Understanding Structural Equation Models

Models of Relationships Between Variables

Phillip K. Wood

• Publisher: Chapman and Hall/CRC
• Year: 2025
• eBook ISBN: 9781040678435
• Topic: Mathematics
• Subtopic: Personal Success
• Index: Mathematics

The field of structural equation models (SEMs) is rapidly expanding. A researcher who wants to select and apply SEMs to their data faces several challenges: (1) They can often become extremely complex, with many parameters to estimate. Small samples or those with relatively few variables often cannot support this complexity reliably, leading to under-identified models, poor power, or unstable estimates; (2) Researchers must choose an appropriate measurement model, and these choices are not often well understood in advance; (3) No single "correct" SEM exists, although "better" ones do, and the existence of competing plausible alternatives is often overlooked; and (4) Critical examination of model assumptions involving the linearity of parameters and the existence of influential or outlying observations is often overlooked. This book provides an overview of SEMs as a flexible, skeptical, and iterative scientific process.

Key Features:

• Emphasis on multiverse analysis, right-sizing statistical models to data, and the generation of plausible skeptical alternatives
• Robust assumption checking (LOESS regression, regression and SEM diagnostics)
• Detailed, visual coverage of a variety of path diagrams, their links to matrix-based specifications, and data exploration using heat-map visualization and tests of dimensionality
• A variety of SEMs including mediational models, psychometrics (e.g., parallel, tau-equivalent, congeneric measurement), growth curve models, exploratory factor analysis, multigroup, categorical, and exploratory structural equation modeling

This text is designed for graduate students, early-career researchers, and advanced undergraduates who wish to move beyond plug-and-play SEMs to a deeper, more philosophical and data-conscious understanding. Its careful balance of theory, worked examples, and emphasis on skepticism will help its audience build confidence in using SEMs flexibly and responsibly for a broad range of social and behavioral science research.

Table of contents

• Cover Page
• Half Title page
• Series Page
• Title Page
• Copyright Page
• Contents
• Preface
• The Author
• 1 Introduction
• 2 Data Representation and Basic Matrix Algebra
• 3 Path Diagrams
• 4 Three-Variable Models
• 5 Assumption Checking
• 6 Vector Algebra
• 7 Reliability Models
• 8 Confirmatory Factor Analysis
• 9 Model Fit and Comparison
• 10 Measurement Models
• 11 Matrix Notation Models
• 12 Parsimonious Factor Models
• 13 Change and Growth
• 14 Multiple Groups
• 15 Exploratory Factor Analysis
• 16 Factor Rotation
• 17 SEM Assumption Checking
• 18 Categorical Variable Dependent Variables
• 19 Postscript
• References
• Index