A Beginner's Guide to. Randall E. Schumacker. The University of Alabama. Richard G. Lomax. The Ohio State University. Routledge

Transcription

1 A Beginner's Guide to Randall E. Schumacker The University of Alabama Richard G. Lomax The Ohio State University Routledge Taylor & Francis Group New York London

2 About the Authors Preface xv xvii 1 Introduction What Is Structural Equation Modeling? History of Structural Equation Modeling Why Conduct Structural Equation Modeling? Structural Equation Modeling Software Programs Summary.'.' 10 References 11 2 Data Entry and Data Editing Issues Data Entry Data Editing Issues Measurement Scale Restriction of Range Missing Data LISREL-PRELIS Missing Data Example Outliers Linearity Nonnormality Summary 29 References 31 3 Correlation Types of Correlation Coefficients Factors Affecting Correlation Coefficients Level of Measurement and Range of Values Nonlinearity Missing Data Outliers Correction for Attenuation Nonpositive Definite Matrices Sample Size Bivariate, Part, and Partial Correlations Correlation versus Covariance Variable Metrics (Standardized versus Unstandardized) Causation Assumptions and Limitations Summary 49 References 51 vii

3 viii Contents 4 SEM Basics Model Specification Model Identification Model Estimation Model Testing Model Modification Summary 67 References 69 5 Model Fit.' Types of Model-Fit Criteria LISREL-SIMPLIS Example Data Program Output Model Fit Chi-Square (% 2 ) Goodness-of-Fit Index (GFI) and Adjusted Goodness-of-Fit Index (AGFI) Root-Mean-Square Residual Index (RMR) Model Comparison Tucker-Lewis Index (TLI) Normed Fit Index (NFI) and Comparative Fit Index (CFI) Model Parsimony Parsimony Normed Fit Index (PNFI) Akaike Information Criterion (AIC) Summary Parameter Fit Power and Sample Size Model Fit Power Sample Size Model Comparison Parameter Significance Ill Summary Two-Step Versus Four-Step Approach to Modeling Summary 116 Chapter Footnote 118 Standard Errors 118 Chi-Squares 118 References 120

4 ix 6 Regression Models Overview An Example Model Specification Model Identification Model Estimation Model Testing Model Modification Summary Measurement Error Additive Equatioh 137 Chapter Footnote 138 Regression Model with Intercept Term 138 LISREL-SIMPLIS Program (Intercept Term) 138 References Path Models An Example Model Specification Model Identification Model Estimation Model Testing Model Modification Summary 156 Appendix: LISREL-SIMPLIS Path Model Program 156 Chapter Footnote 158 Another Traditional Non-SEM Path Model-Fit Index 158 LISREL-SIMPLIS program 158 References Confirmatory Factor Models An Example Model Specification Model Identification Model Estimation Model Testing Model Modification Summary 174 Appendix: LISREL-SIMPLIS Confirmatory Factor Model Program References Developing Structural Equation Models: Part Observed Variables and Latent Variables Measurement Model 184

5 9.3 Structural Model Variances and Covariance Terms Two-Step/Four-Step Approach Summary 192 References Developing Structural Equation Models: Part II An Example Model Specification Model Identification.;, Model Estimation ' Model Testing Model Modification Summary 207 Appendix: LISREL-SIMPLIS Structural Equation Model Program 207 References Reporting SEM Research: Guidelines and Recommendations Data Preparation Model Specification Model Identification Model Estimation Model Testing Model Modification Summary 219 References Model Validation 223 Key Concepts Multiple Samples Model A Computer Output Model B Computer Output Model C Computer Output Model D Computer Output Summary Cross Validation ECVI CVI Bootstrap PRELIS Graphical User Interface LISREL and PRELIS Program Syntax Summary 241 References 243

6 xi 13 Multiple Sample, Multiple Group, and Structured Means Models Multiple Sample Models 245 Sample Sample Multiple Group Models Separate Group Models...: Similar Group Model Chi-Square Difference Test Structured Means Models Model Specification and Identification Model Fit Model Estimation and Testing Summary 263 Suggested Readings 267 Multiple Samples 267 Multiple Group Models 267 Structured Means Models 267 Chapter Footnote 268 SPSS ' 268 References Second-Order, Dynamic, and Multitrait Multimethod Models Second-Order Factor Model Model Specification and Identification Model Estimation and Testing Dynamic Factor Model Multitrait Multimethod Model (MTMM) Model Specification and Identification Model Estimation and Testing Correlated Uniqueness Model Summary 286 Suggested Readings 290 Second-Order Factor Models 290 Dynamic Factor Models 290 Multitrait Multimethod Models 290 Correlated Uniqueness Model 291 References Multiple Indicator-Multiple Indicator Cause, Mixture, and Multilevel Models Multiple Indicator-Multiple Cause (MIMIC) Models Model Specification and Identification Model Estimation and Model Testing 294

7 xii Contents Model Modification 297 Goodness-of-Fit Statistics 297 Measurement Equations 297 Structural Equations Mixture Models Model Specification and Identification Model Estimation and Testing Model Modification Robust Statistic Multilevel Models Constant Effects Time Effects Gender Effects Multilevel Model Interpretation Intraclass Correlation Deviance Statistic Summary 320 Suggested Readings 324 Multiple Indicator-Multiple Cause Models 324 Mixture Models 325 Multilevel Models 325 References Interaction, Latent Growth, and Monte Carlo Methods Interaction Models Categorical Variable Approach Latent Variable Interaction Model Computing Latent Variable Scores Computing Latent Interaction Variable Interaction Model Output Model Modification Structural Equations No Latent Interaction Variable Two-Stage Least Squares (TSLS) Approach Latent Growth Curve Models Latent Growth Curve Program Model Modification Monte Carlo Methods PRELIS Simulation of Population Data Population Data from Specified Covariance Matrix SPSS Approach SAS Approach LISREL Approach 355

8 xiii Covariance Matrix from Specified Model Summary 365 Suggested Readings 368 Interaction Models 368 Latent Growth-Curve Models 368 Monte Carlo Methods 368 References Matrix Approach to Structural Equation Modeling General Overview of Matrix Notation Free, Fixed, and Constrained Parameters LISREL Model Example in Matrix Notation 382 LISREL8 Matrix Program Output (Edited and Condensed) Other Models in Matrix Notation Path Model Multiple-Sample Model Structured Means Model Interaction Models 410 PRELIS Computer Output 412 LISREL Interaction Computer Output Summary 421 References 423 Appendix A: Introduction to Matrix Operations 425 Appendix B: Statistical Tables 439 Answers to Selected Exercises 449 Author Index 489 Subject Index 495