Longitudinal Structural Equation Modeling with Mplus

A Latent State-Trait Perspective

Christian Geiser

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October 9, 2020
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An in-depth guide to executing longitudinal confirmatory factor analysis (CFA) and structural equation modeling (SEM) in Mplus, this book uses latent state–trait (LST) theory as a unifying conceptual framework, including the relevant coefficients of consistency, occasion specificity, and reliability. Following a standard format, chapters review the theoretical underpinnings, strengths, and limitations of the various models; present data examples; and demonstrate each model's application and interpretation in Mplus, with numerous screen shots and output excerpts. Coverage encompasses both traditional models (autoregressive, change score, and growth curve models) and LST models for analyzing single- and multiple-indicator data. The book discusses measurement equivalence testing, intensive longitudinal data modeling, and missing data handling, and provides strategies for model selection and reporting of results. User-friendly features include special-topic boxes, chapter summaries, and suggestions for further reading. The companion website features data sets, annotated syntax files, and output for all of the examples.

This title is part of the Methodology in the Social Sciences Series, edited by Todd D. Little, PhD.


“Geiser introduces readers to longitudinal SEM by building from simple to more complex models. Assuming only basic prior knowledge about SEM and factor analysis, Geiser offers a careful, clear analysis of advantages and limitations of each method, and includes discussions of missing data, Bayesian analysis, dynamic SEM for intensive longitudinal data, and model selection strategies. This book is an ideal companion text for a second course in SEM that tackles the analysis of longitudinal data. It is a useful reference for more experienced researchers and methodologists who want to learn about LST models. The book is unique in using LST theory to scaffold the presentation of a variety of models for longitudinal data. Discussion of the various models is skillfully interwoven with path diagrams, equations, and Mplus code. Even a beginning SEM user will have no trouble understanding this book.”

—Kristopher J. Preacher, PhD, Department of Psychology and Human Development, Peabody College, Vanderbilt University


“This is the first English-language book to introduce longitudinal latent variable analysis based on the crucial distinctions between states, traits, measurement error, and method effects. The book provides an extended and readable introduction to LST theory and, in particular, its implications for a meaningful analysis of longitudinal data. I highly recommend this book for students who want to learn about fundamental concepts of differential and developmental psychology; latent variables, in general; and the analysis of latent variables in longitudinal designs with Mplus, the most comprehensive program for the analysis of manifest and latent variables. I have no doubt that students will profit a lot from this great book written by an outstanding, authoritative scientist in the field of latent variable modeling.”

—Rolf Steyer, PhD, Institute of Psychology, Friedrich-Schiller University of Jena, Germany


“A much-needed addition to the literature. Geiser writes in an extremely clear and engaging style, avoiding unnecessary jargon while communicating essential concepts in a rigorous manner. The boxes within the chapters provide additional technical information to provide readers with a deeper dive into certain topics without interrupting the flow of the book. The most appealing aspect of this book for an instructor using it as a didactic tool or a researcher using it as a reference is the well-documented Mplus examples. These are truly key to bringing the methods alive for the reader. I recommend this book as a primary text in a course on longitudinal data analysis or latent variable modeling. It provides students with both the technical background to understand LST models and the applied tools to fit them using Mplus.”

—Holmes Finch, PhD, George and Frances Ball Distinguished Professor of Educational Psychology, Ball State University


“The book offers a profound, flexible, and extremely useful framework for longitudinal SEM. It will be of interest to users and theoreticians alike—it has much to offer for graduate courses or for researchers working with longitudinal data in psychology and related disciplines. Even though the primary topic is modeling, the book also provides inspiration for formulating research questions. Coming from a different angle with a different modeling language, I found it highly accessible and appealing. The book builds on earlier developments in LST theory and extrapolates the basic principles to a large variety of possible model specifications.”

—Paul De Boeck, PhD, Department of Psychology, The Ohio State University


“Using a measurement theory perspective, Geiser explains the rationale and procedures for a variety of longitudinal models, including simplex models, latent change score models, latent growth curve models, latent state models, and LST models. He translates longitudinal modeling techniques into digestible concepts and frames the relations between these concepts using LST theory. Geiser guides readers through complex issues related to analyzing longitudinal data so that readers can apply these methods to their own research. Easy-to-follow examples and annotated Mplus syntax and output clarify the concepts and illustrate the techniques. While this book is broadly accessible to substantive researchers, its technical rigor also will satisfy quantitative specialists. It can serve as a text for graduate-level courses or self-study of longitudinal data analysis and SEM.”

—Sara Finney, PhD, Department of Graduate Psychology, James Madison University

Table of Contents

List of Abbreviations

Guide to Statistical Symbols

1. A Measurement Theoretical Framework for Longitudinal Data: Introduction to Latent State–Trait Theory

1.1 Introduction

1.2 Latent State–Trait Theory

1.3 Chapter Summary

1.4 Recommended Readings

2. Single-Factor Longitudinal Models for Single-Indicator Data sample

2.1 Introduction

2.2 The Random Intercept Model

2.3 The Random and Fixed Intercepts Model

2.4 The ?-Congeneric Model

2.5 Chapter Summary

2.6 Recommended Reading

3. Multifactor Longitudinal Models for Single-Indicator Data

3.1 Introduction

3.2 The Simplex Model

3.3 The Latent Change Score Model

3.4 The Trait–State–Error Model

3.5 Latent Growth Curve Models

3.6 Chapter Summary

3.7 Recommended Readings

4. Testing Measurement Equivalence in Longitudinal Studies

4.1 Introduction

4.2 The Latent State (LS) Model

4.3 The Latent State Model with Indicator-Specific Residual Factors (LS-IS Model)

4.4 Chapter Summary

4.5 Recommended Readings

5. Multiple-Indicator Longitudinal Models

5.1 Introduction

5.2 Latent State Change (LSC) Models

5.3 The Latent Autoregressive/Cross-Lagged States (LACS) Model

5.4 Latent State–Trait (LST) Models

5.5 Latent Trait Change (LTC) Models

5.6 Chapter Summary

5.7 Recommended Readings

6. Modeling Intensive Longitudinal Data

6.1 Introduction

6.2 Special features of Intensive Longitudinal Data

6.3 Specifying Longitudinal SEMs for Intensive Longitudinal Data

6.4 Chapter Summary

6.5 Recommended Readings

7. Missing Data Handling

7.1 Introduction

7.2 Missing Data Mechanisms

7.3 Maximum Likelihood Missing Data Handling

7.4 Multiple Imputation (MI)

7.5 Planned Missing Data Designs

7.6 Chapter Summary

7.7 Recommended Readings

8. How to Choose between Models and Report the Results

8.1 Model Selection

8.2 Reporting Results

8.3 Chapter Summary

8.4 Recommended Readings

References

Author Index

Subject Index


About the Author

Christian Geiser, PhD, is Professor of Psychology at Utah State University and Director of the Quantitative Psychology PhD Specialization. His research interests are in psychometrics and structural equation modeling, particularly in longitudinal data analysis and multitrait–multimethod modeling. As part of his methodological work, he has presented new longitudinal structural equation modeling approaches for examining effects of situations and person–situation interactions, as well as models for integrating information from multiple reporters or other methods in longitudinal analyses.

Audience

Researchers and graduate students in psychology, education, management, family studies, public health, sociology, and social work.

Course Use

May serve as a core or supplemental text in graduate-level courses on longitudinal data analysis, SEM, multivariate analysis, or applied statistics.