Understanding Structural Equation Models: Models of Relationships Between Variables

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
• Supplemented by a website featuring code, data, lecture slides, and additional material

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.

Phillip K. Wood is Professor of Psychological Sciences at the University of Missouri–Columbia, where he has taught graduate seminars in quantitative methods, including beginning and advanced structural equation modeling (SEM), for over 30 years

He earned his Ph.D. in Educational Psychology and Measurement from the University of Minnesota, and earlier degrees from the University of Iowa and Wartburg College.

Dr. Wood’s research spans advanced latent variable modeling techniques―particularly SEM, latent growth, growth-mixture models, state–trait modeling, longitudinal data analysis and models for longitudinally intensive data as applied to developmental processes, substance abuse within young adult populations and life-span development.

A strong advocate of methodological transparency and reproducibility, Wood maintains open-access resources, including SAS, Mplus, lavaan, and Onyx code, accessible through his university-hosted repositories

He regularly moderates the Transcontinental Karl Popper Conference, which explores philosophy of science in psychological research, highlighting his commitment to the interplay between methodological rigor and theoretical skepticism.

Combining decades of classroom instruction with cutting-edge research, Phillip Wood brings a practical, data-conscious perspective fueled by a belief that SEM should be inquisitive, skeptical, and disciplined―a perfect guide for readers navigating the complexities of latent variable modeling.