# A Beginner's Guide to Structural Equation Modeling: Third Edition

**by**Schumacker; Randall E.

### 9781841698915

from Private Sellers

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## Summary

This best-seller introduces readers to structural equation modeling (SEM) so they can conduct their own analysis and critique related research. Noted for its accessible, applied approach, chapters cover basic concepts and practices and computer input/output from the free student version of Lisrel 8.8 in the examples.

Each chapter features an outline, key concepts, a summary, numerous examples from a variety of disciplines, tables, and figures, including path diagrams, to assist with conceptual understanding.

The book first reviews the **basics of SEM**, data entry/editing, and correlation. Next the authors highlight the basic steps of SEM: model specification, identification, estimation, testing, and modification, followed by issues related to model fit and power and sample size. Chapters 6 through 10 follow the steps of modeling using regression, path, confirmatory factor, and structural equation models.

Next readers find a chapter on reporting SEM research including a checklist to guide decision-making, followed by one on model validation. Chapters 13 through 16 provide examples of various **SEM model applications**. The book concludes with the matrix approach to SEM using examples from previous chapters.

## Table of Contents

About the Authors | p. xv |

Preface | p. xvii |

Introduction | p. 1 |

What Is Structural Equation Modeling? | p. 2 |

History of Structural Equation Modeling | p. 4 |

Why Conduct Structural Equation Modeling? | p. 6 |

Structural Equation Modeling Software Programs | p. 8 |

Summary | p. 10 |

References | p. 11 |

Data Entry and Data Editing Issues | p. 13 |

Data Entry | p. 14 |

Data Editing Issues | p. 18 |

Measurement Scale | p. 18 |

Restriction of Range | p. 19 |

Missing Data | p. 20 |

LISREL-PRELIS Missing Data Example | p. 21 |

Outliers | p. 27 |

Linearity | p. 27 |

Nonnormality | p. 28 |

Summary | p. 29 |

References | p. 31 |

Correlation | p. 33 |

Types of Correlation Coefficients | p. 33 |

Factors Affecting Correlation Coefficients | p. 35 |

Level of Measurement and Range of Values | p. 35 |

Nonlinearity | p. 36 |

Missing Data | p. 38 |

Outliers | p. 39 |

Correction for Attenuation | p. 39 |

Nonpositive Definite Matrices | p. 40 |

Sample Size | p. 41 |

Bivariate, Part, and Partial Correlations | p. 42 |

Correlation versus Covariance | p. 46 |

Variable Metrics (Standardized versus Unstandardized) | p. 47 |

Causation Assumptions and Limitations | p. 48 |

Summary | p. 49 |

References | p. 51 |

SEM Basics | p. 55 |

Model Specification | p. 55 |

Mode] Identification | p. 56 |

Model Estimation | p. 59 |

Model Testing | p. 63 |

Model Modification | p. 64 |

Summary | p. 67 |

References | p. 69 |

Model Fit | p. 73 |

Types of Model-Fit Criteria | p. 74 |

LISREL-SIMPLIS Example | p. 77 |

Data | p. 77 |

Program | p. 80 |

Output | p. 81 |

Model Fit | p. 85 |

Chi-Square (X^{2}) | p. 85 |

Goodness-of-Fit Index (GFI) and Adjusted Goodness-of-Fit Index (AGFI) | p. 86 |

Root-Mean-Square Residual Index (RMR) | p. 87 |

Model Comparison | p. 88 |

Tucker-Lewis Index (TLI) | p. 88 |

Normed Fit Index (NFI) and Comparative Fit Index (CFI) | p. 88 |

Model Parsimony | p. 89 |

Parsimony Normed Fit Index (PNFI) | p. 90 |

Akaike Information Criterion (AIC) | p. 90 |

Summary | p. 91 |

Parameter Fit | p. 92 |

Power and Sample Size | p. 93 |

Model Fit | p. 94 |

Power | p. 94 |

Sample Size | p. 99 |

Model Comparison | p. 108 |

Parameter Significance | p. 111 |

Summary | p. 113 |

Two-Step Versus Four-Step Approach to Modeling | p. 114 |

Summary | p. 116 |

Chapter Footnote | p. 118 |

Standard Errors | p. 118 |

Chi-Squares | p. 118 |

References | p. 120 |

Regression Models | p. 125 |

Overview | p. 126 |

An Example | p. 130 |

Model Specification | p. 130 |

Model Identification | p. 131 |

Model Estimation | p. 131 |

Model Testing | p. 133 |

Model Modification | p. 134 |

Summary | p. 135 |

Measurement Error | p. 136 |

Additive Equation | p. 137 |

Chapter Footnote | p. 138 |

Regression Model with Intercept Term | p. 138 |

LISREL-SIMPLIS Program (Intercept Term) | p. 138 |

References | p. 139 |

Path Models | p. 143 |

An Example | p. 144 |

Model Specification | p. 147 |

Model Identification | p. 150 |

Model Estimation | p. 151 |

Model Testing | p. 154 |

Model Modification | p. 155 |

Summary | p. 156 |

Appendix: LISREL-SIMPLIS Path Model Program | p. 156 |

Chapter Footnote | p. 158 |

Another Traditional Non-SEM Path Model-Fit Index | p. 158 |

LISREL-SIMPLIS program | p. 158 |

References | p. 161 |

Confirmatory Factor Models | p. 163 |

An Example | p. 164 |

Model Specification | p. 166 |

Model Identification | p. 167 |

Model Estimation | p. 169 |

Model Testing | p. 170 |

Model Modification | p. 173 |

Summary | p. 174 |

Appendix: LISREL-SIMPLIS Confirmatory Factor Model Program | p. 174 |

References | p. 177 |

Developing Structural Equation Models: Part I | p. 179 |

Observed Variables and Latent Variables | p. 180 |

Measurement Model | p. 184 |

Structural Model | p. 186 |

Variances and Covariance Terms | p. 189 |

Two-Step/Four-Step Approach | p. 191 |

Summary | p. 192 |

References | p. 193 |

Developing Structural Equation Models: Part II | p. 195 |

An Example | p. 195 |

Model Specification | p. 197 |

Model Identification | p. 200 |

Model Estimation | p. 202 |

Model Testing | p. 203 |

Model Modification | p. 205 |

Summary | p. 207 |

Appendix: LISREL-SIMPLIS Structural Equation Model Program | p. 207 |

References | p. 208 |

Reporting SEM Research: Guidelines and Recommendations | p. 209 |

Data Preparation | p. 212 |

Model Specification | p. 213 |

Model Identification | p. 215 |

Model Estimation | p. 216 |

Model Testing | p. 217 |

Model Modification | p. 218 |

Summary | p. 219 |

References | p. 220 |

Model Validation | p. 223 |

Key Concepts | p. 223 |

Multiple Samples | p. 223 |

Model A Computer Output | p. 226 |

Model B Computer Output | p. 227 |

Model C Computer Output | p. 228 |

Model D Computer Output | p. 229 |

Summary | p. 229 |

Cross Validation | p. 229 |

ECVI | p. 230 |

CVI | p. 231 |

Bootstrap | p. 234 |

PRELIS Graphical User Interface | p. 234 |

LISREL and PRELIS Program Syntax | p. 237 |

Summary | p. 241 |

References | p. 243 |

Multiple Sample, Multiple Group, and Structured Means Models | p. 245 |

Multiple Sample Models | p. 245 |

p. 247 | |

p. 247 | |

Multiple Group Models | p. 250 |

Separate Group Models | p. 251 |

Similar Group Model | p. 255 |

Chi-Square Difference Test | p. 258 |

Structured Means Models | p. 259 |

Model Specification and Identification | p. 259 |

Model Fit | p. 261 |

Model Estimation and Testing | p. 261 |

Summary | p. 263 |

Suggested Readings | p. 267 |

Multiple Samples | p. 267 |

Multiple Group Models | p. 267 |

Structured Means Models | p. 267 |

Chapter Footnote | p. 268 |

SPSS | p. 268 |

References | p. 269 |

Second-Order, Dynamic, and Multitrait Multimethod Models | p. 271 |

Second-Order Factor Model | p. 271 |

Model Specification and Identification | p. 271 |

Model Estimation and Testing | p. 272 |

Dynamic Factor Model | p. 274 |

Multitrait Multimethod Model (MTMM) | p. 277 |

Model Specification and Identification | p. 279 |

Model Estimation and Testing | p. 280 |

Correlated Uniqueness Model | p. 281 |

Summary | p. 286 |

Suggested Readings | p. 290 |

Second-Order Factor Models | p. 290 |

Dynamic Factor Models | p. 290 |

Multitrait Multimethod Models | p. 290 |

Correlated Uniqueness Model | p. 291 |

References | p. 291 |

Multiple Indicator-Multiple Indicator Cause, Mixture, and Multilevel Models | p. 293 |

Multiple Indicator-Multiple Cause (MIMIC) Models | p. 293 |

Model Specification and Identification | p. 294 |

Model Estimation and Model Testing | p. 294 |

Model Modification | p. 297 |

Goodness-of-Fit Statistics | p. 297 |

Measurement Equations | p. 297 |

Structural Equations | p. 298 |

Mixture Models | p. 298 |

Model Specification and Identification | p. 299 |

Model Estimation and Testing | p. 301 |

Model Modification | p. 302 |

Robust Statistic | p. 305 |

Multilevel Models | p. 307 |

Constant Effects | p. 313 |

Time Effects | p. 313 |

Gender Effects | p. 315 |

Multilevel Model Interpretation | p. 318 |

Intraclass Correlation | p. 319 |

Deviance Statistic | p. 320 |

Summary | p. 320 |

Suggested Readings | p. 324 |

Multiple Indicator-Multiple Cause Models | p. 324 |

Mixture Models | p. 325 |

Multilevel Models | p. 325 |

References | p. 325 |

Interaction, Latent Growth, and Monte Carlo Methods | p. 327 |

Interaction Models | p. 327 |

Categorical Variable Approach | p. 328 |

Latent Variable Interaction Model | p. 331 |

Computing Latent Variable Scores | p. 331 |

Computing Latent Interaction Variable | p. 333 |

Interaction Model Output | p. 335 |

Model Modification | p. 336 |

Structural Equations-No Latent Interaction Variable | p. 336 |

Two-Stage Least Squares (TSLS) Approach | p. 337 |

Latent Growth Curve Models | p. 341 |

Latent Growth Curve Program | p. 343 |

Model Modification | p. 344 |

Monte Carlo Methods | p. 345 |

PRELIS Simulation of Population Data | p. 346 |

Population Data from Specified Covariance Matrix | p. 352 |

SPSS Approach | p. 352 |

SAS Approach | p. 354 |

LISREL Approach | p. 355 |

Covariance Matrix from Specified Model | p. 359 |

Summary | p. 365 |

Suggested Readings | p. 368 |

Interaction Models | p. 368 |

Latent Growth-Curve Models | p. 368 |

Monte Carlo Methods | p. 368 |

References | p. 369 |

Matrix Approach to Structural Equation Modeling | p. 373 |

General Overview of Matrix Notation | p. 373 |

Free, Fixed, and Constrained Parameters | p. 379 |

LISREL Model Example in Matrix Notation | p. 382 |

LISREL8 Matrix Program Output (Edited and Condensed) | p. 385 |

Other Models in Matrix Notation | p. 400 |

Path Model | p. 400 |

Multiple-Sample Model | p. 404 |

Structured Means Model | p. 405 |

Interaction Models | p. 410 |

PRELIS Computer Output | p. 412 |

LISREL Interaction Computer Output | p. 416 |

Summary | p. 421 |

References | p. 423 |

Introduction to Matrix Operations | p. 425 |

Statistical Tables | p. 439 |

Answers to Selected Exercises | p. 449 |

Author Index | p. 489 |

Subject Index | p. 495 |

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