Measurement invariance across cultures: a comparison between Chinese adolescents in China and in U.S.

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Content MEASUREMENT INVARIANCE ACROSS CULTURES:
A COMPARISON BETWEEN CHINESE ADOLESCENTS
IN CHINA AND IN U.S
by

Yu-Ling Chen

A Thesis Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOURTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
MASTER OF SCIENCE
(BIOSTATISTICS)

May 2007

Copyright 2007 Yu-Ling Chen

ii
DEDICATION
This thesis is dedicated to my parents and my sister Yi-Hsun for their
understanding, encouragement and loving support.

iii
ACKNOWLEDGEMENTS
I would like to express my deepest appreciation to Dr. Chih-Ping Chou for his
invaluable guidance in my work on thesis. I also want to thank Dr. Stanley Azen
and Dr. Bin Xie greatly for reviewing my thesis and serving on my thesis
committee.

iv
TABLE OF CONTENTS

DEDICATION …………………………………………………………………... ii

ACKNOWLEDGEMENTS ………………………………………………………... iii

LIST OF TABLES …………………………………………………………………... v

LIST OF FIGURES ……………………………………………………………... vi

ABSTRACT ………………………………………………………………………... vii

CHAPTER I: INTRODUCTION …………………………………………………... 1

CHAPTER II: METHODS ………………………………………………………... 3
Study design …………………………………………………………………... 3
Measures …………………………………………………………………... 4
Statistical analyses ………………………………………………………... 7

CHAPTER III: RESULTS ………………………………………………………... 11
Subject Characteristics …………………………………………………... 11
Complete CFA model with 23 Items ………………………………………... 14
Model Modification …………………………………………………... 15
Invariance test of intercepts ………………………………………... 16
Invariance test of factor loadings …………………………………... 17
Invariance test of factor correlations …………………………………... 18
The validity and reliability of the observed variables …………………... 18
Reduced CFA model with 21 Items ………………………………………... 19
Model Modification …………………………………………………... 20
Invariance test of intercepts ………………………………………... 21
Invariance test of factor loadings …………………………………... 21
Invariance test of factor correlations …………………………………... 21
CFA model with Invariance Factors ………………………………………... 23

CHAPTER IV: CONCLUSION …………………………………………………... 26

REFERENCES …………………………………………………………………... 29

Appendix A: Items Used for the Test of Measurement Invariance ………... 34

Appendix B: EQS Set-Up for Confirmatory ………….……………………... 36

v
LIST OF TABLES

Table 1: Demographic Characteristics, Smoking status, and
Parent's education level of Year 3 sample ………………………... 11

Table 2: Comparison Factor Scores of between two study groups ………... 12

Table 3a: Means, Standard Deviations of smoking related psychosocial
behaviors by site ………………………………………………..…. 12

Table 3b: Inter-Correlations of smoking related psychosocial behaviors
by site …………………………………………………………………... 13

Table 4: Model Improvement for Complete CFA Model by Group ………... 14

Table 5: Test of Measurement Invariance With Complete CFA Model …... 16

Table 6: Test of Measurement Invariance with Reduced CFA Model …... 20

Table 7: Model Improvement for the CFA Model with Invariant Factors …... 24

Table 8: Test of Measurement Invariance for the CFA Model with
Invariance Factors …………………………………………………... 24

.
vi
LIST OF FIGURES

Figure 1: Parameter Estimates of the Complete CFA Model …………………... 17

Figure 2: Reliabilities of Items by Culture ………………………………………... 19

Figure 3: Parameter Estimate of the Reduced CFA Model ………………....... 22

Figure 4: Parameter Estimates of the CFA Model with Invariant Factors …... 25

vii
ABSTRACT
The datasets were obtained from Wave3 of both Southern California Smoking
Prevention Trial (SCSPT) and Wuhan Smoking Prevention Trial (WSPT). For
the purpose of this study, only Chinese or Chinese-Americans were selected from
the SCSPT. The 3
rd
year follow-up surveys which contained substantial
overlapped items were used to investigate measurement invariance. The
factor-scores between two study groups were compared by Student t-test. The
confirmatory factor analysis (CFA) models were developed for each study groups.
Multiple-group CFA procedures were used to test measurement invariance.
Result from multiple-group CFA indicated that the major of items associated
with “opinion”, “depression”, “respecto”, and “familism” factors are not invariant
between two cultures. Items in “simpatia”, “machismo”, and “hostility” factors
demonstrated evidence of factor invariance between two cultures.
In summary, two items in simpatia, three items in machismo, and four items in
hostility factors indicated the evidence of factors validity and invariance between
two different cultures.
1
CHAPTER I
Introduction
To obtain meaningful comparison between groups, it is necessary that the
items used in survey-type instruments have the same meaning to individuals from
different groups [11]. Measurement invariance is an exceedingly important
assumption when comparing groups. The assumption of the measurement
invariance is that these measures must have the same scale and meaning in
order to compare groups of individuals regarding to their levels on a trait or to
investigate whether trait-level scores have differential correlates between groups
[16 & 17]. If the assumption of measurement invariance cannot be established,
the finding of difference between groups cannot be unambiguously interpreted.
Measurement invariance is critical in cross-cultural comparison study, especially
when the cultures speak different languages and the study uses translated
versions of a survey instrument [21, 34-35, &40].
The purpose of this study was to evaluate the equivalence of cigarette use
related psychosocial measures between Chinese adolescents in Southern
California and Wuhan, China using the confirmatory factor analysis. According
to the studies of Chinese adolescents in China, social influence is a very strong
motivator of tobacco use which is similar to the findings in United States and other
countries around the world. There are over one-fourth of the world’s 1.25 billion
smokers live in China, and smoking is a significant health problem in the country
[12, 24, 44, & 47]. Since smoking behavior mostly starts during pre-teen period,
2
school-based smoking prevention curricula are important intervention strategies
for tobacco use prevention among adolescents [2, 7, 9, 18, 30, 37, 42-43, & 45].
Moreover, culture factors, such as acceptability of smoking in various age and
gender groups, social stereotypes of smokers, smoking to facilitate social
interactions, and cigarette refusal strategies, also play an important role in
adolescent smoking. Previous smoking prevention intervention curricula,
however, were developed without a culture focus while other curricula have used
a more culturally grounded approach and targeted to specific issues facing
specific minority groups [1, 4-6, 10, 14, 19-20, 22-23, 25. 28-29, 32, 39, & 41].
Smoking prevention curricula can be more effective if they address specific
culture risk and protective factors [22]. Many large-scale trials of smoking
prevention programs for adolescents have not specifically addressed issues of
race, ethnicity, or culture [3, 26, 30, 31, & 36]. Comparisons made on the
difference between groups in mean levels or in the pattern of correlations may be
substantively misleading if trait scores are not comparable [37]. This study
focused on cross-cultural comparisons on the same ethnicity, Chinese or
Chinese-American adolescents, but grew up in different cultures, China and U.S.
The purpose of this study is to investigate one of the major issues in cross-cultural
studies on whether the measures obtained from the different cultures bear the
same meaning, or if the factors were the same between cultures among Chinese
adolescents.

3
CHAPTER II
Methods
Study design
The Southern California Smoking Prevention Trial (SCSPT) and the Wuhan
Smoking Prevention Trial (WSPT) were designed for evaluating a school-based
smoking prevention curriculum for high schools in Southern California and for
adolescents in urban Wuhan, China, respectively. The WSPT questionnaire was
developed in US and translated into Chinese with some additional items in order
to accommodate Chinese culture. Baseline data collection started in December
1998 for the WSPT and 2000 for the SCSPT. The follow-ups were conducted
approximately every year for both SCSPT and WSPT. In order to examine the
issue of cross-cultural measurement invariance, the data from SCSPT and the
data from WSPT are used for this thesis. Both the SCSPT and WSPT were
randomized, school-based smoking prevention, and longitudinal trials. The
SCSPT focused on Hispanic and Chinese American students, while WSPT
focused only on Chinese students. All consent procedures and survey
instruments were approved by the Institutional Review Boards of the University of
Southern California Keck School of Medicine and Wuhan city.
For the purpose of this study, only Chinese or Asian-Americans are included,
and the 3
rd
year follow-up surveys which contained substantial overlapped items
were used to investigate measurement invariance. For the 3
rd
year follow-up,
the sample size was 291 students (6.52% of the overall sample) in California
4
group and 4174 students (93.42% of the overall sample) in Wuhan group (urban
and rural students). The sample comprised 166 female (57.04%) in California
group and 1993 female (47.75%) in Wuhan group. The average age for
California group was around 13.13 years old (8
th
grade), as for Wuhan group was
14.54 years old (9
th
grade). For the California groups 96.91% never smoked,
whereas for the Wuhan group 61.92% never smoked (p < 0.01).
Measures
All students completed a self-report paper-and-pencil questionnaire. The
Southern California Smoking Prevention Trial questionnaire consisted of 163
items while the Wuhan Smoking Prevention Trial questionnaire consisted of 200
items. Both surveys included demographic characteristics, opinions on smoking,
smoking behaviors, attitudes, depressions, and social influences. The variables
included in the evaluation of measurement invariance are “ever smoking” and
“recent smoking”, as well as related psychosocial factors of “opinion”,
“depression”, “respecto”, “familism”, “simpatia”, “machismo”, and “hostility”. Ever
smoking was defined as ever tried smoking even just a few puffs, and the
measures were coded as 0= “no, do not smoke” and 1= “yes, ever smoke”.
Recent smoking was defined as ever smoke in the last 30 days, and the
measures were coded as 0= “no, do not smoke in the last 30 days” and 1= “yes,
smoke in the last 30 days even just a few puffs”.
Factors considered for the evaluation of measurement invariance in this
study are summarized as following (More detailed information on the measures
used in this study can be found in Appendix A).
5
Opinion. The factor of “opinion” was measured as the opinion about the
benefit and loss of smoking. There were five items, used to measure Opinion
factors are labeled as Opi1, Opi2, Opi3, Opi4, and Opi5. The five items are
“smoking causes you to lose friends who do not smoke”, “smoking causes bad
breath”, “young people who smoke are more popular”, “smoking makes young
people look more mature”, and “smoking makes young people look cool”. The
five items are adapted from “Independent Evaluation of the California Tobacco
Control Program: Relationships Between Program Exposure and Outcomes” [33].
There were six responses coded as 0= “do not smoke”, 1= “definitely not”, 2=
“maybe not”, 3= “maybe yes”, 4= “definitely yes”, and 5= “do not know”.
Depression. The factor of “depression” was measured as the frequency of
feeling depressed, lonely and sad in a week. Depression factor included three
items, labeled as Dep1, Dep2 and Dep3, which are “I felt depressed during the
past week”, “I felt lonely during the past week”, and “I felt sad during the past
week”. The three items are adapted from “The CES-D scale: A self-report
depression scale for research in the general population” [46]. There were four
responses coded as 1= “almost never”, 2= “seldom”, 3= “occasionally”, and 4=
“often”.
Respecto. The factor of “respecto” was measured as the inclination of
respecting elders. “Always showing respect for older people”, “being a good
person so that people know that my parents raised me right”, and “always respect
my parents, even if I don’t agree with them” were the three items, labeled as Rep1,
6
Rep2 and Rep3, included in respecto factor. The three items are adapted from
“Cultural / Interpersonal Values and Smoking Among California Adolescents” [38].
There were six responses coded as 0= “do not smoke”, 1= “definitely not”, 2=
“maybe not”, 3= “maybe yes”, 4= “definitely yes”, and 5= “do not know”.
Familism. The factor of “familism” was measured as the attitude about
reliability of the family. “Expect my relatives to help me when I need them”, “if
anyone in my family needed help, we would all be there to help them”, and “my
family could help me solve most problems” were the three items, labeled as Fam1,
Fam2 and Fam3, included in familism factor. The three items are adapted from
“Hispanic familism and acculturation: What changes and what doesn’t?” [13].
There were six responses coded as 0= “do not smoke”, 1= “definitely not”, 2=
“maybe not”, 3= “maybe yes”, 4= “definitely yes”, and 5= “do not know”.
Machismo. The factor of “machismo” was measured as the pride in being
male. “The father should make the final decision in the family”, “the father is the
boss of the family”, and “a husband should make more money than his wife does”
were the three items, labeled as Mac1, Mac2 and Mac3, included in machismo
factor. The three items are adapted from “Cognitive referents of acculturation:
Assessment of cultural constructs in Mexican Americans” [8]. There were six
responses coded as 0= “do not smoke”, 1= “definitely not”, 2= “maybe not”, 3=
“maybe yes”, 4= “definitely yes”, and 5= “do not know”.
Simpatia. The factor of “simpatia” was measured as the degree of sympathy
for others. “Try not to get into an argument, even if someone makes me really
7
mad” and “try not to say things that make people feel bad” were the two items,
labeled as Sim1 and Sim2, included in simpatia factor. The two items are
adapted from “Cultural / Interpersonal Values and Smoking Among California
Adolescents” [38]. There were six responses coded as 0= “do not smoke”, 1=
“definitely not”, 2= “maybe not”, 3= “maybe yes”, 4= “definitely yes”, and 5= “do
not know”.
Hostility. The factor of “hostility” was measured as the frequency of acting
unfriendly to others. “I lose my temper easily”, “sometimes feel bothered for
arounded”, “be rude to people I do not like”, and “have been kind of grouchy
lately” were the four items, labeled as Hos1, Hos2, Hos3, and Hos4, included in
hostility factor. The four items are adapted from “An inventory for assessing
different kinds of hostility” [27]. There were six responses coded as 0= “do not
smoke”, 1= “definitely not”, 2= “maybe not”, 3= “maybe yes”, 4= “definitely yes”,
and 5= “do not know”.
Statistical analyses
Mean, standard deviation and percentage were used to summarize the
general characteristics of the sample. Student t-test was used to compare
seven factor-scores between 2 study groups. The Confirmatory Factor Analysis
(CFA) models were developed to specify the structural relationships of the items
and corresponding factors for comparisons. The fundamental hypothesis of CFA
model in this study is that each observed variable was affected by its factor and
measurement error. The validity and reliability of the observed variables were
8
also addressed in CFA models. CFA model with multiple-group approach was
used to test measurement invariance. Specifically, a CFA model was developed
and evaluated separately for each group. The Lagrange Multiplier (LM) test was
used for model modification to develop more acceptable CFA model for each
group. Final CFA model from each group was then combined for the testing of
measurement invariance. The goodness-of-fit Q
2
test statistics available in
structural equation modeling approach were used to evaluate modeling fitting and
model comparisons to investigate measurement invariance. In addition, Norm fit
indices (NFI: Bentler & Bonett, 1980) and comparative fit indices (CFI: Bentler,
1990) were used as the practical fitting indices.
Evaluation of measurement invariance involved the following steps:
1. Performed a CFA model separately on each group. Use chi-square
analysis, norm fit indices (NFI: Bentler & Bonett, 1980), and
comparative fit indices (CFI: Bentler, 1990) as basic measurement
model fit indications.
2. Modified the basic CFA models for each group by, first, including factor
loadings that are consistently suggested by the Lagrange Multiplier
(LM) test for different groups. Secondly, within-factor correlated
measurement errors terms, and common between-factors correlated
measurement errors, which are common between two groups were
considered for model improvement.

9
3. Combined two separate modified models and developed the
combined model further by setting equality constraints using CFA with
multiple-group approach.
4. Performed the following test on equality constraints.
a. Invariance test of intercepts between groups
b. Invariance test of factor loading between groups
c. Invariance test of factor correlations between groups
5. Removed inappropriate regression intercept, factor loading, and factor
correlation constraints as suggested by LM tests.
6. Used likelihood ratio test to examine the difference of Q
2
values
between M and M
*
models and p-value to evaluate whether model M
*
,
a model with relevant parameters partially constrained equal between
groups, was significantly improved.
The hypothesis testing of measurement invariance in all models was carried out
using EQS (Bentler 1996). An Example of EQS setup us provided in Appendix II.
Following the steps listed above, we first developed basic models M
SC0
and
M
W0
for the California group and Wuhan group respectively. To obtain a better
fitted model for each group, we included meaningful parameters suggested by the
Lagrange Multiplier (LM) test. We modified the basic models by first adding
factor loading consistently suggested by the LM test for both groups. The
common correlated measurement errors within the same factor were then
considered and followed by the common correlated errors across factors. After
10
we got the better fitted basic models, the two resulting models were combined for
further model development with multiple-group approach. Let the Model M
0
be
the basic model that combines the final CFA models from each group. The M
0
model is also the most general model with a multi-group approach. A series of
models were developed by sequentially constraining regression intercepts, factor
loading, and then factor correlations in previous models to test measurement
invariance.
Model M
1
was constructed over the model M
0
by adding constraints on
intercepts. The difference between the Q
2
values of M
0
and M
1
models was used
to evaluate invariance of intercepts. If some constraints on intercepts were not
appropriate, partial constrained model M
1
*
was built by releasing those intercept
constraints so that the M
1
*
with partially constrained intercepts can be considered
to be not different from the M
0
model.
Model M
2
was constructed by adding constraints on all factor loadings over
the M
1
*
model. LM tests were used to modify for model M
2
. If the model M
2
was
not appropriate, a model, say model M
2
*
, with partial factor loading constraints
would be developed. Model M
3
was developed from modified model M
2
*
by
constraining all factor correlations to be equal. If the model M
3
was not adequate,
a modified model M
3
*
was developed by releasing some factor correlation
constraints suggested by LM tests. Chi-square difference test, or likelihood
ration test, was used to evaluate the appropriateness of equality constraints.

11
CHAPTER III
Results
Subject Characteristics
The demographic characteristics of the study samples are shown in Table 1.
There were 291 students in California group and 4174 students in Wuhan group.
The sample comprised 166 female (57.04%) and 125 male (42.96%) in California
group and 1993 female (47.75%) and 2181 male (52.25%) in Wuhan group.
96.91% of California group sample were never smoked while 61.12% in Wuhan
group sample were never smoked.
Table 1.
Demographic Characteristics, Smoking status, and Parent's education level of Year 3
California (N=291) Wuhan (N=4174)
Gender
Female 166 (57.04%)0 1993 (47.75%)0
Male 125 (42.96%)0 2181 (52.25%)0
Grade
8
th
Grade 289 (99.31%)0 0 ( 000%)0
9th Grade 0 (00.00%)0 4174 ( 100%)0
Missing 2 (00.69%)0 0 (00.00%)0
Ever Smoke
No 282 (96.91%)0 2551 (61.12%)0
Yes 9 (03.09%)0 1569 (37.59%)0
Missing 0 (00.00%)0 54 (01.29%)0
Recent Smoker (past month)
No 288 (98.97%)0 3650 (87.45%)0
Yes 3 (01.03%)0 522 (12.50%)0
Missing 0 (00.00%)0 2 (00.05%)0
12
The summary of the factors scores for complete 23 items are presented in
Table 2. “Opinion”, “Depression”, “Respecto”, “Familism”, “Machismo”, and
“Hostility” Mean Factor Scores were significantly different between the two groups
(p S 0.05). The means of “Simpatia” Factor Scores are 0.00 in both California
group and Wuhan group (p = 0.99).
The means, standard deviations, and inter-correlations for 23 common
variables obtained from the California and Wuhan groups are summarized in
Table 3a & 3b. Each variable is named in terms of its underlying constructs; for
example, the first item of Opinion factor is Opi1.

Table 3a. Means, Standard Deviations of smoking related psychosocial behaviors by site.

Opi1 Opi2 Opi3 Opi4 Opi5 Dep1 Dep2 Dep3 Res1 Res2 Res3
Mean 3.60 3.88 1.44 1.29 1.33 1.55 1.49 1.68 3.52 3.28 3.46
California
SD 0.70 0.39 0.69 0.62 0.67 0.94 0.88 1.00 0.71 0.86 0.68
Mean 3.03 3.50 2.48 2.06 1.90 2.33 2.30 2.46 3.74 3.09 3.38
Wuhan
SD 0.91 0.76 1.00 1.01 0.97 0.98 1.13 1.00 0.64 0.83 0.71
Fam1 Fam2 Fam3 Sim1 Sim2 Mac1 Mac2 Mac3 Hos1 Hos2 Hos3 Hos4
Mean 2.88 3.09 3.08 3.59 3.45 2.13 2.04 1.98 2.49 2.62 2.81 2.29
California
SD 1.03 0.88 0.93 0.67 0.69 0.96 0.98 1.02 0.94 1.06 0.97 1.00
Mean 2.68 3.06 3.11 3.22 3.16 2.56 2.62 2.52 2.77 2.20 2.74 2.44
Wuhan
SD 0.96 0.87 0.91 0.86 0.95 1.02 1.09 1.09 0.87 0.98 0.93 1.00
Table 2. Comparison Factor Scores of between two study groups

California Wuhan
Mean SD Mean SD p-value*
Opinion -0.51 0.54 0.03 0.94 <0.01
Depression 0.16 1.15 -0.01 0.88 0.01
Respecto 0.26 0.50 -0.02 0.64 <0.01
Familism 0.09 0.81 -0.01 0.80 0.05
Simpatia 0.00 0.70 0.00 0.71 0.99
Machismo -0.44 0.86 0.03 0.88 <0.01
Hostility 0.50 0.85 -0.03 0.83 <0.01
* p-value obtained by using two-sample student t-test.
13
Table 3b. Inter-Correlations of smoking related psychosocial behaviors by site.
Opi1 Opi2 Opi3 Opi4 Opi5 Dep1 Dep2 Dep3 Res1 Res2 Res3 Fam1 Fam2 Fam3 Sim1 Sim2 Mac1 Mac2 Mac3 Hos1 Hos2 Hos3 Hos4
Opinion Opi1 1.00 0.43 -0.31 -0.16 -0.24 -0.18 -0.06 -0.08 0.15 0.26 0.26 0.19 0.19 0.13 0.28 0.17 0.01 -0.05 0.02 -0.02 -0.03 0.01 -0.08
Opi2 0.37 1.00 -0.07 -0.02 -0.13 -0.03 -0.03 0.00 0.20 0.14 0.21 0.09 0.09 0.15 0.19 0.14 -0.01 -0.07 -0.01 0.03 0.03 -0.02 -0.03
Opi3 -0.08 -0.08 1.00 0.35 0.53 0.04 0.11 0.08 -0.12 -0.10 -0.14 -0.13 -0.09 -0.09 -0.21 -0.11 0.14 0.11 0.10 0.10 0.09 0.06 0.09
Opi4 -0.19 -0.16 0.41 1.00 0.32 0.07 0.06 0.08 -0.07 -0.03 -0.10 0.01 -0.14 -0.01 -0.16 -0.10 0.22 0.26 0.25 -0.01 -0.02 -0.01 -0.02
Opi5 -0.15 -0.14 0.35 0.77 1.00 0.01 0.10 0.02 -0.13 -0.19 -0.15 -0.06 -0.15 -0.16 -0.24 -0.14 0.09 0.09 0.08 0.11 0.07 0.13 0.11
Depression Dep1 0.00 -0.01 0.01 -0.03 0.01 1.00 0.68 0.80 -0.02 -0.23 -0.29 -0.32 -0.10 -0.01 -0.13 -0.20 -0.02 -0.04 0.10 0.24 0.20 0.06 0.38
Dep2 0.03 -0.07 0.01 0.04 0.04 0.44 1.00 0.67 -0.09 -0.15 -0.18 -0.25 -0.04 -0.09 -0.14 -0.26 -0.06 -0.04 0.15 0.20 0.32 0.08 0.32
Dep3 -0.01 -0.04 0.01 0.05 0.05 0.55 0.54 1.00 -0.02 -0.17 -0.22 -0.37 -0.03 -0.01 -0.05 -0.19 -0.05 -0.04 0.14 0.24 0.24 0.07 0.42
Respecto Res1 0.10 0.24 -0.08 -0.16 -0.14 -0.09 -0.06 -0.10 1.00 0.29 0.27 0.30 0.28 0.24 0.40 0.53 0.19 0.18 0.04 -0.11 -0.10 -0.22 -0.18
Res2 0.03 0.06 0.04 0.04 0.04 0.00 -0.03 0.04 0.12 1.00 0.59 0.44 0.28 0.06 0.24 0.32 0.11 0.13 0.00 -0.15 -0.07 0.01 -0.18
Res3 0.10 0.16 0.00 -0.05 -0.06 -0.04 -0.06 0.01 0.22 0.28 1.00 0.49 0.31 0.12 0.28 0.31 0.06 0.09 -0.03 -0.14 -0.15 -0.02 -0.20
Familism Fam1 0.06 0.01 0.04 0.06 0.06 -0.13 -0.08 -0.11 0.07 0.28 0.35 1.00 0.30 0.16 0.22 0.42 0.17 0.15 0.03 -0.17 -0.27 -0.10 -0.24
Fam2 0.14 0.09 -0.08 -0.09 -0.12 0.01 -0.05 -0.06 0.16 0.03 0.15 0.13 1.00 0.46 0.24 0.35 0.08 0.06 0.14 -0.24 -0.20 -0.24 -0.16
Fam3 0.01 0.02 -0.02 -0.03 -0.03 0.02 -0.01 0.04 0.13 0.13 0.15 0.06 0.27 1.00 0.20 0.29 0.10 0.00 0.03 -0.11 -0.20 -0.28 -0.17
Simpatia Sim1 0.19 0.07 0.06 0.03 0.02 -0.05 -0.01 0.00 0.09 0.12 0.18 0.23 0.15 0.15 1.00 0.48 0.09 0.12 0.10 -0.07 -0.12 -0.12 -0.09
Sim2 0.11 0.05 0.02 -0.15 -0.09 -0.09 -0.09 -0.10 0.13 0.15 0.21 0.20 0.27 0.12 0.33 1.00 0.17 0.20 0.07 -0.20 -0.23 -0.21 -0.25
Machismo Mac1 0.08 0.04 0.11 0.11 0.12 -0.02 -0.04 -0.02 0.01 0.11 0.12 0.28 0.03 0.03 0.16 0.17 1.00 0.76 0.40 -0.06 -0.23 -0.15 -0.11
Mac2 0.09 0.09 0.03 0.06 0.10 -0.04 -0.02 -0.01 0.06 0.00 0.10 0.22 0.02 0.00 0.17 0.11 0.65 1.00 0.47 -0.07 -0.15 -0.07 -0.09
Mac3 0.05 0.04 0.13 0.23 0.23 0.03 0.02 0.01 -0.10 0.04 -0.03 0.16 -0.02 -0.05 0.13 0.08 0.31 0.33 1.00 -0.06 -0.07 -0.09 0.03
Hostility Hos1 0.01 0.04 0.08 0.08 0.10 0.14 0.19 0.12 0.02 -0.02 -0.01 -0.09 -0.18 -0.02 0.06 -0.10 -0.01 0.11 0.07 1.00 0.40 0.34 0.43
Hos2 0.02 0.01 0.01 0.10 0.11 0.14 0.14 0.14 -0.16 -0.08 -0.12 -0.02 -0.06 -0.08 0.02 -0.04 0.08 0.08 0.06 0.29 1.00 0.47 0.38
Hos3 0.01 0.01 0.13 0.22 0.22 0.10 0.11 0.09 -0.03 0.08 -0.08 0.04 -0.18 -0.04 0.08 0.01 0.12 0.09 0.18 0.35 0.29 1.00 0.34
Hos4 0.03 -0.02 0.04 0.17 0.13 0.19 0.24 0.29 -0.10 0.02 -0.05 -0.06 -0.19 -0.02 0.05 -0.09 0.05 0.03 0.07 0.50 0.28 0.34 1.00
Above the diagonal is California group (N = 291); below the diagonal is Wuhan group (N = 4174).
Opi = Opinion; Dep = Depression; Res = Respecto; Fam = Familism; Sim = Simpatia; Mac = Machismo; Hos = Hostility.
14

Complete CFA Model with 23 Items
Following the steps listed in Statistical Analyses section, we first performed a
CFA model with all 23 items for each group and then modified the basic CFA
model to each groups. The results of measurement model development for each
group were summarized in Table 4. The basic models M
SC0
and M
W0
both
contained 209 degree of freedom. Both M
SC0
model (NFI = 0.83 and CFI = 0.91)
and M
W0
model (NFI = 0.87 and CFI = 0.88) did not have satisfactory fit. After
model improvement procedure, the final CFA model for each group had better
model fitting with CFI greater than 0.90.

Table 4. Model Improvement for Complete CFA Model by Group.
Group Q
2
df p NFI CFI
California
M
SC0
411.46 209 <0.01 0.83 0.91
M
SC1
368.21 206 <0.01 0.85 0.93
M
SC2
317.10 205 <0.01 0.87 0.95
M
SC3
291.49 202 <0.01 0.88 0.96
Wuhan
M
W0
3226.79 209 <0.01 0.87 0.88
M
W1
2460.91 206 <0.01 0.90 0.91
M
W2
1941.64 205 <0.01 0.92 0.93
M
W3
1918.12 202 <0.01 0.92 0.93
Note: M SC0 and M W0 = basic theoretical models for California (N=291) and Wuhan (N=4174) groups.
M SC1 and M W1 = modified models with factor loadings suggested by LM test on M SC0 and M W0
respective.
M SC2 and M W2 = modified models with within-factor correlated errors suggested by LM test on
M SC1 and M W1 respective.
M SC3 and M W3 = modified models with between-factor correlated errors suggested by LM test on
M SC2 and M W2 respective.
NFI: norm fit indices (Bentler & Bonett, 1980)
CFI: comparative fit indices (Bentler, 1990)
15

Model Modification. We modified the basic models for each group by adding
free parameters guided by LM tests of the EQS program. We first added
common factor loadings, such as Opi2 on Familism factor, Sim2 on Familism
factor, and Hos2 on Depression factor suggested by the LM test for both groups.
Then we added common within-factor correlated errors and last added common
between-factor correlated errors suggested by LM tests. The common
within-factor correlated error, Opi1 and Opi2, and the common between-factor
correlated errors, Opi4 and Mac3, Dep2 and Hos2, and Sim1 and Mac3, were
added for model fitting purposes. None of the modified models had statistically
satisfactory fit to the sample covariance matrices; however, the NFIs (Bentler &
Bonett, 1980) and the CFIs (Bentler, 1990) showed improvement after each time
we included free parameters guided by LM tests procedure.
Invariance test of intercept. To evaluate measurement invariance, we used
the SEM with multiple-group approach. The basic model with multiple-group
approach, M
0
, was built from combining models M
SC3
and M
W3
in Table 4. We
first tested the invariance of intercept parameters between the California and
Wuhan groups. Model M
1
was developed by adding 23 equality constraints on
intercepts between the two groups from model M
0
. The difference between the
chi-square values of model M
0
and M
1
indicated the changes of model fitting due
to the 23 equality constraints on intercepts.
The results of the CFA models and models for testing measurement
invariance between groups with all 23 measured variables are summarized in
16

Note: An asterisk indicates a model with relevant parameters partially constrained equally between group.
M 0 = basic model combining California and Wuhan groups.
M 1 = model with all mean constrained equally between groups.
M 2 = model with all factor loadings constrained equally between groups over M 1
*
.
M 3 = model with all factor correlations constrained equally between groups over M2
*
.
Table 5. From the result of likelihood ratio test by taking the difference of Q
2
values of (M
1
-M
0
), the null hypothesis that all 23 intercepts are equal between two
groups is rejected (Q
2
(23) = 634.86 and p < 0.01). LM tests suggested only
constraining intercepts of Dep2, Fam2, Fam3, Sim1, and Sim1 to be equal
between the two groups were reasonable. The M
1
*
model dropped the 18
constraints from M
1
model as suggested by LM tests and yielded Q
2
(409) =
2212.70 and p < 0.01. The difference test of (M
1
*
-M
0
) gave Q
2
(5) = 3.10 and p =
0.68; thus the remaining constraints were considered appropriate.

Table 5. Test of Measurement Invariance with Complete CFA Model.
Group Q
2
df p NFI CFI
California & Wuhan
M
0
2209.60 404 < 0.01 0.92 0.93
M
1
2844.47 427 < 0.01 0.91 0.93
M
1
-M
0
634.86 23 < 0.01
M
1
*
2212.70 409 < 0.01 0.92 0.93
M
1
*
-M
0
3.10 5 0.68
M
2
2599.99 435 < 0.01 0.91 0.92
M
2
-M
1
*
387.29 26 < 0.01
M
2
*
2228.86 420 < 0.01 0.92 0.93
M
2
*
-M
1
*
16.16 11 0.14
M
3
2326.90 441 < 0.01 0.92 0.93
M
3
-M
2
*
98.05 21 < 0.01
M
3
*
2234.57 428 < 0.01 0.92 0.93
M
3
*
-M
2
*
5.71 8 0.68
17

Invariance test of factor loadings. The M
2
model was then created by
imposing equality constraint on all 26 factor loadings in M
1
*
for testing factor
loading invariance. The difference test of (M
2
- M
1
*
) rejected the null hypothesis
that all factor loadings were equal between two groups (Q
2
(26) = 387.29 and p <
0.01). As suggested by the LM test, M
2
*
model freed 15 constraints from M
2
model and yielded an acceptable Q
2
(11) = 16.16 with p = 0.14.
Figure1. Parameter Estimates of the Complete CFA Model.
The intercept of each measured variable is shown next to the variable name in the rectangle.
A parameter with one value indicates that the parameter was constrained equal across groups.
A parameter with two values indicates that the parameter was not constrained equal with
estimate for the Wuhan group shown in parentheses.
An underlined coefficient indicates that the parameter was fixed at those values for identification
purposes.
Red coefficient indicates that p-value smaller than 0.05.
18

Invariance test of factor correlation. The final step was to investigate the
issue of invariance of factor correlations. The M
3
model was developed by
imposing 21 equality constraints on factor correlations in the M
2
*
model. The
result of likelihood ratio for comparing Q
2
(M
3
)-Q
2
(M
2
*
) indicated not all factor
correlations could be considered equal between these two groups (Q
2
(21) = 98.05
and p < 0.01). M
3
*
was built as a model with partial equality imposed factor
correlation with 8 factor constraints constrained equal. The partial equality factor
correlations appeared to be adequate as indicated by the difference test of
(M
3
*
-M
2
*
). The partial measurement invariance was statistically acceptable (Q
2
(8)
= 5.71 and p = 0.68).
The validity and reliability of the observed variables
From the standardized solution outputs of the basis CFA model by group, we
detected that the R-square values of variable Opi1 in Wuhan group and variable
Opi2 in California group were much smaller than the other variables, R
Opi1
= 0.015
for Wuhan and R
Opi2
= 0.026 for California. This indicated that the variables of
Opi1 in Wuhan group and Opi2 in California group were not reliable. Therefore,
we dropped variables Opi1 and Opi2 in both group and re-ran the models.

19

Reduced CFA model with 21 Items
Since the variables of Opi1 and Opi2 were not reliable, we decided to test the
models and went through all the procedures again without variables Opi1 and
Opi2 in both groups. The results of the CFA models and models for testing
measurement invariance between groups without variables Opi1 and Opi2 were
summarized in Table 6.
Figure2. Reliabilities of Items by Culture.
The coefficients indicate that R-squared values of parameters in California group and Wuhan
group shown in parentheses.
20

Table 6. Test of Measurement Invariance with Reduced CFA Model.
Group Q
2
df p NFI CFI
California & Wuhan
M
0 1620.61 330
< 0.01
0.94 0.95
M
1 2192.69 351
< 0.01
0.93 0.94
M
1
-M
0 572.08 21
< 0.01
M
1
*
1623.69 335
< 0.01
0.94 0.95
M
1
*
-M
0 3.07 5
0.69
M
2 1877.19 356
< 0.01
0.93 0.94
M
2
-M
1
*
253.51 21
< 0.01
M
2
*
1631.11 346
< 0.01
0.94 0.95
M
2
*
-M
1
*
7.42 11
0.76
M
3 1719.53 367
< 0.01
0.93 0.95
M
3
-M
2
*
88.42 21
< 0.01
M
3
*
1637.42 354
< 0.01
0.93 0.95
M
3
*
-M
2
*
6.31 8
0.61
Model Modification. We modified the basic models and did the same
procedures by adding free parameters guided by LM tests of the EQS program.
In this CFA model, there were no any common factor loadings and common
within-factor correlated errors. We only added correlated errors of variables
sharing the same factor, such as Mac3 and Opi4, Mac3 and Sim1, and Hos2 and
Dep2, for model fitting purposes. The chi-square value was significant, and it
Note: An asterisk indicates a model with relevant parameters partially constrained equal across group.
M SC0 and M W0 = basic theoretical models for California (N=291) and Wuhan (N=4174) groups.
M 0 = basic model combining California and Wuhan groups.
M 1 = model with all mean constrained equal across groups.
M 2 = model with all factor loadings constrained equal across groups over M 1
*
.
M 3 = model with all factor correlations constrained equal across groups over M 2
*
.
21

suggested that the modified basic model, M
0
, did not have statistically satisfactory
fit to the sample covariance matrices (Q
2
(330) = 1620.61 and p < 0.01; NFI = 0.94
and CFI = 0.95).
Invariance test of intercepts. To test the invariance of intercepts, we
conducted M
1
model by imposing 21 equality constraints on intercepts (M
1
:
Q
2
(351) = 2192.69 and p < 0.01; NFI = 0.93 and CFI = 0.94). The difference test
of (M
1
-M
0
) indicated that it was not proper to impose all 21 equality constraints on
intercepts, and as suggestion by the LM test, 16 intercept constraints were
dropped. M
1
*
model was only constrained on the intercepts of Dep2, Fam2,
Fam3, Sim1, and Sim2 (M
1
*
:Q
2
(335) = 1623.69 and p < 0.01; NFI = 0.94 and CFI
= 0.95). By the difference test of (M
1
*
-M
0
), M
1
*
model yielded appropriate
equality constraints on intercepts with Q
2
(5) = 3.07 and p = 0.69.
Invariance test of factor loadingss. M
2
model was formed by constraining 21
factor loadings equal in M
1
*
model (M
2
:Q
2
(356) = 1877.19 and p < 0.01; NFI =
0.93 and CFI = 0.94). In the M
2
*
model, 10 factor loading constraints guided by
the LM test were freed from M
2
model. The difference test of (M
2
*
-M
1
*
) had a non
significant chi-square value which indicated that M
2
*
model contained more
adequate constraints than the M
2
model (Q
2
(11) = 7.42 and p = 0.76).
Invariance test of factor correlations. We then developed M
3
model by
constraining 21 equality factor correlations in M
2
*
model for testing invariance of
22

factor correlations. Guided by the LM test, M
3
*
model was conducted from M
3
model by freeing 13 factor correlations equalities. The (M
3
*
-M
2
*
) test indicated
that the chi-square value was not significant which meant the M
3
*
model appeared
to adequate in terms of equality constraints on factor correlations (Q
2
(8) = 6.31
and p = 0.61).

Figure 3. Parameter Estimates of the Reduced CFA Model.
The intercept of each measured variable is shown next to the variable name in the rectangle.
A parameter with one value indicates that the parameter was constrained equal across groups.
A parameter with two values indicates that the parameter was not constrained equal with estimate
for the Wuhan group shown in parentheses.
An underlined coefficient indicates that the parameter was fixed at that value for identification
purposes. Red coefficient indicates that p-value smaller than 0.05
23

CFA model with Invariant Factors.
Results from the above analyses involving 7 factors indicated that 3 factors
could be considered invariant while 4 factors were different between the California
and Wuhan samples. In order to make sure these three factors, Simpatia,
Machismo, and Hostility, were invariant, we also separated the CFA model into
invariant-factors CFA model and variant-factors CFA model. The
invariant-factors CFA model contained three factors, Simpatia, Machismo, and
Hostility, while the variant-factors CFA model contained four factors, Opinion,
Depression, Respecto, and Familism. The results of both invariant-factors and
variant-factors CFA models were quite consistent with the overall CFA model.
Summary of the results of factor invariance measurement model development for
each group was shown in Table 7. The basic models M
SC0
and M
W0
both
contained 24 degree of freedom. Both M
SC0
model (NFI = 0.94 and CFI = 0.98)
and M
W0
model (NFI = 0.98 and CFI = 0.98) showed statistically significant
satisfactory fit.
The results of the CFA models and models for testing measurement
invariance between groups with 21 measured variables were summarized in Table
8. The difference tests (M
1
*
-M
0
), (M
2
*
-M
1
*
), and (M
3
*
-M
2
*
) yielded Q
2
(2) = 0.05
and p = 0.97, Q
2
(8) = 10.28 and p = 0.25, and Q
2
(1) = 0.29 and p = 0.59
respectively; thus the remaining constraints of interception, factor loading, and
factor correlation are appropriate.

24

Note: M SC0 and M W0 = basic theoretical models for California (N=291) and Wuhan (N=4174) groups.
M SC1 and M W1 = modified models with factor loadings suggested by LM test on M SC0 and M W0
respective.
M SC2 and M W2 = modified models with within-factor correlated errors suggested by LM test on
M SC1 and M W1 respective.
M SC3 and M W3 = modified models with between-factor correlated errors suggested by LM test on
M SC2 and M W2 respective.
Table 7. Model Improvement for the CFA Model with Invariant Factors.
Group Q
2
df p NFI CFI
California
M
SC0
39.97 24 0.02 0.94 0.98
M
SC1
39.97 24 0.02 0.94 0.98
M
SC2
35.01 23 0.05 0.95 0.98
Wuhan
M
W0
180.92 24 < 0.01 0.98 0.98
M
W1
180.92 24 < 0.01 0.98 0.98
M
W2
174.57 23 < 0.01 0.98 0.98
Table 8. Test of Measurement Invariance for the CFA Model with Invariant Factors.

Group Q
2
df p NFI CFI
California & Wuhan
M
0 209.58 46
< 0.01
0.97 0.98
M
1 427.43 55
< 0.01
0.97 0.97
M
1
-M
0 217.85 9
< 0.01
M
1
*
209.64 48
< 0.01
0.97 0.98
M
1
*
-M
0 0.05 2
0.97
M
2 234.76 57
< 0.01
0.97 0.98
M
2
-M
1
*
25.12 9
0.00
M
2
*
219.92 56
< 0.01
0.97 0.98
M
2
*
-M
1
*
10.28 8
0.25
M
3 244.84 59
< 0.01
0.97 0.98
M
3
-M
2
*
24.92 3
0.00
M
3
*
220.21 57
< 0.01
0.97 0.98
M
3
*
-M
2
*
0.29 1
0.59
Note: An asterisk indicates a model with relevant parameters partially constrained equal across group.
M 0 = basic model combining California and Wuhan groups.
M 1 = model with all mean constrained equal across groups.
M 2 = model with all factor loadings constrained equal across groups over M 1
*
.
M 3 = model with all factor correlations constrained equal across groups over M 2
*
.
25

Figure4. Parameter Estimates of the CFA model with Invariant Factors.
The intercept of each measured variable is shown next to the variable name in the rectangle.
A parameter with one value indicates that the parameter was constrained equal across groups.
A parameter with two values indicates that the parameter was not constrained equal with estimate
for the Wuhan group shown in parentheses. An underlined coefficient indicates that the
parameter was fixed at those values for identification purposes.
26

CHAPTER IV
Conclusion
This study utilized measures obtained from two randomized, school-based
smoking prevention interventions in Southern California and Wuhan, China
schools to compare measurement invariance between two different cultures in the
same race. The assumptions were that the smoking related psychosocial factors
were not different between cultures in the same ethnic group, and the factor
loadings and factor correlations would not be different among Chinese
adolescents in S. California and Wuhan. With these assumptions, the
procedures used to test the measurement invariance included:
1. Using chi-square analysis, norm fit indices (NFI: Bentler & Bonett, 1980),
and comparative fit indices (CFI: Bentler, 1990) as basic measurement
model fitting indications. Establishing a well-fitted CFA model
separately for each group.
2. Modifying the basic CFA models for each group. Following the LM test
procedure; including necessary common factor loadings in two basic
models, common within-factor correlated measurement errors terms,
and then common between-factors correlated measurement errors.
3. Combining two separate modified models and developing the combined
model further by setting equality constraints.
4. Determining the appropriateness of fully constrained or partially
constrained equalities between groups in terms of means (regression
27

intercepts), factor loading (regression slopes), and factor correlation as
suggested by LM tests.
5. Useing the difference of Q
2
values between M and M
*
models and
p-value to evaluate whether model M
*
was improved or not.
In research studies of substance use among adolescents, self-concept is
increasingly used all over the world [15]. Therefore, it is important to evaluate
the psychometric properties of these measures systematically when these
instruments are applied in different countries since many self-concept instruments
have been developed in English-speaking countries [15]. The results of this
study indicated that the self-report measurement is valid and reliable for
adolescent smoking behavior between cultures. This study investigated the
issue of measurement invariance of seven self-concept factors: “Simpatia”,
“Machismo”, “Hostility”, “Opinion”, “Depression”, “Respecto”, and “Familism”.
Three factors can be considered invariant, while the other four factors are not.
The invariant factors are simpatia factor, which measured as the degree of
sympathy for others, machismo factor, which measured as the pride in being male,
and hostility factor, which measured as the frequency of acting unfriendly to
others. The variant factors are opinion factor, depression factor, respeto factor,
and familism factor.
The regression weights for most parameters in simpatia factor, machismo
factor, and hostility factor are statistically invariant between two different cultures,
except one parameter in hostility factor. On the other hand, only one parameter
28

in each opinion factor and familism factor and two parameters in respeto factor
have invariant regression weights, but the regression weights for the rest of the
parameters in opinion factor, depression factor, respeto factor, and familism factor
are not invariant among Chinese or Chinese-American adolescents groups
between S. California and Wuhan China.
In conclusion the invariance factors could be adopted to obtain more
meaningful cross-cultural comparison; while the variant factors require further
refinement to offer more adequate comparisons in cross-culture studies.
29

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34
APPENDIX A: ITEMS USED FOR THE TEST OF MEASUREMENT INVARIANCE
Variable
name Label
grade Grade03
sex Sex 0=male, 1=female
CIGEVER Ever tried smoking (even just a few puffs)? 0=no,1=yes
CIG100 at least one hundred cigarettes 0=no,1=yes
CIGPSTM
Past 30 days (one month), on how many of these days did you
smoke?
0=0days, 1=1~2days, 2=3~5days, 3=6~9days, 4=more than 9days,
5=I do not know
CIGAVRG Average number cigarettes/day in past month
0=do not smoke, 1=less than 1, 2=1, 3=2~5, 4=6~10, 5=11~20,
6=more than 20
CIGRCNT Recently Smoke 0=no,1=yes
CIGINIT Age started smoking
1=do not smoke, 2=7yearsold or younger, 3=8years old, 4=9years old,
5=10years old, 6=11years old, 7=12years old, 8=13years old, 9=14
years old, 10=15years or older, 11= do not know
CIGINT Start smoking sometime during the next 12 months (one-year)? 0=no,1=yes
CIGEASY Easy to get cigarettes?
0=do not smoke, 1=very hard, 2=fairly hard, 3=fairly easy, 4=very
easy
CIGEXP
Past seven days, were you in a room where someone else was
smoking?
1=0days, 2=1 or 2days, 3=3 or 4days, 4=5 or 6days, 5=7days, 6=I do
not know
CIGNORM
In your opinion, how many out of 100 people your age smoke
at least once a month?
0=none, 1=about10, 2=about 20, 3=about30, 4=about40, 5=about 50,
6=about 60, 7=about70, 8=about80, 9=about90, 10=about 100
CIGACPT
Do most people your age think it is acceptable to smoke on
occasion?
0=I do not know, 1=yes, 2=probably yes, 3=probably no, 4=no
Opi1 Smoking causes you to lose friends who do not smoke.
0=do not smoke, 1=definitely not, 2=maybe not, 3=maybe yes,
4=definitely yes
Opi2 Smoking causes bad breath. 1=definitely not, 2=maybe not, 3=maybe yes, 4=definitely yes
Opi3 Young people who smoke are more popular.
0=do not smoke, 1=definitely not, 2=maybe not, 3=maybe yes,
4=definitely yes, 5=do not know
35
APPENDIX A: Continued
Opi4 Smoking makes young people look more mature. 1=definitely not, 2=maybe not, 3=maybe yes, 4=definitely yes
Opi5 Smoking makes young people look cool.
0=do not smoke, 1=definitely not, 2=maybe not, 3=maybe yes,
4=definitely yes, 5=do not know
Dep1 During the past week, I felt depressed. 1=almost never, 2=seldom, 3=occasionally, 4=often
Dep2 During the past week, I felt lonely. 1=almost never, 2=seldom, 3=occasionally, 4=often
Dep3 During the past week, I felt sad. 1=almost never, 2=seldom, 3=occasionally, 4=often
Res1 Always show respect for older people. 1=Definitely not, 2=Maybe not, 3=Maybe yes, 4=Definitely yes
Res2
Be a good person so that people know that my parents raised
me right.
1=Definitely not, 2=Maybe not, 3=Maybe yes, 4=Definitely yes
Res3 Always respect my parents, even if I don't agree with them. 1=Definitely not, 2=Maybe not, 3=Maybe yes, 4=Definitely yes
Fam1 Expect my relatives to help me when I need them. 1=Definitely not, 2=Maybe not, 3=Maybe yes, 4=Definitely yes
Fam2
If anyone in my family needed help, we would all be there to
help them.
1=Definitely not, 2=Maybe not, 3=Maybe yes, 4=Definitely yes
Fam3 My family could help me solve most problems. 1=Definitely not, 2=Maybe not, 3=Maybe yes, 4=Definitely yes
Sim1
Try not to get into an argument, even if someone makes me
really mad.
1=Definitely not, 2=Maybe not, 3=Maybe yes, 4=Definitely yes
Sim2 Try not to say things that make other people feel bad. 1=Definitely not, 2=Maybe not, 3=Maybe yes, 4=Definitely yes
Mac1 The father should make the final decisions in the family. 1=Definitely not, 2=Maybe not, 3=Maybe yes, 4=Definitely yes
Mac2 The father is the boss of the family. 1=Definitely not, 2=Maybe not, 3=Maybe yes, 4=Definitely yes
Mac3 A husband should make more money than his wife does. 1=Definitely not, 2=Maybe not, 3=Maybe yes, 4=Definitely yes
Hos1 I lose my temper easily 1=Definitely not, 2=Maybe not, 3=Maybe yes, 4=Definitely yes
Hos2 Sometimes feel bothered for arounded 1=Definitely not, 2=Maybe not, 3=Maybe yes, 4=Definitely yes
Hos3 Be rude to people I do not like? 1=Definitely not, 2=Maybe not, 3=Maybe yes, 4=Definitely yes
Hos4 Lately, I have been kind of grouchy 1=Definitely not, 2=Maybe not, 3=Maybe yes, 4=Definitely yes
36
APPENDIX B: EQS SET-UP FOR CONFIRMATORY

EQS Set-Up for Confirmatory Factor Analysis with Multi-group Approach

/TITLE
Multiple Group Factor Analysis IRP GROUP Wave 3
/SPECIFICATIONS
DATA='C:\Documents and Settings\ling\Desktop\GVF_missing imputation
\WO_dep45_irp03.ess';
VARIABLES=37; CASES=291;
METHODS=ML; MISSING=ML; ANALYSIS=MOM; MATRIX=RAW; GROUP=2;
/LABELS
V1=group; V2=id; V3=grade03; V4=sex; V5=V0311;
V6=V0313; V7=V0314; V8=V0315; V9=V0316; V10=V0318;
V11=V0319; V12=V0320; V13=V0321; V14=V0322; V15=Opi3_1;
V16=Opi3_2; V17=Opi3_3; V18=Opi3_4; V19=Opi3_5; V20=Dep3_1;
V21=Dep3_2; V22=Dep3_3; V23=Res3_1; V24=Fam3_1; V25=Fam3_2;
V26=Fam3_3; V27=Sim3_1; V28=Sim3_2; V29=Res3_2; V30=Res3_3;
V31=Mac3_1; V32=Mac3_2; V33=Mac3_3; V34=Hos3_1; V35=Hos3_2;
V36=Hos3_3; V37=Hos3_4;
/EQUATIONS ! SECTION FOR GROUP 1
V17 = 1.425*V999+ .498*F1 + 1.000 E17 ;
V18 = 1.273*V999+ .296*F1 + 1.000 E18 ;
V19 = 1.317*V999+ .476*F1 + 1.000 E19 ;
V20 = 1.554*V999+ .857*F2 + 1.000 E20 ;
V21 = 1.491*V999+ .690*F2 + 1.000 E21 ;
V22 = 1.684*V999+ .900*F2 + 1.000 E22 ;
V23 = 3.532*V999+ .481*F3 + 1.000 E23 ;
V24 = 3.280*V999+ .589*F4 + 1.000 E24 ;
V25 = 3.483*V999+ .501*F4 + 1.000 E25 ;
V26 = 2.886*V999+ .702*F4 + 1.000 E26 ;
V27 = 3.077*V999+ .721*F5 + 1.000 E27 ;
V28 = 3.084*V999+ .548*F5 + 1.000 E28 ;
V29 = 3.578*V999+ .407*F3 + 1.000 E29 ;
V30 = 3.462*V999+ .549*F3 + 1.000 E30 ;
V31 = 2.132*V999+ .790*F6 + 1.000 E31 ;
V32 = 2.035*V999+ .886*F6 + 1.000 E32 ;
V33 = 1.977*V999+ .468*F6 + 1.000 E33 ;
V34 = 2.489*V999+ .604*F7 + 1.000 E34 ;
V35 = 2.621*V999+ .720*F7 + 1.000 E35 ;
V36 = 2.805*V999+ .592*F7 + 1.000 E36 ;
V37 = 2.284*V999+ .621*F7 + 1.000 E37 ;

/VARIANCES ! SECTION FOR GROUP 1
V999= 1.000 ;
F1= 1.000 ;
F2= 1.000 ;
F3= 1.000 ;
F4= 1.000 ;
F5= 1.000 ;
F6= 1.000 ;
F7= 1.000 ;
37
APPENDIX B: Continued

E17= .211* ;
E18= .276* ;
E19= .205* ;
E20= .160* ;
E21= .345* ;
E22= .198* ;
E23= .279* ;
E24= .396* ;
E25= .204* ;
E26= .566* ;
E27= .279* ;
E28= .563* ;
E29= .319* ;
E30= .172* ;
E31= .276* ;
E32= .165* ;
E33= .784* ;
E34= .530* ;
E35= .608* ;
E36= .591* ;
E37= .614* ;

/COVARIANCES ! SECTION FOR GROUP 1
F2,F1 = .067* ;
F3,F1 = -.258* ;
F3,F2 = -.252* ;
F4,F1 = -.230* ;
F4,F2 = -.396* ;
F4,F3 = .606* ;
F5,F1 = -.190* ;
F5,F2 = -.120* ;
F5,F3 = .558* ;
F5,F4 = .489* ;
F6,F1 = .219* ;
F6,F2 = -.009* ;
F6,F3 = .246* ;
F6,F4 = .175* ;
F6,F5 = .098* ;
F7,F1 = .123* ;
F7,F2 = .436* ;
F7,F3 = -.391* ;
F7,F4 = -.319* ;
F7,F5 = -.456* ;
F7,F6 = -.200* ;
E33,E18 = .074* ;
E33,E27 = .098* ;
E35,E21 = .110* ;
/END
38
APPENDIX B: Continued

/TITLE
Multiple Group Factor Analysis Wuhan GROUP Wave 3
/SPECIFICATIONS
DATA='C:\Documents and Settings\ling\Desktop\GVF_missing imputation
\WO_dep45_wuhan03.ess';
VARIABLES=37; CASES=4174;
METHODS=ML; MISSING=ML; ANALYSIS=MOM; MATRIX=RAW;
/LABELS
V1=group; V2=id; V3=grade03; V4=sex; V5=V0311;
V6=V0313; V7=V0314; V8=V0315; V9=V0316; V10=V0318;
V11=V0319; V12=V0320; V13=V0321; V14=V0322; V15=Opi3_1;
V16=Opi3_2; V17=Opi3_3; V18=Opi3_4; V19=Opi3_5; V20=Dep3_1;
V21=Dep3_2; V22=Dep3_3; V23=Res3_1; V24=Fam3_1; V25=Fam3_2;
V26=Fam3_3; V27=Sim3_1; V28=Sim3_2; V29=Res3_2; V30=Res3_3;
V31=Mac3_1; V32=Mac3_2; V33=Mac3_3; V34=Hos3_1; V35=Hos3_2;
V36=Hos3_3; V37=Hos3_4;
/EQUATIONS ! SECTION FOR GROUP 2
V17 = 2.299*V999+ .507*F1 + 1.000 E17 ;
V18 = 1.850*V999+ .880*F1 + 1.000 E18 ;
V19 = 1.703*V999+ .784*F1 + 1.000 E19 ;
V20 = 1.442*V999+ .554*F2 + 1.000 E20 ;
V21 = 1.449*V999+ .566*F2 + 1.000 E21 ;
V22 = 1.442*V999+ .688*F2 + 1.000 E22 ;
V23 = 3.666*V999+ .373*F3 + 1.000 E23 ;
V24 = 3.045*V999+ .460*F4 + 1.000 E24 ;
V25 = 3.426*V999+ .545*F4 + 1.000 E25 ;
V26 = 2.842*V999+ .548*F4 + 1.000 E26 ;
V27 = 3.063*V999+ .635*F5 + 1.000 E27 ;
V28 = 3.081*V999+ .553*F5 + 1.000 E28 ;
V29 = 3.213*V999+ .499*F3 + 1.000 E29 ;
V30 = 3.241*V999+ .531*F3 + 1.000 E30 ;
V31 = 2.577*V999+ .828*F6 + 1.000 E31 ;
V32 = 2.627*V999+ .850*F6 + 1.000 E32 ;
V33 = 2.394*V999+ .514*F6 + 1.000 E33 ;
V34 = 2.328*V999+ .661*F7 + 1.000 E34 ;
V35 = 1.771*V999+ .486*F7 + 1.000 E35 ;
V36 = 2.402*V999+ .538*F7 + 1.000 E36 ;
V37 = 1.773*V999+ .690*F7 + 1.000 E37 ;

/VARIANCES ! SECTION FOR GROUP 2
V999= 1.000 ;
F1= 1.000 ;
F2= 1.000 ;
F3= 1.000 ;
F4= 1.000 ;
F5= 1.000 ;
F6= 1.000 ;
F7= 1.000 ;
E17= .840* ;
E18= .176* ;
39
APPENDIX B: Continued

E19= .258* ;
E20= .299* ;
E21= .367* ;
E22= .169* ;
E23= .470* ;
E24= .539* ;
E25= .310* ;
E26= .594* ;
E27= .410* ;
E28= .611* ;
E29= .503* ;
E30= .564* ;
E31= .347* ;
E32= .407* ;
E33= .919* ;
E34= .470* ;
E35= .611* ;
E36= .698* ;
E37= .416* ;

/COVARIANCES ! SECTION FOR GROUP 2
F2,F1 = .124* ;
F3,F1 = -.008* ;
F3,F2 = -.059* ;
F4,F1 = .034* ;
F4,F2 = -.065* ;
F4,F3 = .784* ;
F5,F1 = -.044* ;
F5,F2 = .004* ;
F5,F3 = .711* ;
F5,F4 = .552* ;
F6,F1 = .232* ;
F6,F2 = -.027* ;
F6,F3 = .412* ;
F6,F4 = .372* ;
F6,F5 = .190* ;
F7,F1 = .241* ;
F7,F2 = .484* ;
F7,F3 = .008* ;
F7,F4 = .081* ;
F7,F5 = -.103* ;
F7,F6 = .102* ;
E33,E18 = .023* ;
E33,E27 = -.036* ;
E35,E21 = .022* ;
/CONSTRAINTS
(1,V17,V999) = (2,V17,V999);
(1,V18,V999) = (2,V18,V999);
(1,V19,V999) = (2,V19,V999);
(1,V20,V999) = (2,V20,V999);
40
APPENDIX B: Continued

(1,V21,V999) = (2,V21,V999);
(1,V22,V999) = (2,V22,V999);
(1,V23,V999) = (2,V23,V999);
(1,V24,V999) = (2,V24,V999);
(1,V25,V999) = (2,V25,V999);
(1,V26,V999) = (2,V26,V999);
(1,V27,V999) = (2,V27,V999);
(1,V28,V999) = (2,V28,V999);
(1,V29,V999) = (2,V29,V999);
(1,V30,V999) = (2,V30,V999);
(1,V31,V999) = (2,V31,V999);
(1,V32,V999) = (2,V32,V999);
(1,V33,V999) = (2,V33,V999);
(1,V34,V999) = (2,V34,V999);
(1,V35,V999) = (2,V35,V999);
(1,V36,V999) = (2,V36,V999);
(1,V37,V999) = (2,V37,V999);

/PRINT
RETEST='WO_dep45_coef_equality_m1.eqs';
/LMTEST
SET=NO;
/END

Asset Metadata

Creator Chen, Yu-Ling (author)

Core Title Measurement invariance across cultures: a comparison between Chinese adolescents in China and in U.S.

School Keck School of Medicine

Degree Master of Science

Degree Program Biostatistics

Publication Date 05/03/2007

Defense Date 04/02/2007

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag Chinese adolescents in China and in U.S.,measurement invariance across cultures,oai:digitallibrary.usc.edu:usctheses,OAI-PMH Harvest

Place Name China (countries), USA (countries)

Language English

Advisor Azen, Stanley Paul (committee chair), Chou, Chih-Ping (committee chair), Xie, Bin (committee member)

Creator Email yulingc@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m479

Unique identifier UC1290359

Identifier etd-Chen-20070503 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-484760 (legacy record id),usctheses-m479 (legacy record id)

Legacy Identifier etd-Chen-20070503.pdf

Dmrecord 484760

Document Type Thesis

Rights Chen, Yu-Ling

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Repository Name Libraries, University of Southern California

Repository Location Los Angeles, California

Repository Email uscdl@usc.edu

Abstract (if available)

Abstract The datasets were obtained from Wave3 of both Southern California Smoking Prevention Trial (SCSPT) and Wuhan Smoking Prevention Trial (WSPT). For the purpose of this study, only Chinese or Chinese-Americans were selected from the SCSPT. The 3rd year follow-up surveys which contained substantial overlapped items were used to investigate measurement invariance. The factor-scores between two study groups were compared by Student t-test. The confirmatory factor analysis (CFA) models were developed for each study groups. Multiple-group CFA procedures were used to test measurement invariance. -- Result from multiple-group CFA indicated that the major of items associated with "opinion", "depression", "respecto", and "familism" factors are not invariant between two cultures. Items in "simpatia", "machismo", and "hostility" factors demonstrated evidence of factor invariance between two cultures. -- In summary, two items in simpatia, three items in machismo, and four items in hostility factors indicated the evidence of factors validity and invariance between two different cultures.