A beginner's guide to structural equation modeling

A Beginner’s Guide to Structural Equation Modeling......Page 4
Copyright......Page 5
Contents......Page 8
About the Authors......Page 16
Preface......Page 18
1 Introduction......Page 22
1.1 What Is Structural Equation Modeling?......Page 23
1.2 History of Structural Equation Modeling......Page 25
1.3 Why Conduct Structural Equation Modeling?......Page 27
1.4 Structural Equation Modeling Software Programs......Page 29
1.5 Summary......Page 31
References......Page 32
2 Data Entry and Data Editing Issues......Page 34
2.1 Data Entry......Page 35
2.2.1 Measurement Scale......Page 39
2.2.2 Restriction of Range......Page 40
2.2.3 Missing Data......Page 41
2.2.4 LISREL–PRELIS Missing Data Example......Page 42
2.2.6 Linearity......Page 48
2.2.7 Nonnormality......Page 49
2.3 Summary......Page 50
References......Page 52
3.1 Types of Correlation Coefficients......Page 54
3.2.1 Level of Measurement and Range of Values......Page 56
3.2.2 Nonlinearity......Page 57
3.2.3 Missing Data......Page 59
3.2.5 Correction for Attenuation......Page 60
3.2.6 Nonpositive Definite Matrices......Page 61
3.2.7 Sample Size......Page 62
3.3 Bivariate, Part, and Partial Correlations......Page 63
3.4 Correlation versus Covariance......Page 67
3.5 Variable Metrics (Standardized versus Unstandardized)......Page 68
3.6 Causation Assumptions and Limitations......Page 69
3.7 Summary......Page 70
References......Page 72
4.1 Model Specification......Page 76
4.2 Model Identification......Page 77
4.3 Model Estimation......Page 80
4.4 Model Testing......Page 84
4.5 Model Modification......Page 85
4.6 Summary......Page 88
References......Page 90
5 Model Fit......Page 94
5.1 Types of Model-Fit Criteria......Page 95
5.1.1.1 Data......Page 98
5.1.1.2 Program......Page 101
5.1.1.3 Output......Page 102
5.2.1 Chi-Square (χ2)......Page 106
5.2.2 Goodness-of-Fit Index (GFI) and Adjusted Goodness-of-Fit Index (AGFI)......Page 107
5.2.3 Root-Mean-Square Residual Index (RMR)......Page 108
5.3.2 Normed Fit Index (NFI) and Comparative Fit Index (CFI)......Page 109
5.4 Model Parsimony......Page 110
5.4.2 Akaike Information Criterion (AIC)......Page 111
5.4.3 Summary......Page 112
5.5 Parameter Fit......Page 113
5.6 Power and Sample Size......Page 114
5.6.1.1 Power......Page 115
5.6.1.2 Sample Size......Page 120
5.6.2 Model Comparison......Page 129
5.6.3 Parameter Significance......Page 132
5.6.4 Summary......Page 134
5.7 Two-Step Versus Four-Step Approach to Modeling......Page 135
5.8 Summary......Page 137
Chi-Squares......Page 139
References......Page 141
6 Regression Models......Page 146
6.1 Overview......Page 147
6.3 Model Specification......Page 151
6.5 Model Estimation......Page 152
6.6 Model Testing......Page 154
6.7 Model Modification......Page 155
6.8 Summary......Page 156
6.8.1 Measurement Error......Page 157
6.8.2 Additive Equation......Page 158
LISREL–SIMPLIS Program (Intercept Term)......Page 159
References......Page 160
7 Path Models......Page 164
7.1 An Example......Page 165
7.2 Model Specification......Page 168
7.3 Model Identification......Page 171
7.4 Model Estimation......Page 172
7.5 Model Testing......Page 175
7.6 Model Modification......Page 176
Appendix: LISREL–SIMPLIS Path Model Program......Page 177
LISREL–SIMPLIS program......Page 179
References......Page 182
8 Confirmatory Factor Models......Page 184
8.1 An Example......Page 185
8.2 Model Specification......Page 187
8.3 Model Identification......Page 188
8.4 Model Estimation......Page 190
8.5 Model Testing......Page 191
8.6 Model Modification......Page 194
Appendix: LISREL–SIMPLIS Confirmatory Factor Model Program......Page 195
References......Page 198
9 Developing Structural Equation Models: Part I......Page 200
9.1 Observed Variables and Latent Variables......Page 201
9.2 Measurement Model......Page 205
9.3 Structural Model......Page 207
9.4 Variances and Covariance Terms......Page 210
9.5 Two-Step/Four-Step Approach......Page 212
9.6 Summary......Page 213
References......Page 214
10.1 An Example......Page 216
10.2 Model Specification......Page 218
10.3 Model Identification......Page 221
10.4 Model Estimation......Page 223
10.5 Model Testing......Page 224
10.6 Model Modification......Page 226
Appendix: LISREL–SIMPLIS Structural Equation Model Program......Page 228
References......Page 229
11 Reporting SEM Research: Guidelines and Recommendations......Page 230
11.1 Data Preparation......Page 233
11.2 Model Specification......Page 234
11.3 Model Identification......Page 236
11.4 Model Estimation......Page 237
11.5 Model Testing......Page 238
11.6 Model Modification......Page 239
11.7 Summary......Page 240
References......Page 241
12.1 Multiple Samples......Page 244
12.1.1 Model A Computer Output......Page 247
12.1.2 Model B Computer Output......Page 248
12.1.3 Model C Computer Output......Page 249
12.2 Cross Validation......Page 250
12.2.1 ECVI......Page 251
12.2.2 CVI......Page 252
12.3.1 PRELIS Graphical User Interface......Page 255
12.3.2 LISREL and PRELIS Program Syntax......Page 258
12.4 Summary......Page 262
References......Page 264
13.1 Multiple Sample Models......Page 266
Sample 2......Page 268
13.2 Multiple Group Models......Page 271
13.2.1 Separate Group Models......Page 272
13.2.2 Similar Group Model......Page 276
13.2.3 Chi-Square Difference Test......Page 279
13.3.1 Model Specification and Identification......Page 280
13.3.3 Model Estimation and Testing......Page 282
13.4 Summary......Page 284
Structured Means Models......Page 288
SPSS......Page 289
References......Page 290
14.1.1 Model Specification and Identification......Page 292
14.1.2 Model Estimation and Testing......Page 293
14.2 Dynamic Factor Model......Page 295
14.3 Multitrait Multimethod Model (MTMM)......Page 298
14.3.1 Model Specification and Identification......Page 300
14.3.2 Model Estimation and Testing......Page 301
14.3.3 Correlated Uniqueness Model......Page 302
14.4 Summary......Page 307
Multitrait Multimethod Models......Page 311
References......Page 312
15.1 Multiple Indicator–Multiple Cause (MIMIC) Models......Page 314
15.1.2 Model Estimation and Model Testing......Page 315
Measurement Equations......Page 318
15.2 Mixture Models......Page 319
15.2.1 Model Specification and Identification......Page 320
15.2.2 Model Estimation and Testing......Page 322
15.2.3 Model Modification......Page 324
15.2.4 Robust Statistic......Page 326
15.3 Multilevel Models......Page 328
15.3.2 Time Effects......Page 334
15.3.3 Gender Effects......Page 336
15.3.4 Multilevel Model Interpretation......Page 339
15.3.5 Intraclass Correlation......Page 340
15.4 Summary......Page 341
Multiple Indicator–Multiple Cause Models......Page 345
References......Page 346
16.1 Interaction Models......Page 348
16.1.1 Categorical Variable Approach......Page 349
16.1.2.1 Computing Latent Variable Scores......Page 352
16.1.2.2 Computing Latent Interaction Variable......Page 354
16.1.2.3 Interaction Model Output......Page 356
16.1.2.5 Structural Equations—No Latent Interaction Variable......Page 357
16.1.3 Two-Stage Least Squares (TSLS) Approach......Page 358
16.2 Latent Growth Curve Models......Page 362
16.2.1 Latent Growth Curve Program......Page 364
16.2.2 Model Modification......Page 365
16.3 Monte Carlo Methods......Page 366
16.3.1 PRELIS Simulation of Population Data......Page 367
16.3.2.1 SPSS Approach......Page 373
16.3.2.2 SAS Approach......Page 375
16.3.2.3 LISREL Approach......Page 376
16.3.3 Covariance Matrix from Specified Model......Page 380
16.4 Summary......Page 386
Monte Carlo Methods......Page 389
References......Page 390
17.1 General Overview of Matrix Notation......Page 394
17.2 Free, Fixed, and Constrained Parameters......Page 400
17.3 LISREL Model Example in Matrix Notation......Page 403
LISREL8 Matrix Program Output (Edited and Condensed)......Page 406
17.4.1 Path Model......Page 421
17.4.2 Multiple-Sample Model......Page 425
17.4.3 Structured Means Model......Page 426
17.4.4 Interaction Models......Page 431
PRELIS Computer Output......Page 433
LISREL Interaction Computer Output......Page 437
17.5 Summary......Page 442
References......Page 444
Appendix A: Introduction to Matrix Operations......Page 446
Appendix B: Statistical Tables......Page 460
Answers to Selected Exercises......Page 470
Author Index......Page 510
Subject Index......Page 516