Longitudinal Structural Equation Modeling

Todd D. Little
Foreword by Noel A. Card

Hardcovere-bookprint + e-book
March 25, 2013
ISBN 9781462510160
Price: $73.00 $54.75
386 Pages
Size: 7" x 10"
April 18, 2013
Price: $73.00 $54.75
386 Pages
print + e-book
Hardcover + e-Book (PDF) ?
Price: $146.00 $80.30
386 Pages

Featuring actual datasets as illustrative examples, this book reveals numerous ways to apply structural equation modeling (SEM) to any repeated-measures study. Initial chapters lay the groundwork for modeling a longitudinal change process, from measurement, design, and specification issues to model evaluation and interpretation. Covering both big-picture ideas and technical “how-to-do-it” details, the author deftly walks through when and how to use longitudinal confirmatory factor analysis, longitudinal panel models (including the multiple-group case), multilevel models, growth curve models, and complex factor models, as well as models for mediation and moderation. User-friendly features include equation boxes that clearly explain the elements in every equation, end-of-chapter glossaries, and annotated suggestions for further reading. The companion website (www.guilford.com/little-materials) provides datasets for all of the examples—which include studies of bullying, adolescent students' emotions, and healthy aging—with syntax and output from LISREL, Mplus, and R (lavaan).

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

“It is rare for a scholar or a teacher to simultaneously demonstrate wisdom, erudition, vision for the future of the field, and the capacity to explain complex ideas and methods to beginners, while also advancing the skill sets of seasoned researchers. Yet these valued attributes are all found in abundance in this volume. This is more than a book about longitudinal SEM; it is a guide to understanding and conducting good science. If any book can be identified as a classic on publication, this one certainly can.”

—Richard M. Lerner, PhD, Bergstrom Chair in Applied Developmental Science, and Director, Institute for Applied Research in Youth Development, Tufts University

“Novices and experts alike will learn something new from this book. Little is a born teacher, and it shows in his writing. His approach assumes little background knowledge and provides an entrée to the literature for students and researchers who want to know more. Examples from Little's experience as an applied researcher make the concepts concrete and accessible. This is an ideal text to accompany graduate courses on SEM or longitudinal data analysis and a useful reference for researchers who want to add longitudinal SEM to their methodological toolboxes.”

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

“Little has used his gifts as a researcher, teacher, and writer to create a wonderfully accessible volume that will benefit applied researchers and graduate students alike. Each chapter is complete with highly readable explanations, fresh and interesting examples drawn from the author's own considerable experience, beautifully detailed figures, practical modeling tips and tricks, and extensive supporting materials on the Web, all woven together with welcome doses of humor and personality.”

—Gregory R. Hancock, PhD, Department of Human Development and Quantitative Methodology, University of Maryland

“Little leads readers through a thoughtful and pragmatic approach to SEM by explaining how to think about longitudinal designs, weigh modeling options, and make informed decisions. Developed in both conceptual and technical terms, and illustrated with social science examples, this book is particularly suited to those who follow words and sentences more easily than they track symbols and mathematical operators.”

—Melissa Hardy, PhD, Department of Sociology, The Pennsylvania State University

Table of Contents


* A personal introduction and what to expect

How statistics came into my life

My approach to the book

Key features of the book

Overview of the book

* Datasets and measures used

My dataset with the Inventory Felt Energy and Emotion in Life (I FEEL) measure


Gallagher and Johnson's MIDUS example


Negative affect

Dorothy Espelage's bullying and victimization examples

Peer victimization

Substance use

Family conflict

Family closeness


Homophobic teasing

* Overdue gratitude

* Prophylactic apologies


* An overview of the conceptual foundations of SEM

Concepts, constructs, and indicators

From concepts to constructs to indicators to good models

* Sources of variance in measurement

Classical test theorem

Expanding classical test theorem

* Characteristics of indicators and constructs

Types of indicators and constructs

Categorical versus metrical indicators and constructs

Types of correlation coefficients that can be modeled

* A simple taxonomy of indicators and their roles

* Rescaling variables

* Parceling

* What changes and how?

* Some advice for SEM programming

* Philosophical issues and how I approach research

* Summary

* Key terms and concepts introduced in this chapter

* Recommended readings


* Timing of measurements and conceptualizing time

Cross-sectional design

Single-cohort longitudinal design

Cross-sequential design

Cohort-sequential design

Time-sequential design

Other validity concerns

Temporal design

Lags within the interval of measurement

Episodic and Experiential Time

* Missing data imputation and planned missing designs

Missing data mechanisms

Recommendations and caveats

Planned missing data designs in longitudinal research

* Modeling developmental processes in context

* Summary

* Key terms and concepts introduced in this chapter

* Recommended readings


* Drawing and labeling conventions

* Defining the parameters of a construct

* Scale setting

* Identification

* Adding means to the model: Scale setting and identification with means

* Adding a longitudinal component to the CFA model

* Adding phantom constructs to the CFA model

* Summary

* Key terms and concepts introduced in this chapter

* Recommended Readings


* Model fit and types of fit indices

Statistical rationale

Modeling rationale

The longitudinal null model

Summary and cautions

* Sample Size

* Power

* Summary

* Key terms and concepts introduced in this chapter

* Recommended readings


* Factorial invariance

* A small (nearly perfect) data example

Configural factorial invariance

Weak factorial invariance

Strong factorial invariance

Evaluating invariance constraints

Model modification

Partial invariance

* A larger example followed by tests of the latent construct relations

Testing the latent construct parameters

* An application of a longitudinal SEM to a repeated-measures experiment

* Summary

* Key terms and concepts introduced in this chapter

* Recommended readings


* Basics of a panel model

* The basic simplex change process

* Building a panel model

Covariate/control variables

Building the panel model of positive and negative affect

* Illustrative examples of panel models

A simplex model of cognitive development

Two simplex models of non-longitudinal data

A panel model of bullying and homophobic teasing

* Summary

* Key terms and concepts introduced in this chapter

* Recommended readings


* Multiple-group longitudinal SEM

Step 1: Estimate missing data and evaluate the descriptive statistics

Step 2: Perform any supplemental analysis to rule out potential confounds

Step 3: Fit an appropriate multiple-group longitudinal null model

Step 4: Fit the configurally invariant model across time and groups

Step 5: Test for weak factorial (loadings) invariance

Step 6: Test for strong factorial invariance

Step 7: Test for mean-level differences in the latent constructs

Step 8: Test for the homogeneity of the variance–covariance matrix among the latent constructs

Step 9: Test the longitudinal SEM model in each group

* A dynamic p-technique multiple-group longitudinal model

* Summary

* Key terms and concepts introduced in this chapter

* Recommended readings


* Longitudinal growth curve model

* Multivariate growth curve models

* Multilevel longitudinal model

* Summary

* Key terms and concepts introduced in this chapter

* Recommended readings


* Making the distinction between mediators and moderators

Cross-sectional mediation

Half-longitudinal mediation

Full longitudinal mediation

* Moderation

* Summary

* Key terms and concepts introduced in this chapter

* Recommended readings


* Multitrait-multimethod models

* Pseudo-MTMM models

* Bifactor and higher order factor models

* Contrasting different variance decompositions

* Digestif

* Key terms and concepts introduced in this chapter

* Recommended readings

About the Author

Todd D. Little, PhD, is Professor of Educational Psychology and Leadership at Texas Tech University and founding Director of the Texas Tech University Institute for Measurement, Methodology, Analysis, and Policy. Dr. Little is a Fellow of the American Association for the Advancement of Science; the American Psychological Association (APA) Divisions 5, 7, and 15; and the Association for Psychological Science. He is past president of APA Division 5 (Evaluation, Measurement, and Statistics). Dr. Little organizes and teaches in his renowned "Stats Camp" each June. Partly because of the impact and importance of Stats Camp, Dr. Little was awarded the Cohen Award from APA Division 5 for Distinguished Contributions to Teaching and Mentoring.


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

Course Use

May serve as a text in graduate-level courses on longitudinal models, latent variable models, growth curve models, advanced SEM, or advanced quantitative methods.