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Modeled after Barbara Byrne’s other best-selling structural equation modeling (SEM) books, this practical guide reviews the basic concepts and applications of SEM using Mplus Versions 5 & 6. The author reviews SEM applications based on actual data taken from her own research. Using non-mathematical language, it is written for the novice SEM user. With each application chapter, the author "walks" the reader through all steps involved in testing the SEM model including:

an explanation of the issues addressed

illustrated and annotated testing of the hypothesized and post hoc models

explanation and interpretation of all Mplus input and output files

important caveats pertinent to the SEM application under study

a description of the data and reference upon which the model was based

the corresponding data and syntax files available at http://www.psypress.com/sem-with-mplus/datasets .

The first two chapters introduce the fundamental concepts of SEM and important basics of the Mplus program. The remaining chapters focus on SEM applications and include a variety of SEM models presented within the context of three sections: Single-group analyses, Multiple-group analyses, and other important topics, the latter of which includes the multitrait-multimethod, latent growth curve, and multilevel models.

Intended for researchers, practitioners, and students who use SEM and Mplus, this book is an ideal resource for graduate level courses on SEM taught in psychology, education, business, and other social and health sciences and/or as a supplement for courses on applied statistics, multivariate statistics, intermediate or advanced statistics, and/or research design. Appropriate for those with limited exposure to SEM or Mplus, a prerequisite of basic statistics through regression analysis is recommended.

Barbara M. Byrne is Professor Emeritus in the School of Psychology, University of Ottawa, Canada. An internationally recognized expert in the area of SEM, Dr. Byrne’s research focuses on construct validity issues as they relate to theoretical constructs and measuring instruments. She is the author of 7 popular introductory books on SEM and has conducted over 100 SEM workshops at conferences, universities, and test publishers around the globe. In addition to the publication of over 95 book chapters and scholarly journal articles, most of which have addressed SEM application issues, she is the author of an important reference book, Measuring Self-concept Across the Lifespan: Issues and Instrumentation. Dr. Byrne is the recipient of three Distinguished Teaching Awards presented by the Canadian Psychological Association, the American Psychological Association (APA), and the APA, Division 5 (Jacob Cohen Award). She is a Fellow in two APA Divisions, is a Foundation member on the International Board of the SELF Research Centre, University of Western Sydney, Australia, and is an elected member of the Society of Multivariate Experimental Psychology.

Contents
Preface..................................................................................................................xi
Acknowledgments......................................................................................... xvii
Section I: Introduction
Chapter 1 Structural Equation Models: The Basics................................. 3
Basic Concepts..................................................................................................... 4
The General Structural Equation Model......................................................... 9
The General Mplus Structural Equation Model............................................ 15
Notes................................................................................................................... 17
Chapter 2 Using the Mplus Program........................................................ 19
Mplus Notation and Input File Components and Structure....................... 19
The Mplus Language Generator...................................................................... 26
Model Specification From Two Perspectives................................................. 27
The Concept of Model Identification.............................................................. 31
Overview of Remaining Chapters.................................................................. 39
Notes................................................................................................................... 40
Section II: Single-Group Analyses
Chapter 3 Testing the Factorial Validity of a Theoretical
Construct: First-Order Confirmatory Factor
Analysis Model..........................................................................43
The Hypothesized Model................................................................................ 43
Mplus Input File Specification and Output File Results.............................. 48
Hypothesis 2: Self-Concept Is a Two-Factor Structure................................ 89
Mplus Input File Specification and Output File Results.............................. 89
Hypothesis 3: Self-Concept Is a One-Factor Structure................................ 91
Notes................................................................................................................... 93
Chapter 4 Testing the Factorial Validity of Scores From
a Measuring Instrument: First-Order Confirmatory
Factor Analysis Model.............................................................. 95
The Measuring Instrument Under Study...................................................... 96
The Hypothesized Model................................................................................ 96
Mplus Input File Specification and Output File Results............................ 101
Notes................................................................................................................. 121
Addendum....................................................................................................... 122
Chapter 5 Testing the Factorial Validity of Scores From a
Measuring Instrument: Second-Order Confirmatory
Factor Analysis Model............................................................ 125
The Hypothesized Model.............................................................................. 126
Analysis of Categorical Data......................................................................... 126
Mplus Input File Specification and Output File Results............................ 133
Notes................................................................................................................. 146
Chapter 6 Testing the Validity of a Causal Structure:
Full Structural Equation Model............................................ 147
The Hypothesized Model.............................................................................. 147
Mplus Input File Specification and Output File Results............................ 153
Post Hoc Analyses........................................................................................... 168
Notes................................................................................................................. 188
Section III: Multiple-Group Analyses
Chapter 7 Testing the Factorial Equivalence of a Measuring
Instrument: Analysis of Covariance Structures................ 193
Testing Multigroup Invariance: The General Notion................................ 194
Testing Multigroup Invariance Across Independent Samples................. 197
The Hypothesized Model.............................................................................. 197
Mplus Input File Specification and Output File Results............................ 208
Notes................................................................................................................. 226
Chapter 8 Testing the Equivalence of Latent Factor Means:
Analysis of Mean and Covariance Structures................... 227
Testing Latent Mean Structures: The Basic Notion.................................... 227
The Hypothesized Model.............................................................................. 231
Testing Multigroup Invariance..................................................................... 231
Mplus Input File Specification and Output File Results............................ 241
Testing Multigroup Invariance: Other Considerations............................. 254
Notes................................................................................................................. 257
Chapter 9 Testing the Equivalence of a Causal Structure:
Full Structural Equation Model............................................ 259
Cross-Validation in Structural Equation Modeling................................... 259
Testing Invariance Across Calibration and Validation Samples.............. 261
The Hypothesized Model.............................................................................. 262
Mplus Input File Specification and Output File Results............................ 264
Notes................................................................................................................. 282
Section IV: Other Important Topics
Chapter 10 Testing Evidence of Construct Validity:
The Multitrait–Multimethod Model.................................... 285
The General CFA Approach to MTMM Analyses...................................... 286
The Hypothesized Model.............................................................................. 287
Mplus Input File Specification and Output File Results............................ 288
Examining Evidence of Construct Validity at the Matrix Level.............. 295
Examining Evidence of Construct Validity at the Parameter Level........ 301
The Correlated Uniquenesses Approach to MTMM Analyses................ 303
Notes..................................................................................................................311
Chapter 11 Testing Change Over Time:
The Latent Growth Curve Model......................................... 313
Measuring Change in Individual Growth Over Time:
The General Notion.........................................................................................316
The Hypothesized Dual-Domain LGC Model............................................316
Mplus Input File Specification and Output File Results............................ 321
Hypothesized Covariate Model: Age and Surgery as Predictors
of Change......................................................................................................... 338
Notes................................................................................................................. 344
Chapter 12 Testing Within- and Between-Level Variability:
The Multilevel Model............................................................. 345
Overview of Multilevel Modeling................................................................ 346
The Hypothesized Model.............................................................................. 350
Mplus Input File Specification and Output File Results............................ 354
Notes................................................................................................................. 371
References........................................................................................................ 373
Author Index.................................................................................................... 395
Subject Index.................................................................................................... 401
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