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Confirmatory Factor Analysis

Confirmatory Factor Analysis

March 2022 | 144 pages | SAGE Publications, Inc
Measurement connects theoretical concepts to what is observable in the empirical world, and is fundamental to all social and behavioral research. In this volume, J. Micah Roos and Shawn Bauldry introduce a popular approach to measurement: Confirmatory Factor Analysis (CFA). As the authors explain, CFA is a theoretically informed statistical framework for linking multiple observed variables to latent variables that are not directly measurable. The authors begin by defining terms, introducing notation, and illustrating a wide variety of measurement models with different relationships between latent and observed variables. They proceed to a thorough treatment of model estimation, followed by a discussion of model fit.  Most of the volume focuses on measures that approximate continuous variables, but the authors also devote a chapter to categorical indicators. Each chapter develops a different example (sometimes two) covering topics as diverse as racist attitudes, theological conservatism, leadership qualities, psychological distress, self-efficacy, beliefs about democracy, and Christian nationalism drawn mainly from national surveys. Data to replicate the examples are available on a companion website at, along with code for R, Stata, and Mplus.
Chapter 1: Introduction
Chapter 2: Model Specification
Chapter 3: Identification and Estimation
Chapter 4: Model Evaluation and Respecification
Chapter 5: Measurement Invariance
Chapter 6: Categorical Indicators
Chapter 7: Conclusion
Appendix: Reliability of Scales


Student Study Site

Example code as well as data (variously in R using lava, Stata, and Mplus) is provided by chapter.

Confirmatory Factor Analysis is well written and easy to read, The book covers the essentials necessary for understanding and using CFA. It is appropriate for graduate students and professors new to this analysis approach.

Jerry J. Vaske
Colorado State University

The authors provide a masterful and fluid overview of confirmatory factor analysis that will guide readers to the best practices whether conducting their own research or evaluating the research of others.

John Hoffmann
Brigham Young University

This is a well-written and comprehensive text.

Michael D. Biderman
University of Tennessee at Chattanooga

Roos and Bauldry lucidly set out foundations of confirmatory factor analysis (CFA) as applied in the assessment and construction of scales. Beginning with model specification, they discuss identification, estimation, and assessment of CFA models, before developing extensions to assessing measurement invariance and categorical (rather than quantitative) indicators.

Peter V. Marsden
Harvard University