Basics of structural equation modeling

328 Pages·1998·13.43 MB·English

by  Maruyama

BASICS OF
STRUCTURLA (cid:4)
EQUATION
MODELING
To members of my family, who made this project possible, (cid:4)
I dedicate this book: (cid:4)
my parents, George and Helen; (cid:4)
my wife, Barbara; (cid:4)
and our children, Kristie and Dan. (cid:4)
BASIC S OF
STRUCTURA L
EQUATIO N
MODELIN G
GEOFFREY M. MARUYAMA (cid:4)
SAGE Publication s
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Library of Congress Cataloging-in-Publication Data
Maruyama , Geoffre y M.
Basics of structura l equatio n modeling/b y Geoffre y M. Maruyama .
p. cm. (cid:4)
Include s bibliographica l reference s an d index . (cid:4)
ISBN 0-8039-7408-6 (cloth).—ISB N 0-8039-7409-4 (pbk. ) (cid:4)
1. Multivariat e analysis . 2. Socia l sciences—Statistica l methods .
I. Title .
QA278.M37 4 1997 97-4839 (cid:4)
519.5'35—dc2 1 (cid:4)
03 10 9 8 7 6
Acquiring Editor: C. Debora h Laughto n
Editorial Assistant: Eilee n Carr
Production Editor: Dian a E. Axelse n
Production Assistant: Denii e Sanioy o
l^plsitttrlDesipur: Mario n Warre n
Covtr Dtsigntr: Candic e Harma n
Print Buyer: Anna Chin
c t
X t
Prefac e (cid:5)
XI (cid:4)
Acknowledgment s (cid:5) xv (cid:4)
PART 1: Backgroun d
1.(cid:5) What Does It Mean to Model Hypothesize d (cid:4)
Causa l Processe s Wit h Nonexperimenta l Data ? (cid:4)
Method s for Structura l Equatio n Analyse s 9 (cid:4)
Overvie w 12 (cid:4)
Histor y and Logic of Structura l Equatio n Modelin g 15 (cid:4)
Histor y 15 (cid:4)
Sewell Wight 15 (cid:4)
Path Analysis in the Social Sciences 17 (cid:4)
Unidirectiona l Flow Model s 17 (cid:4)
Movin g Beyon d Pat h Analysi s in Structura l (cid:4)
Equatio n Modelin g Researc h 20 (cid:4)
Why Use Structura l Equatio n Modelin g Techniques ? 20 (cid:4)
I PART 2: Basic Approache s to Modelin g With
Singl e Observe d Measure s of Theoretica l Variable s
3. The Basics: Path Analysi s and Partitionin g of Varianc e 29 (cid:4)
Logic of Correlation s and Covariance s 30 (cid:4)
Decomposin g Relationship s Betwee n Variable s (cid:4)
Int o Causa l an d Noncausa l Component s 35 (cid:4)
Direct Causal Effects 39 (cid:4)
Indirect Causal Effects 40 (cid:4)
Noncausal Relationships Due to Shared Antecedents 41 (cid:4)
Noncausal Unanalyzed Prior Association Relationships 42 (cid:4)
Approache s for Decomposin g Effects 44 (cid:4)
Determinin g Degree s of Freedo m of Model s 48 (cid:4)
Presentin g Partia l Regressio n an d Partia l (cid:4)
Correlatio n as Path Model s 49 (cid:4)
Partial Regression 49 (cid:4)
Partial Correlation 51 (cid:4)
Peer Popularit y and Academi c Achievement : (cid:4)
An Illustratio n 53 (cid:4)
4. Effects of Collinearit y on Regressio n (cid:4)
and Path Analysi s 60 (cid:4)
Regressio n and Collinearit y 62 (cid:4)
Illustratin g Effects of Collinearit y 66 (cid:4)
Confidenc e Interval s for Correlation s 70 (cid:4)
Ridg e or Reduce d Varianc e Regressio n 73 (cid:4)
5. Effects of Rando m and Nonrando m Error (cid:4)
on Path Model s 79 (cid:4)
Measuremen(cid:5) t Erro r 79 (cid:4)
Background 79 (cid:4)
Specifying Relationships Between Theoretical (cid:4)
Variables and Measures 81 (cid:4)
Random Measurement Error 84 (cid:4)
Nonrandom Error 87 (cid:4)
Metho d Varianc e and Multitrait-Multimetho d Model s 88 (cid:4)
Method Variance 89 (cid:4)
Additive Multitrait-Multimethod Models 92 (cid:4)
Nonadditive Multitrait-Multimethod Models 96 (cid:4)
Summar y (cid:5) 97 (cid:4)
6.(cid:5) Recursiv e an d Longitudina l Models : Wher e Causalit y (cid:4)
Goes in More Than One Direction and Where Data (cid:4)
Are Collected Over Time 99 (cid:4)
Model s With Multidirectiona l Path s 100 (cid:4)
Logic of Nonrecursive Models 100 (cid:4)
Estimation of Nonrecursive Models 103 (cid:4)
Mode l Identificatio n(cid:4) 105
Longitudina l Model s(cid:4) 108
Logic Underlying Longitudinal(cid:4) Models 109
Terminology of Panel Models (cid:4) 110
Identification(cid:4) 111
Stability(cid:4) 112
Temporal Lags in Panel Models 115 (cid:4)
Growth Across Time in Panel Models 117 (cid:4)
Stability of Causal Processes 118 (cid:4)
Effects of Excluded Variables 119 (cid:4)
Correlatio n and Regressio n Approache s for Analyzin g (cid:4)
Pane l Dat a 120 (cid:4)
Summar y 122 (cid:4)
I(cid:5) PART 3: Factor Analysi s and Path Modelin g
7. Introducin g the Logic of Factor Analysi s and (cid:4)
Multipl e Indicator s to Pat h Modelin g 131 (cid:4)
Facto r Analysi s(cid:5) 132 (cid:4)
Logic of Factor Analysis 132 (cid:4)
Exploratory Factor Analysis 136 (cid:4)
Confirmatory Factor Analysis 139 (cid:4)
Use of Confirmatory Factor Analysis Techniques 140 (cid:4)
Constrainin g Relation s of Observe d Measure s With Factor s 147 (cid:4)
Confirmator y Factor Analysis and Method Factors 148 (cid:4)
The Basic Confirmatory Factor Analysis Path (cid:4)
Model for Multitrait-Multimethod Matrices 148 (cid:4)
Confirmatory Factor Analysis Approaches to (cid:4)
Multitrait-Multimethod Matrices and (cid:4)
Model Identification 152 (cid:4)
Summary of Confirmatory Factor Analysis (cid:4)
and Multitrait-Multimethod Models 154 (cid:4)
Initia l Testin g of Plausibilit y of Models : Consistenc y Tests 154 (cid:4)
Number of Indicators and Consistency Tests 155 (cid:4)
Costner's Original Consistency Model 158 (cid:4)
I PART 4: Laten t Variabl e Structura l Equatio n Model s
8. Puttin g It All Together : Laten t Variabl e (cid:4)
Structura l Equatio n Modelin g 177 (cid:4)
The Basic Laten t Variabl e Structura l Equatio n Mode l 178 (cid:4)
The Measurement Model 178 (cid:4)
Reference Indicators 181 (cid:4)
The Structural Model 184 (cid:4)
An Illustratio n of Structura l Equatio n Model s 187 (cid:4)
Model Specification 187 (cid:4)
Identification 188 (cid:4)
Equations and Matrices 192 (cid:4)
Basic Idea s Underlyin g FhVSignificanc e Testin g 195 (cid:4)
Individual Parameter Significance 195 (cid:4)
Model Fitting 196 (cid:4)
The Measurement Model 201 (cid:4)
The Structural Model 201 (cid:4)
The Variance/Covariance Matrices 202 (cid:4)
9. Usin g Laten t Variabl e Structura l Equatio n (cid:4)
Modelin g to Examin e Plausibilit y of Model s 203 (cid:4)
Exampl e 1: A Longitudina l Pat h Mode l 204 (cid:4)
Exampl e 2: A Nonrecursiv e Multiple-Indicato r Mode l 209 (cid:4)
Exampl e 3: A Longitudina l Multiple-Indicato r (cid:4)
Pane l Mode l 214 (cid:4)
10. Logic of Alternativ e Model s and Significanc e Tests 234 (cid:4)
Neste d Model s 235 (cid:4)
Tests of Overal l Mode l Fit 238 (cid:4)
Absolute Indexes 242 (cid:4)
Relative Indexes 243 (cid:4)
Adjusted Indexes 245 (cid:4)
Fit Indexe s for Comparin g Non-Neste d Model s 246 (cid:4)
Settin g Up Neste d Model s 247 (cid:4)
Why Model s May Not Fit 249 (cid:4)
Illustratin g Fit Tests 250 (cid:4)
11. Variation s on the Basic Laten t Variabl e (cid:4)
Structura l Equatio n Mode l 255 (cid:4)
Analyzin g Structura l Equatio n(cid:5) Model s Whe n Multipl e (cid:4)
Population s Are Availabl e 257 (cid:4)
Overview of Methods 257 (cid:4)
Comparing Processes Across Samples 259 (cid:4)
Testing Plausibility of Contraints 261 (cid:4)
Constraints in the Measurement Model 261 (cid:4)
Constraints in the Structural Model 262 (cid:4)
When and How to Impose Equality Constraints 262 (cid:4)
Second-Orde r Facto r Model s 265 (cid:4)
All-Y Model s 268 (cid:4)
12.(cid:5) Wrappin g Up 271 (cid:4)
Criticism s of Structura l Equatio n Modelin g Approache(cid:5)s 272 (cid:4)
"Internal" Critics 272 (cid:4)
"External" Critics 275 (cid:4)
Emerging Criticisms 277 (cid:4)
Post Hoc Mode l Modificatio n 278 (cid:4)
Topics Not Covere d 280 (cid:4)
Power Analysis 280 (cid:4)
Nonlinear Relationships 280 (cid:4)
Alternative Estimation Techniques 281 (cid:4)
Analysis of Noncontinuous Variables 282 (cid:4)
Adding Analysis of Means 282 (cid:4)
Multilevel Structural Equation Modeling 282 (cid:4)
Writing Up Papers Containing Structural (cid:4)
Equation Modeling Analysis 283 (cid:4)
Selecting a Computer Program to Do Latent (cid:4)
Variable Structural Equation Modeling 283 (cid:4)
Appendi x A: A Brief Introductio n to Matri x Algebr a (cid:4)
and Structura l Equatio n Modelin g 285 (cid:4)
What Is a Matrix? 285 (cid:4)
Matrix Operations 288 (cid:4)
Inverting Matrices 291 (cid:4)