0.20522 9.618E-8 0.000387 0 0.814
8 0 9 0 0.20522 1.315E-8 0.000073 0 0.739
9 0 10 0 0.20522 1.93E-9 0.000058 0 0.684
10 0 11 0 0.20522 2.99E-10 0.000015 0 0.646
Optimization Results

Iterations 10 Function Calls 12

Jacobian Calls 11 Active Constraints 0

Objective Function 02052166539 Max Abs Gradient Element

00000153051

Lambda 0 Actual Over Pred Change 06463869104

Radius 0.0001 579666

' GCONV convergence criterion satisﬁed.

112

The SAS System 19:38 Thursday, March 8, 2007 149

The CALIS Procedure
Covariance Structure Analysis: Maximum Likelihood Estimation
Predicted Model Matrix
V1 V3 V4 V5 V6

V1 0.1930987249 01016287360 00636315857 00406478183
00239796332

V3 0.1016287360 0.1840066816 00859572040 00549094097
00323930670

V4 0.0636315857 0.0859572040 0.1450543396 00343797724
00202818839 '
V5 0.0406478183 0.0549094097 0.0343 797724 02482846991
00464095625

V6 0.0239796332 0.0323930670 0.0202818839 0.0464095625
01441856309

V8 00345267628 00466407360 00292026066 00668222047
00394208600

V1 1 00000000000 00000000000 00000000000 003787481 19
00223437354

V12 00000000000 00000000000 00000000000 00540365554
00318781383

V13 00000000000 00000000000 00000000000 00294427796
00173693714

V15 00000000000 00000000000 00000000000 00374517821
0.0220941746 '

Predicted Model Matrix
V8 V11 V12 V13 V15
V1 0.0345267628 00000000000 00000000000 00000000000
00000000000
V3 0.0466407360 00000000000 00000000000 00000000000
00000000000
V4 0.0292026066 00000000000 00000000000 00000000000
00000000000
V5 0.0668222047 00378748119 0.0540365554 0.0294427796
0.0374517821
V6 0.0394208600 0.0223437354 0.0318781383 0.0173693714
0.0220941746
V8 02452977299 00321713366 00458993227 00250090634
00318120098

V11 0.0321713366 0.2164296484 00722521900 00393678925
00298978336

113

V12 0.0458993227 0.0722521900 0.1716196329 00561667556
00426556822

V13 0.0250090634 0.0393678925 0.0561667556 0.1370184256
00232417081 ‘

V15 0.0318120098 0.0298978336 0.0426556822 0.0232417081
0.3668846041

Determinant 1.9497274E-8 Ln -l7.752991

The SAS System 19:38 Thursday, March 8, 2007 150

The CALIS Procedure
Covariance Structure Analysis: Maximum Likelihood Estimation
Fit Function 0.2052
Goodness of Fit Index (GFI) 0.9604
GFI Adjusted for Degrees of Freedom (AGFI) 0.9319
Root Mean Square Residual (RMR) 0.0096
Parsimonious GFI (Mulaik, 1989) 0.6829
Chi-Square 33.6555
Chi-Square DF 32
Pr > Chi-Square 0.3872
Independence Model Chi-Square 278.00
Independence Model Chi-Square DF 45
RMSEA Estimate 0.0178
RMSEA 90% Lower Conﬁdence Limit .
RMSEA 90% Upper Conﬁdence Limit 0.0614
ECVI Estimate 0.5059
ECVI 90% Lower Conﬁdence Limit .
ECVI 90% Upper Conﬁdence Limit 0.6187
Probability of Close Fit 0.8608
Bentler's Comparative Fit Index 0.9929
Normal Theory Reweighted LS Chi-Square 33.8538
Akaike's Information Criterion -303445
Bozdogan's (1987) CAIC -161.7347
Schwarz's Bayesian Criterion -129.7347
McDonald's (1989) Centrality 0.9950
Bentler & Bonett's (1980) Non-normed Index 0.9900
Bentler & Bonett's (1980) NF I 0.8789
James, Mulaik, & Brett (1982) Parsimonious NFI 0.6250
Z-Test of Wilson & Hilferty (1931) 0.2868
Bollen (1986) Normed Index Rhol 0.8298
Bollen (1988) Non-normed Index Delta2 0.9933
Hoelter's (1983) Critical N 227

WARNING: The central parameter matrix _PHI_ has probably 1 negative eigenvalue(s).

114

The SAS System 19:38 Thursday, March 8, 2007 151
The CALIS Procedure
Covariance Structure Analysis: Maximum Likelihood Estimation
Raw Residual Matrix

V1 V3 V4 V5 V6
V1 00000000000 -.0007899033 00059923927 -.0047453955 -.0028402261
V3 -.0007899033 00000000000 -.0010355518 00053868972 00040441706
V4 0.0059923927 -.0010355518 00000000000 00125142925 -.0025011229
V5 -.0047453955 0.0053868972 0.0125142925 00024959093 00105606135
V6 -.0028402261 0.0040441706 -.0025011229 0.0105606135 00008687087
V8 00039551529 00057865485 -.0145263886 -.0117607741 00055600821
V11 0.0270892346 -.0089083928 -.0116108472 -.0170656750 -.0036508562
V12 0.0144942371 0.0165958942 0.0202398737 00139205045 -.005555889l
V13 0.0120839675 -.0090538542 -.0017157161 -.0097566210 -.0130243944
V15 -.0223793336 0.0011692141 0.0026644777 00000455578 00108738348

Raw Residual Matrix

V8 V11 V12 V13 V15
V1 0.0039551529 0.0270892346 0.0144942371 0.0120839675 -.0223793336
V3 0.0057865485 -.0089083928 0.0165958942 -.0090538542 0.0011692141
V4 -.0145263886 -.0116108472 0.0202398737 -.0017157161 0.0026644777
V5 -.0117607741 -.0170656750 00139205045 -.0097566210 00000455578
V6 0.0055600821 -.0036508562 -.0055558891 -.0130243944 0.0108738348
V8 00018007382 00136127678 00132600967 00096018697 -.0151646119
V11 0.0136127678 00000000000 -.0013056411 00063424244 00025219226
V12 0.0132600967 -.0013056411 00000000000 -.0007597127 -.0031446409
V13 0.0096018697 0.0063424244 -.0007597127 00000000000 00068786114
V15 -.0151646119 0.0025219226 -.0031446409 0.0068786114 00000000000

Average Absolute Residual 0.007121
Average Off-diagonal Absolute Residual 0.008589

Rank Order of the 10 Largest Raw Residuals
Row Column Residual

V11 V1 0.02709
V15 V1 -002238
V12 V4 0.02024
V11 V5 -001707
V12 V3 0.01660
V15 V8 -001516
V8 V4 -001453
V12 V1 0.01449
V12 V5 0.01392

V11 V8 0.01361

115

The SAS System 19:38 Thursday, March 8, 2007 152
The CALIS Procedure
Covariance Structure Analysis: Maximum Likelihood Estimation
Asymptotically Standardized Residual Matrix

V1 V3 V4 V5 V6
V1 0000000000 -0.655913123 1.360182363 -0367163191 -0266097662
V3 -0655913123 0000000000 -0.917999339 0561186719 0468345195
V4 1.360182363 -0917999339 0000000000 1.101702654 -0267759010
V5 -0367163191 0.561186719 1.101702654 0837042520 1.363217320
V6 -0266097662 0.468345195 -0.267759010 1.363217320 0837109558
V8 0291646616 0541391050 -l.222333178 -1.310036191 0597061647
V11 1.696955985 -0571670932 -0839193463 -1.236255335 -0.3l7835192
V12 1.019633504 1.195975545 1.642785554 1.540862766 -0677543868
V13 0951376199 -0730212288 -0155852044 —0878834367 -1.4148l9873
V15 -1.076749372 0057628118 0147912170 0003039818 0774662309

Asymptotically Standardized Residual Matrix

V8 V11 V12 V13 V15
V1 0.291646616 1.696955985 1.019633504 0.951376199 -1.076749372
V3 0541391050 -0571670932 1.195975545 0730212288 0.057628118
V4 -l.222333178 -0839193463 1.642785554 0155852044 0.147912170
V5 -1.310036191 -1.236255335 1.540862766 0878834367 0.003039818
V6 0.597061647 0317835192 0677543868 4414819873 0.774662309
V8 0837012715 0934477875 1.309846639 0821577909 0878834326
V11 0.934477875 0000000000 0487532058 0823338239 0149963103
V12 1.309846639 0487532058 0000000000 0340042594 0517665020
V13 0.821577909 0.823338239 0340042594 0000000000 0507090953
V15 0878834326 0.149963103 -0517665020 0.507090953 0000000000

Average Standardized Residual 0.681879
Average Off-diagonal Standardized Residual 0.777605

Rank Order of the 10 Largest Asymptotically Standardized Residuals

Row Column Residual
V11 .V1 1.69696
V12 V4 1.64279
V12 V5 1.54086
V13 V6 -1.41482

V6 V5 1.36322
V4 V1 1.36018
V8 V5 -1.31004
V12 V8 1.30985

V1 1 V5 -1.23626
V8 V4 -1.22233

116

The SAS System

The CALIS Procedure

19:38 Thursday, March 8, 2007 153

Covariance Structure Analysis: Maximum Likelihood Estimation
Distribution of Asymptotically Standardized Residuals

Each * Represents 1 Residuals

Freq Percent

---------- Range-«mm
-1.50000 -1.25000
-l.25000 -1.00000
-1.00000 075000
075000 0.50000
0.50000 025000
025000 0

0 0.25000
0.25000 0.50000
0.50000 0.75000
0.75000 1.00000
1.00000 1.25000
1.25000 1.50000
1.50000 1.75000

WWWOO-D-N:v—-o\m_pw~

3.64
5.45
7.27
9.09
10.91
1.82
20.00
3.64
7.27
14.55
5.45
5.45
5.45

117

**
***
****
*****
******
*
***********
**
****
********
***
***
***

The SAS System 19:38 Thursday, March 8, 2007 154

The CALIS Procedure
Covariance Structure Analysis: Maximum Likelihood Estimation

Manifest Variable Equations with Estimates

Vl = O.2743*F3 + 1.0000 El
Std Err 0.0358 LV1F3

t Value 7.6689

V3 = 03705*F3 + 1.0000 E3
Std Err 0.0354 LV3F3

t Value 10.4759

V4 = 02320*F 3 + 1.0000 E4
Std Err 0.0310 LV4F3

t Value 7.4825

V5 = 02805*F2 + 1.0000 E5
Std Err 00473 LV5F2

t Value 5.9299

V6 = O.1655*F2 + 1.0000 E6
Std Err 0.0355 LV6F2

t Value 4.6545

V8 = 02382*F2 + 1.0000 E8
Std Err 0.0463 LV8F2

t Value 5.1413

V11 = 0.2250*F4 + 1.0000 Ell
Std Err 0.0429 LV11F4

t Value 5.2459

V12 = O.3211*F4 + 1.0000 E12
Std Err 0.0426 LV12F4

t Value 7.5431

V13 = 01749*F4 + 1.0000 E13
Std Err 0.0341 LV13F4

t Value 5.1326

V15 = 1.0000 F1 + 1.0000 E15

118

Variances of Exogenous Variables

Standard

Variable Parameter Estimate Error t Value
F3 1.00000

F2 1.00000

F4 1.00000

F1 1.00000

E1 VAREl 0.11787 0.01640 7.19
E3 VARE3 0.04672 0.01809 2.58
E4 VARE4 0.09123 0.01238 7.37
E5 VARE5 0.16962 0.02575 6.59
E6 VARE6 0.11681 0.01479 7.90
E8 VARE8 0.18854 0.02501 7.54
E11 VAREll 0.16579 0.02172 7.63
E12 VARE12 0.06854 0.02241 3.06

The SAS System 19:38 Thursday, March 8, 2007 155

The CALIS Procedure
Covariance Structure Analysis: Maximum Likelihood Estimation

Variances of Exogenous Variables

Standard
Variable Parameter Estimate Error t Value
E13 VARE13 0.10641 0.01376 7.73
E15 VAREIS 0.63312 0.04052 -15.63

Covariances Among Exogenous Variables

Standard
Varl Var2 Parameter Estimate Error t Value
F3 F2 CF2F3 0.52836 0.10290 5.13
F2 F4 CF2F4 0.60006 0.11433 5.25
F2 F1 CF1F2 0.13353 0.06276 2.13
F4 F1 CF1F4 0.13286 0.05712 2.33

119

scooqoxmpww...

V11

V12

V13

The SAS System

19:38 Thursday, March 8, 2007 156

The CALIS Procedure

Covariance Structure Analysis: Maximum Likelihood Estimation
Manifest Variable Equations with Standardized Estimates

Vl =

V3 =

V4 =

V5 =

V6 =

V8 =

V15 =

Variable
V1

V3

V4

V5

V6

V8

V11
V12
V13

06242*F3 + 0.7813 E1
LV1F3

O.8638*F3 + 0.5039 E3
LV3F3

O.6091*F3 + 0.7931 E4
LV4F3

0.5629*F2 + 0.8265 E5
LV5F2

O.4358*F2 + 0.9001 E6
LV6F2

04810*F2 + 0.8767 E8
LV8F2

04837*F4 + 0.8752 E11
LV11F4

07750*F4 + 0.6319 E12
LV12F4

0.4726*F4 + 0.8813 E13
LV13F4

1.6510 Fl + 1.0000 E15

Squared Multiple Correlations

Error Total
Variance Variance R-Square
0.11787 0.19310 0.3896
0.04672 0.18401 0.7461
0.09123 0.14505 0.3710
0.16962 0.24828 0.3168
0.11681 0.14419 0.1899
0.18854 0.24530 0.2314
0.16579 0.21643 0.2340
0.06854 0.17162 0.6006
0.10641 0.13702 0.2234
0.63312 0.36688 2.7257

V15

Correlations Among Exogenous Variables

Varl Var2 Parameter
F2 CF2F3
F4 CF2F4
F1 CF1F2

F3
F2
F2

F4 F1 CF1F4

Estimate
0.52836
0.60006
0.13353
0.13286

120

PROC CALIS COVARIANCE CORR RESIDUAL MODIFICATION;

LINEQS

Vl = LV1F3 F3 + 131,
V3 = F3 +153,
V4 = LV4F3 F3 + E4,
vs = F2 + E5,
V6 = LV6F2 F2 + E6,

V8 = LV8F2 F2 + E8,
V11 = LV11F4 F4 + Ell,
V12 = F4 + E12,
V13 = LV13F4 F4 + E13,
V15 = F1,
F1= PF1F2 F2 + PF1F4 F4 + D1,
F2 = PF2F3 F3 + PF2F4 F4 + D2;
STD
E1 = VARE],
E3-E6 = VARE3-VARE6,
E8 = VARE8,
Ell-E13 = VARE11-VARE13,
F3 = VARF3,
F4 = VARF4,
D1 = VARDl,
D2 = VARD2;
VAR V1-V6 V8 V11-V13 V15;
RUN;
The SAS System 19:38 Thursday, March 8, 2007 244
The CALIS Procedure
Covariance Structure Analysis: Pattern and Initial Values

Automatic Variable Selection, the Following Manifest Variables are not Used in the

Model V2

Using the VAR statement for variable selection could save memory and computing time.

LINEQS Model Statement
Matrix Rows Columns ------ Matrix Type -------
Term 1 1 _SEL_ 10 25 SELECTION

2 _BETA_ 25 25 EQSBETA IMINUSINV
3 _GAMMA_ 25 13 EQSGAMMA
4 _PHI_ 13 13 SYMMETRIC

The 12 Endogenous Variables

Manifest V1 V3 V4 V5 V6 V8 V11 V12 V13 V15
Latent F1 F2

121

The 13 Exogenous Variables

Manifest
Latent F3 F4
Error E1 E3 E4 E5 E6 E8 E11E12 E13 D1 D2

The SAS System 19:38 Thursday, March 8, 2007 245
The CALIS Procedure

Covariance Structure Analysis: Pattern and Initial Values

Manifest Variable Equations with Initial Estimates

Vl = .*F3 + 1.0000 E1
LV1F3

V3 = 1.0000 F3 + 1.0000 E3

V4 = .*F3 + 1.0000 E4
LV4F3

V5 = 1.0000 F2 + 1.0000 E5

V6 = .*F2 + 1.0000 E6
LV6F2

V8 = .*F2 + 1.0000 E8
LV8F2

V11 = .*F4 + 1.0000 E11
LV11F4

V12 = 1.0000 F4 + 1.0000 E12

V13 = .*F4 + 1.0000 E13
LV13F4

V15 = 1.0000 F1

The SAS System 19:38 Thursday, March 8, 2007 246

The CALIS Procedure
Covariance Structure Analysis: Pattern and Initial Values

Latent Variable Equations with Initial Estimates

F1 = .*F2 + .*F4 +1.0000D1
PF1F2 PF1F4

F2 = .*F3 + .*F4 + 1.0000 D2
PF2F3 PF2F4

122

Variances of Exogenous Variables

Variable Parameter Estimate

F3 VARF3
F4 VARF 4
E1 VAREl
E3 VARE3
E4 VARE4
E5 VARE5
E6 VARE6
E8 VARE8
E1 1 VARE] 1
E12 VARE12
E13 VARE13
D1 VARDl
D2 VARD2

The SAS System 19:38 Thursday, March 8, 2007 247

The CALIS Procedure
Covariance Structure Analysis: Maximum Likelihood Estimation
Observations 165 Model Terms 1
Variables 10 Model Matrices 4
Informations 55 Parameters 23

Variable Mean Std Dev

V1 0 0.43943
V3 0 0.42896
V4 0 0.38086
V5 0 0.50078
V6 0 0.38086
V8 0 0.49709
V11 0 0.46522
V12 0 0.41427
V13 0 0.37016
V15 0 0.60571

123

V1
V6
V1 0. 1930987249
0.021 1394070
V3 0.1008388327
0.0364372376
V4 0.0696239785
0.0177807609
V5 0.0359024228
0.0569701760
V6 0.021 1394070
0. 1450543396
V8 0.0384819157
(10449809421
V1 1 0.0270892346
0.0186928792
V12 0.0144942371
0. 0263222492
V13 0.0120839675
0. 0043449770 '
V15 -.0223793336
0. (3329680095

V8
V15
V1 0.0384819157
.0223793336
V3 0.0524272846
0.0011692141
V4 0.0146762180
0. 0 026644777
V s 0.0550614306
0.0 3 74973398
V 6 0.0449809421
0-0 3 29680095
V 8 0.2470984681
0-0 1 66473979
V 1 1 0.0457841044
0-03 24197561
V 1 2 0.0591594194
O-0395110413
V 1 3 0.0346109332
O.0301203195

Covariances
V3

0.1008388327
0.1840066816
00849216522
0.0602963069
0.03643723 76
0.0524272846
-.0089083928
0.0165958942
-.OO90538542
0.0011692141
Covariances
V1 1
0.0270892346
-.0089083928
-.0116108472
0.0208091369
0.0186928792

00457841044

0.2164296484
00709465489

0.0457103169

124

V4

0.0696239785

0.0849216522

0.1450543396

0.0468940649

0.0177807609

0.0146762180

-.0116108472

0.0202398737

-.0017157161

0.0026644777

V12

0.0144942371

0.0165958942

0.0202398737

0.0679570598

0.0263 222492

0.0591594194

0.0709465489
0.1716196329

0.0554070429

V5

0.03 59024228

0.0602963069

00468940649

0.2507806084

0.0569701760

0.0550614306

0.0208091369

0.0679570598

0.0196861586

0.0374973398

V13

0.0120839675

-.0090538542

-.0017157161

0.0196861586

0.0043449770

0.0346109332

0.0457103169

0.0554070429

0.1370184256

V15 0.0166473979 0.0324197561 0.0395110413 0.0301203195
0.3668846041
The SAS System 19:38 Thursday, March 8, 2007 248
The CALIS Procedure

Covariance Structure Analysis: Maximum Likelihood Estimation
Determinant 1.5879961E-8 Ln -l7.958208

NOTE: Some initial estimates computed by instrumental variable method.
NOTE: Some initial estimates computed by two-stage LS method.

Vector of Initial Estimates

Parameter Estimate Type

1 LV6F2 0.55428 Matrix Entry: _BETA_[5:12]

2 LV8F2 0.76552 Matrix Entry: _BETA_[6z12]

3 PF1F2 024459 Matrix Entry: _BETA_[l 1 :12]
4 LV1F3 0.80315 Matrix Entry: _GAMMA_[1:1]
5 LV4F 3 0.61319 Matrix Entry: _GAMMA_[3:1]
6 LV1 1 F4 0.58322 Matrix Entry: _GAMMA_[722]
7 LV13F4 0.42347 Matrix Entry: _GAMMA_[9:2]
8 PF1F4 0.47840 Matrix Entry: _GAMMA_[I 1:2]
9 PF2F 3 0.39366 Matrix Entry: _GAMMA_[12:1]
10 PF2F4 0.45289 Matrix Entry: _GAMMA_[12z2]
11 VARF 3 0.13244 Matrix Entry: _PHI_[]:I]

12 VARF4 0.13115 Matrix Entry: _PHI_[2z2]

13 VAREl 0.10767 Matrix Entry: _PHI_[3:3]

14 VARE3 0.05157 Matrix Entry: _PHI_[4:4]

15 VARE4 0.09526 Matrix Entry: _PHI_[5:5]

16 VARE5 0.16430 Matrix Entry: _PHI_[6z6]

17 VARE6 011849 Matrix Entry: _PHI_[7:7]

18 VARE8 0.19642 Matrix Entry: _PHI_[8z8]

19 VAREll 0.17182 Matrix Entry: _PHI_[9:9]
20 VARE12 0.04047 Matrix Entry: _PHI_[10z10]
21 VARE13 0.11350 Matrix Entry: _PHI_[11:11]
22 VARDl 0.35974 Matrix Entry: _PHI_[12:12]
23 VARD2 0.03396 Matrix Entry: _PHI_[13213]

Predetermined Elements of the Predicted Moment Matrix
V4 V5 V6

V1

125

V8

V11
V12
V13
V15

GOO
GOO
GOO

Predetermined Elements of the Predicted Moment Matrix
V8 V1 1 V 12 V13 V1 5

V1 . O O 0

V3 . 0 0 0

V4 . 0 0 0

V5

V6

V8

V1 1

V 12

V13

V15

WARNING: The predicted moment matrix has 9 constant elements whose values differ
from those of the observed moment matrix. The sum of squared differences is
O - 0020740952.

NOTE: Only 46 elements of the moment matrix are used in the model speciﬁcation.

The SAS System 19:38 Thursday, March 8, 2007 251
The CALIS Procedure
Covariance Structure Analysis: Maximum Likelihood Estimation

Levenberg-Marquardt Optimization .
Scaling Update of More (1978)

Parameter Estimates 23
Functions (Observations) 55
Optimization Start
Aetive Constraints 0 Objective Function 0.23 68104747
M ax Abs Gradient Element 05712920506 Radius 6.7884311243
Ratio
Between
Actual
Objective Max Abs and
Function Active Objective Function Gradient Predicted

Iter Restarts Calls Constraints Function Change Element Lambda
1'lange

126

1 0 2 0 0.21184 0.0250 0.2138 0 0.941
2 O 3 0 0.20986 0.00199 0.0169 0 1.013
3 0 4 0 0.20983 0.000030 0.00393 0 1.081
4 0 5 0 0.20983 1.778E-6 0.000951 0 1.123
5 O 6 0 0.20983 1.306E-7 0.000305 0 1.123
6 O 7 0 0.20983 1.076E-8 0.000116 0 1.075
7 O 8 0 0.20983 9.94E-10 0.000039 0 0.983
Optimization Results

Iterations 7 Function Calls 9

Jacobian Calls 8 Active Constraints 0

Objective Function 0.2098250768 Max Abs Gradient Element

00000389679

Lambda 0 Actual Over Pred Change 09833174177

Radius 00002906044

GCONV convergence criterion satisﬁed.

The SAS System 19:38 Thursday, March 8, 2007 252
The CALIS Procedure
Covariance Structure Analysis: Maximum Likelihood Estimation

Predicted Model Matrix
V1 V3 V4 V5
V6
V1 0.1930987249 01015702181 00631648145 00400465926
00234509643
V3 0.1015702181 0.1840066816 00860781623 00545736914
00319579173
V4 0.0631648145 0.0860781623 0.1450543396 00339384631
00198740926
V5 0.0400465926 0.0545736914 0.0339384631 02482534324
0.0456115350

V6 0.0234509643 0.0319579173 0.0198740926 0.0456115350
01441878045
V8 00347448168 00473486703 00294453437 00675777934

00395730154
V11 00000000000 00000000000 00000000000 00387461674

00226894458
V12 00000000000 00000000000 00000000000 00541492468

0.0317093659
V13 00000000000 00000000000 00000000000 00301407513

00176501829
V15 00023808878 00032445666 00020177415 00272158403

00159373784

127

Predicted Model Matrix

V8
V15
V1 00347448168
0.0023808878
V3 0.0473486703
0.0032445666
V4 0.0294453437
0.0020177415
V5 0.0675777934
0.0272158403
V6 0.0395730154
0.0159373784
V8 02451961766
00236127302
V11 00336165551
00321933068
V12 00469804180
0.0449913 741
V13 00261504117
00250432628
V15 0.0236127302
0.3667597823

Determinant 1.9587333E-8 Ln

V11

00000000000

00000000000

00000000000

00387461674

00226894458

0.0336165551

02164296483

00716626640

00398891335

0.0321933068

128

V 12 V13
00000000000 00000000000
00000000000 00000000000
00000000000 00000000000
0.0541492468 00301407513
0.0317093659 0.0176501829
0.0469804180 0.0261504117

0.0716626640 0.0398891335
0.1716196329 00557465855

0.0557465855

0.0449913741

-17.748383

0.1370184255

0.0250432628

The SAS System 19:38 Thursday, March 8, 2007 253

The CALIS Procedure
Covariance Structure Analysis: Maximum Likelihood Estimation
Fit Function 0.2098
Goodness of Fit Index (GFI) 0.9591
GFI Adjusted for Degrees of Freedom (AGFI) 0.9297
Root Mean Square Residual (RMR) 0.0098
Parsimonious GFI (Mulaik, 1989) 0.6820
Chi-Square 34.41 13
Chi-Square DF 32
Pr > Chi-Square 0.3530
Independence Model Chi-Square 278.00
Independence Model Chi-Square DF 45
RMSEA Estimate 0.0214
RMSEA 90% Lower Conﬁdence Limit .
RMSEA 90% Upper Conﬁdence Limit 0.0630
ECVI Estimate 0.5105
ECVI 90% Lower Conﬁdence Limit .
ECVI 90% Upper Conﬁdence Limit 0.6251
Probability of Close Fit 0.8414
Bentler's Comparative Fit Index 0.9897
Normal Theory Reweighted LS Chi-Square 34.9478
Akaike's Information Criterion -29.5 887
Bozdogan's (1987) CAIC -1609789
Schwarz's Bayesian Criterion -128.9789
McDonald's (1989) Centrality 0.9927
Bentler & Bonett's (1980) Non-normed Index 0.9854
Bentler & Bonett's (1980) NFI 0.8762
James, Mulaik, & Brett (1982) Parsimonious NF 1 0.6231
Z-Test of Wilson & Hilferty (1931) 0.3775
Bollen (1986) Normed Index Rhol 0.8259
Bollen (1988) Non-normed Index DeltaZ 0.9902
Hoelter's (1983) Critical N 222

The SAS System 19:38 Thursday, March 8, 2007 254

The CALIS Procedure
Covariance Structure Analysis: Maximum Likelihood Estimation

Raw Residual Matrix

V1 V3 V4 V5 V6

V1 00000000000 -.0007313854 00064591640 -.OO41441698 -.0023115573
V3 -.0007313854 00000000000 -.0011565102 00057226155 00044793203
V4 00064591640 -.0011565102 00000000000 00129556018 -.0020933316
V5 -.0041441698 0.0057226155 0.0129556018 00025271760 00113586411
V6 -.OO23115573 0.0044793203 -.0020933316 0.0113586411 00008665351
V8 00037370989 00050786143 -.0147691257 -.0125163628 00054079267

129

V11 0.0270892346 -.0089083928 -.0116108472 -.0179370305 -.0039965666
V12 0.0144942371 0.0165958942 0.0202398737 00138078130 -.0053871166
V13 0.0120839675 -.0090538542 -.0017157161 -.0104545927 -.0133052059
V15 -.0247602214 -.0020753525 00006467362 00102814995 00170306310

Raw Residual Matrix
V8 V11 V12 V13 V15
V1 0.0037370989 0.0270892346 00144942371 0.0120839675 -.02476022l4
V3 0.0050786143 -.0089083928 0.0165958942 -.OO90538542 -.OO20753525
V4 -.0147691257 -.0116108472 0.0202398737 -.0017157161 00006467362
V5 -.0125163628 -.0179370305 0.0138078130 -.0104545927 0.0102814995
V6 0.0054079267 -.0039965666 -.0053871166 -.Ol33052059 0.0170306310
V8 00019022915 00121675493 00121790014 00084605215 -.0069653322
V11 0.0121675493 00000000000 -.0007161151 00058211834 00002264494
V12 0.0121790014 -.0007161151 00000000000 -.0003395426 -.0054803329
V13 0.0084605215 0.0058211834 -.0003395426 00000000000 00050770567
V15 -.OO69653322 00002264494 -.0054803329 0.0050770567 00001248218

Average Absolute Residual 0.007223
Average Off-diagonal Absolute Residual 0.008707

Rank Order of the 10 Largest Raw Residuals

Row Column Residual
V11 V1 0.02709
V15 V1 002476
V12 V4 0.02024
V11 V5 001794
V15 V6 0.01703
V12 V3 0.01660
V8 V4 0.01477
V12 V1 0.01449
V12 V5 0.01381
V13 V6 0.01331

The SAS System 19:38 Thursday, March 8, 2007 255
The CALIS Procedure
Covariance Structure Analysis: Maximum Likelihood Estimation
Asymptotically Standardized Residual Matrix

V1 V3 V4 V5 V6
V1 0000000000 0625729008 1.456149913 0319564053 0215639506
V3 0625729008 0000000000 -1.063129513 0599102870 0518221123
V4 1.456149913 -1.063129513 0000000000 1.138124298 0.223355668
V5 0.319564053 0.599102870 1.138124298 0876192080 1.444879697
V6 -0215639506 0.518221123 0.223355668 1.444879697 0876112184

130

V8 0276601212 0483151390 -1.248270965 -l.423757113 0586486472
V11 1.696955986 -0571670932 0839193463 -l.303878074 -0348778198
V12 1.019633504 1.195975545 1.642785554 1.523401665 0.655798085
V13 0.951376199 -0730212288 -0155852044 0945367033 -1.449119253
V15 -l.444605778 -0166557569 0043093763 0630628925 1.154329780

Asymptotically Standardized Residual Matrix

V8 V11 V12 V13 V15
V1 0.276601212 1.696955986 1.019633504 0.951376199 -1.444605778
V3 0.483151390 0571670932 1.195975545 0730212288 0166557569
V4 -1.248270965 0839193463 1.642785554 0155852044 0.043093763
V5 -1.423757113 -l.303878074 1.523401665 0945367033 0.630628925
V6 0.586486472 0348778198 0655798085 -1.449119253 1.154329780
V8 0876177295 0844715085 1.220373701 0732076419 0386461541
V11 0.844715085 0000000000 0238550525 0749775442 0013513894
V12 1.220373701 -0238550525 0000000000 0136226635 0794818948
V13 0732076419 0749775442 0136226635 0000000000 0375834179
V15 0386461541 0.013513894 0794818948 0.375834179 0876080301

Average Standardized Residual 0.710696
Average Off-diagonal Standardized Residual 0.790749

Rank Order of the 10 Largest Asymptotically Standardized Residuals

Row Column Residual
V11 V1 1.69696
V12 V4 1.64279
V12 V5 1.52340
V4 V1 1.45615
V13 V6 -1 .4491 2
V6 V5 1.44488
V15 V1 -1.44461
V8 V5 -1.42376
V11 V5 -1.30388
V8 V4 -1.24827

The SAS System 19:38 Thursday, March 8, 2007 256

131

The CALIS Procedure
Covariance Structure Analysis: Maximum Likelihood Estimation
Distribution of Asymptotically Standardized Residuals
Each * Represents 1 Residuals

---------- Range--------- Freq Percent
-1.50000 -1.25000 4 7.27 ****
-1.25000 -1.00000 2 3.64 **

-1 .00000 075000 3 5.45 * * *
0.75000 0.50000 4 7.27 ****
050000 025000 3 5.45 ***
025000 0 6 10.91 ******

0 0.25000 8 14.55 ********
0.25000 0.50000 3 5.45 ***
0.50000 0.75000 6 10.91 *"‘*"‘**
0.75000 1.00000 6 10.91 ******
1.00000 1.25000 5 9.09 *****
1.25000 1.50000 2 3 .64 * *
1.50000 1.75000 3 5.45 ***

The SAS System 19:38 Thursday, March 8, 2007 257
The CALIS Procedure

Covariance Structure Analysis: Maximum Likelihood Estimation
Manifest Variable Equations with Estimates

V1 = 0.7338*F3 + 1.0000 E1
Std Err 0.1174 LV1F3
t Value 6.2523
V3 = 1.0000 F3
V4 = 06219*F 3
Std Err 0.1007 LV4F 3
t Value 6.1746
V5 = 1.0000 F2
V6 = 05856*F2
Std Err 0.1569 LV6F 2
t Value 3.7316
V8 = 0.8676*F2
Std Err 0.2145 LV8F2
t Value 4.0443
V11 = 07155*F4 + 1.0000 E11
Std Err 0.1714 LV11F4
t Value 4.1743
V12 = 1.0000 F4 + 1.0000 E12
V13 = 0.5566*F4 + 1.0000 E13
Std Err 0.1349 LV13F4
t Value 4.1256
V15 = 1.0000 F1

+ 1.0000 E3
+ 1.0000 E4

+ 1.0000 E5
+ 1.0000 E6

+ 1.0000 E8

132

The SAS System
The CALIS Procedure
Covariance Structure Analysis: Maximum Likelihood Estimation
Latent Variable Equations with Estimates

19:38 Thursday, March 8, 2007 258

F1 = 0.0595*F2 + 0.4171*F4 + 1.0000 D1
Std Err 0.2930 PF1F2 0.2608 PF1F4

t Value 0.2029 1.5992

F2 = 03943*F3 + 0.5407*F4 + 1.0000 D2
Std Err 0.1007 PF2F3 0.1482 PF2F4

t Value 3.9147 3.6479

Variances of Exogenous Variables

Standard
Variable Parameter Estimate Error t Value
F3 VARF3 0.13842 0.02639 5.25
F4 VARF4 0.10015 0.02632 3.81
E1 VAREI 0.11857 0.01643 7.21
E3 VARE3 0.04559 0.01828 2.49
E4 VARE4 0.09152 0.01240 7.38
E5 VARE5 0.17036 0.02580 6.60
E6 VARE6 0.11748 0.01484 7.92
E8 VARE8 0.18657 0.02506 7.45
E11 VAREll 0.16515 0.02166 7.63
E12 VARE12 0.07147 0.02140 3.34
E13 VARE13 0.10599 0.01373 7.72
D1 VARDl 0.34638 0.03925 8.83
D2 VARD2 0.02710 0.01726 1.57

Covariance Structure Analysis: Maximum Likelihood Estimation
Manifest Variable Equations with Standardized Estimates

Vl = 06213*F3 + 0.7836 E1
LV1F3

V3 = 0.8673 F3 + 0.4978 E3

V4 = 06075*F3 + 0.7943 E4
LV4F3

V5 = 0.5601 F2 + 0.8284 E5

V6 = 0.4304*F2 + 0.9026 E6
LV6F2

V8 = 04890*F2 + 0.8723 E8
LV8F2

V11 = 0.4868*F4 + 0.8735 E11
LV11F4

V12 = 0.7639 F4 + 0.6453 E12

V13 = 04759*F4 + 0.8795 E13
LV13F4

V15 = 1.0000 F1

133

The SAS System
The CALIS Procedure
Covariance Structure Analysis: Maximum Likelihood Estimation
Latent Variable Equations with Standardized Estimates

19:38 Thursday, March 8, 2007 260

F1 = 00274*F2 + 02180*F4 + 0.9718 D1
PF 1F2 PF1F4

F2 = 05256*F3 + 06131*F4 + 0.5898 D2
PF2F3 PF2F4

Squared Multiple Correlations

134

Error Total
Variable Variance Variance R-Square
1 V1 0.11857 0.19310 0.3860
2 V3 0.04559 0.18401 0.7522
3 V4 0.09152 0.14505 0.3690
4 V5 0.17036 0.24825 0.3138
5 V6 0.11748 0.14419 0.1852
6 V8 0.18657 0.24520 0.2391
7 V11 0.16515 0.21643 0.2369
8 V12 0.07147 0.17162 0.5836
9 V13 0.10599 0.13702 0.2265
10 V15 . 0.36676 .
11 F1 0.34638 0.36676 0.0556
12 F2 0.02710 0.07789 0.6521
Stepwise Multivariate Wald Test
------ Cumulative Statistics~---- --Univariate Increment--
Parameter Chi-Square DF Pr > ChiSq Chi-Square Pr > ChiSq
0.04118 1 0.8392 0.04118
VARD2 2.49589 2 0.2871 2.45471

PROC CALIS COVARIANCE CORR RESIDUAL MODIFICATION;
LINEQS

Vl = LV1F3 F3 + E1,

V3 = F3 + E3,

V4 LV4F3 F3 + E4,

V5 F2 + E5,

V6 LV6F2 F2 + E6,

V8 LV8F2 F2 + E8,

V11= LV11F4 F4+E11,

V12 = F4 + E12,

V13 = LV13F4 F4 + E13,

V15 = F1,

F1 = PF1F4 F4 + D1,

F2 = PF2F3 F3 + PF2F4 F4 + D2;
STD

E1 = VAREl,

E3-E6 = VARE3-VARE6,

E8 = VARE8,

Ell-E13 = VARE11-VARE13,
F3 = VARF3,

F4 = VARF4,

D1 = VARDl,

D2 = VARD2;

VAR V1-V6 V8 V11-V13 V15;
RUN;

The SAS System 19:38 Thursday, March 8, 2007 271

The CALIS Procedure
Covariance Structure Analysis: Pattern and Initial Values

Automatic Variable Selection, the Following Manifest Variables are not Used in the

Model V2

Using the VAR statement for variable selection could save memory and computing time.

LINEQS Model Statement
Matrix Rows Columns ------ Matrix Type -------
Term 1 1 _SEL_ 10 25 SELECTION

2 _BETA_ 25 ' 25 EQSBETA IMINUSINV
3 _GAMMA_ 25 13 EQSGAMMA
4 _PHI_ 1 3 13 SYMMETRIC

The 12 Endogenous Variables
Manifest V1 V3 V4 V5 V6 V8 V11 V12 V13 V15
Latent F1 F2

135

The 13 Exogenous Variables

Manifest
Latent F3
Error E1

F4
E3 E4 E5 E6 E8 E11 E12 E13 D1 D2

The SAS System 19:38 Thursday, March 8, 2007 272
The CALIS Procedure

Covariance Structure Analysis: Pattern and Initial Values

F1

F2

Manifest
V1

V3
V4

V5
V6

V8

V11

V12
V13

V15

Variable Equations with Initial Estimates
= .*F3 + 1.0000 E1
LV1F3
1.0000 F3 + 1.0000 E3
.*F3 + 1.0000 E4
LV4F 3
= 1.0000 F2 + 1.0000 E5
= .*F2 + 1.0000 E6
LV6F2
= .*F2 + 1.0000 E8
LV8F2
.*F4 + 1.0000 E11
LV11F4
= 1.0000 F4 + 1.0000 E12
= .*F4 + 1.0000 E13
LV13F4
1.0000 F1

.*F4 +1.0000D1

PF1F4

.*F3 + .*F4 +1.0000D2

PF 2F3 PF2F4

Variances of Exogenous Variables
Variable Parameter Estimate

F3
F4
El
E3
E4
E5
E6
E8
E11
E12
E13
D1
D2

VARF3
VARF4
VAREl
VARE3
VARE4
VARE5
VARE6
VARE8
VARE] 1
VARE12
VARE] 3
VARDl
VARD2

136

 

The SAS System

The CALIS Procedure

19:38 Thursday, March 8, 2007 274

Covariance Structure Analysis: Maximum Likelihood Estimation

Observations 165 Model Terms
Variables 10 Model Matrices 4
Informations 55 Parameters 22
Variable Mean Std Dev
V1 0 0.43943
V3 0 0.42896
V4 0 0.38086
V5 0 0.50078
V6 0 0.38086
V8 0 0.49709
V11 0 0.46522
V12 0 0.41427
V13 0 0.37016
V15 0 0.60571
Covariances
V1 V3 V4
V6
V1 0.1930987249 0.1008388327 0.0696239785
0.0211394070
V3 0.1008388327 0.1840066816 0.0849216522
0.0364372376
V4 0.0696239785 0.0849216522 0.1450543396
0.0177807609
V5 0.0359024228 0.0602963069 0.0468940649
0.0569701760
V6 00211394070 0.0364372376 0.0177807609
0. 1450543396
V8 0.0384819157 0.0524272846 0.0146762180
00449809421
V11 0.0270892346 -.0089083928 -.0116108472
0.0186928792
V12 0.0144942371 0.0165958942 0.0202398737
0.0263222492
V13 0.0120839675 -.0090538542 -.0017157161
0.0043449770
V15 -.0223793336 0.0011692141 0.0026644777
0.0329680095

137

1

V5

0.03 59024228

0.0602963069

0.0468940649

0.2507806084

0.0569701760

0.0550614306

0.0208091369

0.0679570598

0.0196861586

0.0374973398

 

V8
V15
V1 0.0384819157
.0223793336
V3 0.0524272846
0.0011692141
V4 0.0146762180
0.0026644777
V5 0.0550614306
0.0374973398
V6 0.0449809421
0.0329680095
V8 0.2470984681
0.0166473979
V11 0.0457841044
0.0324197561
V12 0.0591594194
0.0395110413
V13 0.0346109332
0.0301203195
V15 0.0166473979
0.3668846041

Covariances

V11 V12 V13
0.0270892346 0.0144942371 0.0120839675 -
-.0089083928 0.0165958942 -.0090538542
-.0116108472 0.0202398737 -.0017157161
0.0208091369 0.0679570598 0.0196861586
0.0186928792 0.0263 222492 0.0043449770
0.0457841044 0.0591594194 0.0346109332
0.2164296484 0.0709465489 0.04571 03 169
0.0709465489 0.1716196329 0.05 54070429
0.0457103169 0.0554070429 0.1370184256
0.0324197561 0.0395110413 0.0301203195
The SAS System 19:38 Thursday, March 8, 2007 275

The CALIS Procedure

Covariance Structure Analysis: Maximum Likelihood Estimation

Determinant 1.5879961E-8 Ln

-17.958208

NOTE: Some initial estimates computed by instrumental variable method.

NOTE: Some initial estimates computed by two-stage LS method.

The SAS System
The CALIS Procedure

19:38 Thursday, March 8, 2007 276

Covariance Structure Analysis: Maximum Likelihood Estimation
Vector of Initial Estimates

 

Parameter

LV6F2
LV8F2
LV1 F3
LV4F3
LV1 1 F4
LV13F4
PF 1 F4

\lO\LIt-bb~ll\.}'—lh

Estimate

0.55428
0.76552
0.80315
0.61319

Type

Matrix Entry: _BETA_[5:12]
Matrix Entry: _BETA_[6:12]
Matrix Entry: _GAMMA_[I : 1]
Matrix Entry: _GAMMA_[3:1]

0.58322 Matrix Entry: _GAMMA_[7z2]
0.42347 Matrix Entry: _GAMMA_[9:2]
0.35715 Matrix Entry: _GAMMA_[11:2]

138

V1
V3
V4
V5
V6
V8
V11
V12
V13
V15

V1
V3
V4
V5
V6
V8
V11
V12
V13
V15

8 PF2F3
9 PF2F 4

10
11
12
13
14
15
16
17
18
19
20
21
22

VARF3
VARF 4
VAREI
VARE3
VARE4
VARE5
VARE6
VARE8

VAREll
VARE12
VARE13

VARDl
VARD2

0.13244
0.131 15
0.10767
0.05157
0.09526
0.16430
0.1 1849
0.19642
0.17182
0.04047
0.11350
0.35016
0.03396

0.39366 Matrix Entry: _GAMMA_[12:1]
045289 Matrix Entry: _GAMMA_[12:2]

Matrix Entry: _PHI_[121]
Matrix Entry: _PHI_[2z2]
Matrix Entry: _PHI_[3:3]
Matrix Entry: _PHI_[4:4]
Matrix Entry: _PHI_[5:5]
Matrix Entry: _PHI_[626]
Matrix Entry: _PHI_[7:7]
Matrix Entry: _PHI_[8z8]
Matrix Entry: _PHI_[9:9]
Matrix Entry: _PHI_[10: 10]
Matrix Entry: _PHI_[11:11]
Matrix Entry: _PHI_[12:12]
Matrix Entry: _PHI_[13213]

Predetermined Elements of the Predicted Moment Matrix

V1

oooo'

V3

OOOO

V4

COCO

V5 V6

Predetermined Elements of the Predicted Moment Matrix

V8

V11

V12 V13 V15
0 0 0
0 0 O
0 0 0

139

 

WARNING: The predicted moment matrix has 12 constant elements whose values differ
from those of
the observed moment matrix. The sum of squared differences is 0.0025833963.

NOTE: Only 43 elements of the moment matrix are used in the model speciﬁcation.

The SAS System 19:38 Thursday, March 8, 2007 278

The CALIS Procedure
Covariance Structure Analysis: Maximum Likelihood Estimation
Levenberg-Marquardt Optimization
Scaling Update of More (1978)
Parameter Estimates 22
Functions (Observations) 55

Optimization Start

Active Constraints 0 Objective Function 02276614427
Max Abs Gradient Element 05340260986 Radius 6.535033911
Ratio
Between
Actual
Objective Max Abs and
Function Active Objective Function Gradient Predicted

Iter Restarts Calls Constraints Function Change Element Lambda
Change

1 O 2 0 0.21227 0.0154 0.2587 0 0.919
2 0 3 0 0.21012 0.00215 0.0286 0 0.970
3 0 4 0 0.21006 0.000059 0.00593 0 0.944
4 0 5 0 0.21006 4.312E-6 0.00159 0 0.975
5 0 6 0 0.21006 3.492E-7 0.000879 0 0.979
6 0 7 0 0.21006 3.139E-8 0.000154 0 0.944
7 0 8 0 0.21006 3.152E-9 0.000122 0 0.873
8 O 9 0 0.21006 3.55E-10 0.000024 0 0.791
Optimization Results

Iterations 8 Function Calls 10

Jacobian Calls 9 Active Constraints 0

Objective Function 02100554043 Max Abs Gradient Element

00000237949

Lambda 0 Actual Over Pred Change 07914788852

Radius 00000982868

GCONV convergence criterion satisﬁed.

140

 

 

The SAS System 19:38 Thursday, March 8, 2007 279

The CALIS Procedure
Covariance Structure Analysis: Maximum Likelihood Estimation
Predicted Model Matrix
V1 V3 V4 V5
V6
V1 01930987249 01015934832 00632325175 00400940755
00234284136
V3 0.1015934832 0.1840066816 00860478559 00545606812
00318817728
V4 0.0632325175 0.0860478559 01450543396 00339589620
00198434456
V5 0.0400940755 0.0545606812 0.0339589620 02482170169
00451896415

V6 0.0234284136 0.0318817728 0.0198434456 0.0451896415
0.1441790803
V8 0.0349366618 00475423873 00295907252 0.0673 87201 2

00393767708
V11 00000000000 00000000000 00000000000 00389213119
0.0227431255
V12 00000000000 00000000000 00000000000 00542635107
0.0317081253
V13 00000000000 00000000000 00000000000 00302785006
00176928194
V15 00000000000 00000000000 00000000000 00248017189
00144925384
Predicted Model Matrix
V8 V11 V12 V13
V15
V1 00349366618 00000000000 00000000000 00000000000
00000000000
V3 0.0475423873 00000000000 00000000000 00000000000
00000000000
V4 0.0295907252 00000000000 00000000000 00000000000
00000000000
V5 00673872012 0.0389213119 0.0542635107 0.0302785006
0.0248017189
V6 0.0393767708 00227431255 00317081253 0.0176928194
0.0144925384
V8 02451520476 00339147540 00472834426 00263836919
0.0216114040

V11 0.0339147540 0.2164296484 00715256071 00399105792
00326915450

141

V12 0.0472834426 0.0715256071 01716196329 00556427324
00455780630
V13 0.0263836919 0.0399105792 00556427324 0.1370184256
00254321070
V15 00216114040 0.0326915450 0.0455780630 0.0254321070
0.3668846041

Determinant 1.9591845E-8 Ln -17.748152

The SAS System
The CALIS Procedure
Covariance Structure Analysis: Maximum Likelihood Estimation

19:38 Thursday, March 8, 2007 280

Fit Function 0.2101
Goodness of Fit Index (GFI) 0.9590
GFI Adjusted for Degrees of Freedom (AGFI) 0.9317
Root Mean Square Residual (RMR) 0.0098
Parsimonious GFI (Mulaik, 1989) 0.7033
Chi-Square 34.4491
Chi-Square DF 33
Pr > Chi-Square 0.3983
Independence Model Chi-Square 278.00
Independence Model Chi-Square DF 45
RMSEA Estimate 0.0164
RMSEA 90% Lower Conﬁdence Limit .
RMSEA 90% Upper Conﬁdence Limit 0.0603
ECVI Estimate 0.4976
ECVI 90% Lower Conﬁdence Limit .

ECVI 90% Upper Conﬁdence Limit 0.6112
Probability of Close Fit 0.8711
Bentler's Comparative Fit Index 0.9938
Normal Theory Reweighted LS Chi-Square 35.0319
Akaike's Information Criterion -31.5509
Bozdogan's (1987) CAIC -167.0471
Schwarz's Bayesian Criterion -134.0471
McDonald's (1989) Centrality 0.9956
Bentler & Bonett's (1980) Non-normed Index 0.9915
Bentler & Bonett's (1980) NFI 0.8761
James, Mulaik, & Brett (1982) Parsimonious NFI 0.6425
Z-Test of Wilson & Hilferty (1931) 0.2579
Bollen (1986) Normed Index Rhol 0.8310
Bollen (1988) Non-normed Index Delta2 0.9941
Hoelter's (1983) Critical N 227

142

The SAS System 19:38 Thursday, March 8, 2007 281
The CALIS Procedure
Covariance Structure Analysis: Maximum Likelihood Estimation
Raw Residual Matrix

V1 V3 V4 V5 V6
V1 00000000000 -.0007546505 00063914609 -.OO41916527 -.0022890066
V3 -.0007546505 00000000000 -.0011262037 00057356257 00045554647
V4 0.0063914609 -.0011262037 00000000000 00129351029 -.OO20626847
V5 -.0041916527 0.0057356257 0.0129351029 00025635915 00117805345
V6 -.0022890066 0.0045554647 -.0020626847 0.0117805345 00008752593
V8 00035452539 00048848973 -.0149l45072 -.0123257706 00056041713
V11 0.0270892346 -.0089083928 -.0116108472 -.0181121750 -.OO40502463
V12 0.0144942371 0.0165958942 0.0202398737 00136935492 -.0053858761
V13 0.0120839675 -.0090538542 -.0017157161 -.0105923421 -.Ol33478424
V15 -.0223793336 0.0011692141 00026644777 00126956209 00184754711

Raw Residual Matrix

V8 V11 V12 V13 V15
V1 0.0035452539 0.0270892346 0.0144942371 0.0120839675 -.0223793336
V3 0.0048848973 -.0089083928 0.0165958942 -.0090538542 0.0011692141
V4 -.0149145072 -.0116108472 0.0202398737 -.0017157161 0.0026644777
V5 -.0123257706 -.0181121750 0.0136935492 -.0105923421 0.0126956209
V6 0.0056041713 -.0040502463 -.0053858761 -.0133478424 0.0184754711
V8 00019464205 00118693504 00118759767 00082272412 -.004964006l
V11 0.0118693504 00000000000 -.0005790582 00057997377 -.0002717889
V12 0.0118759767 -.0005790582 00000000000 -.0002356895 -.0060670217
V13 0.0082272412 0.0057997377 -.0002356895 00000000000 00046882125
V15 -.0049640061 -.0002717889 -.00606702l7 0.0046882125 00000000000

Average Absolute Residual 0.007226
Average Off-diagonal Absolute Residual 0.008712

Rank Order of the 10 Largest Raw Residuals

Row Column Residual
V11 V1 0.02709
V15 V1 002238
V12 V4 0.02024
V15 V6 0.01848
V1 1 V5 0.0181 1
V12 V3 0.01660
V8 V4 001491
V12 V1 0.01449
V12 V5 0.01369
V13 V6 0.01335

143

 

The SAS System 19:38 Thursday, March 8, 2007 282
The CALIS Procedure
Covariance Structure Analysis: Maximum Likelihood Estimation
Asymptotically Standardized Residual Matrix
V1 V3 V4 V5 V6
V1 0000000000 0641617970 1.439716136 0323104014 0213459257
V3 0641617970 0000000000 -1.026951440 0598368417 0526011334
V4 1.439716136 -1.026951440 0000000000 1.135579250 0219963066
V5 0323104014 0.598368417 1.135579250 0882740585 1.485678365
V6 0213459257 0.526011334 0.219963066 1.485678365 0882664477
V8 0262733527 0465105303 -1.261760584 -l.400212129 0606446055
V11 1.696955985 0571670932 0839193463 -1.315602635 0353314866
V12 1.019633504 1.195975545 1.642785554 1.508094735 0655338487
V13 0.951376199 0730212288 0155852044 0957243532 -1.453257285
V15 -1.076749372 0.057628118 0.147912170 0613297544 1.115137101

Asymptotically Standardized Residual Matrix

V8 V11 V12 V13 V15
V1 0.262733527 1.696955985 1.019633504 0.951376199 -1.076749372
V3 0465105303 0571670932 1.195975545 0.730212288 0.057628118
V4 -1.261760584 0839193463 1.642785554 0155852044 0.147912170
V5 -1.400212129 -1.315602635 1.508094735 0.957243532 0.613297544
V6 0.606446055 0353314866 0655338487 -1.453257285 1.115137101
V8 0882711000 0825004624 1.192891255 0712779343 0234681791
V11 0.825004624 0000000000 0186883681 0.744098441 0016173514
V12 1.192891255 0.186883681 0000000000 0091792531 0850094854
V13 0.712779343 0744098441 0091792531 0000000000 0.346170981
V15 0234681791 0016173514 0850094854 0346170981 0000000000

Average Standardized Residual 0.682048
Average Off-diagonal Standardized Residual 0.774767

Rank Order of the 10 Largest Asymptotically Standardized Residuals

Row Column Residual
V1 1 V1 1.69696
V12 V4 1.64279
V12 V5 1.50809
V6 V5 1.48568
V13 V6 -1.45326
V4 V1 1.43972
V8 V5 -1 .40021
V1 1 V5 -1.31560
V8 V4 -1 .26176
V12 V3 1.19598

144

 

The SAS System
The CALIS Procedure
Covariance Structure Analysis: Maximum Likelihood Estimation
Distribution of Asymptotically Standardized Residuals
Each * Represents 1 Residuals

19:38 Thursday, March 8, 2007 283

""""" Range--------- Freq Percent
-1.50000 -1.25000 4 7.27 ****
-1.25000 -1.00000 2 3.64 *1:
-1.00000 -O.75000 3 5.45 ***
-0.75000 -0.50000 4 7.27 ****
-0.50000 -O.25000 2 3.64 H
-0.25000 0 7 12.73 *******

0 025000 9 16.36 *********
0.25000 0.50000 3 5.45 ***
0.50000 0.75000 6 10.91 Mun
0.75000 1.00000 5 9.09 *****
1.00000 1.25000 5 9.09 *****
1.25000 1.50000 2 3.64 **

1.50000 1.75000 3 5.45 ***

Manifest Variable Equations with Estimates
V1 = 07349*F3 + 1.0000 E1
Std Err 0.1174 LV1F3
t Value 6.2606
V3 = 1.0000 F3
V4 = 06224*F3
Std Err 0.1007 LV4F3
t Value 6.1807

V5 1.0000 F2
V6 05843*F2
Std Err 0.1572 LV6F2
t Value 3.7180

V8 = 08714*F2

Std Err 0.2153 LV8F2
t Value 4.0472

V11 = 07173*F4 + 1.0000 E11
Std Err 0.1710 LV11F4

t Value 4.1935

V12 1.0000 F4 + 1.0000 E12
V13 05580*F4 + 1.0000 E13
Std Err 0.1347 LV13F4

t Value 4.1440

V15 = 1.0000 F1

+ 1.0000 E3
+ 1.0000 E4

+ 1.0000 E5
+ 1.0000 E6

+ 1.0000 E8

145

The SAS System
The CALIS Procedure

19:38 Thursday, March 8, 2007 285

Covariance Structure Analysis: Maximum Likelihood Estimation

Latent Variable Equations with Estimates

F1 = 0.4571*F4 + 1.0000 D1

Std Err 0.1885 PF1F4

t Value 2.4247

F2 = 0.3947*F3 + 0.5442*F4 + 1.0000 D2
Std Err 0.1006 PF2F3 0.1478 PF 2F4

t Value 3.9223 3.6810

Variances of Exogenous Variables

Standard
Variable Parameter Estimate Error t Value
F3 VARF3 0.13825 0.02635 5.25
F4 VARF4 0.09972 0.02609 3.82
E1 VARE] 0.11844 0.01643 7.21
E3 VARE3 0.04576 0.01823 2.51
E4 VARE4 0.09150 0.01240 7.38
E5 VARE5 0.17088 0.02578 6.63
E6 VARE6 0.11777 0.01484 7.94
E8 VARE8 0.18643 0.02505 7.44
E11 VAREll 0.16513 0.02164 7.63
E12 VARE12 0.07190 0.02115 3.40
E13 VARE13 0.10597 0.01372 7.73
D1 VARDl 0.34605 0.03926 8.81
D2 VARD2 0.02627 0.01706 1.54

Covariance Structure Analysis: Maximum Likelihood Estimation
Manifest Variable Equations with Standardized Estimates

VI = 0.6218*F3 + 0.7832 E1
LV1F3

V3 = 0.8668 F3 + 0.4987 E3

V4 = 0.6076*F3 + 0.7942 E4
LV4F3

V5 = 0.5582 F2 + 0.8297 E5

V6 = O.4280*F2 + 0.9038 E6
LV6F2

V8 = 0.4894*F2 + 0.8721 E8
LV8F2

V11 = 0.4869*F4 + 0.8735 E11
LV11F4

V12 = 0.7623 F4 + 0.6473 E12

V13 = 0.4760*F4 + 0.8794 E13
LV13F4

V15 = 1.0000 F1

146

The SAS System
The CALIS Procedure
Covariance Structure Analysis: Maximum Likelihood Estimation
Latent Variable Equations with Standardized Estimates

19:38 Thursday, March 8, 2007 287

F1 = 0.2383*F4 + 0.9712 D1
PF 1F4
F2 = 0.5277*F3 + 0.6179*F4 + 0.5829 D2
PF2F 3 PF2F4
Squared Multiple Correlations
Error Total
Variable Variance Variance R-Square
1 V1 0.11844 0.19310 0.3866
2 V3 0.04576 0.18401 0.7513
3 V4 0.09150 0.14505 0.3692
4 V5 0.17088 0.24822 0.3116
5 V6 0.11777 0.14418 0.1831
6 V8 0.18643 0.24515 0.2395
7 V11 0.16513 0.21643 0.2370
8 V12 0.07190 0.17162 0.5811
9 V13 0.10597 0.13702 0.2266
10 V15 0.36688 .
l 1 F1 0.34605 0.36688 0.0568
12 F2 0.02627 0.07734 0.6603
Stepwise Multivariate Wald Test
------ Cumulative Statistics----- --Univariate Increment--
Parameter Chi-Square DF Pr > ChiSq Chi-Square Pr > ChiSq
VARD2 2.37065 1 0.1236 2.37065 0.1236

147

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