Exploratory Factor Analysis. W. Holmes Finch
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ISBN: 9781544339887
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Series Editor’s Introduction
Social and behavioral research rests fundamentally on measurement. Much of what we wish to study cannot be directly observed. Exploratory Factor Analysis describes tools for exploring relationships between observed variables and latent variables, also known as factors.
The volume provides an accessible introduction to applied exploratory factor analysis (EFA) for those new to the method. Professor Finch’s goal is to give readers sufficient background to embark on their own analyses, follow up on topics of interest, and more broadly engage the literature. In doing so, he draws on his experience teaching this material as well as his expertise as a contributor to the literature. Exploratory Factor Analysis is thorough, but understandable. What the reader needs to know is explained “just in time.” Forty years ago, in the early years of the QASS series, Jae-On Kim and Charles W. Mueller contributed two volumes on factor analysis, one introducing the method and the other explaining its application. This volume replaces them both.
Professor Finch begins with problems of measurement, explaining that variables of interest are often latent constructs, not directly observable, and discussing the implications. After a quick review of the mathematical underpinnings of factor analysis, Chapters 3–5 discuss factor extraction, rotation, and retention in that order. Professor Finch walks through the requirements, assumptions, and logic of each of these steps in an EFA. Throughout, he gives much practical advice about how to implement them and about the many choices an analyst must make. For factor extraction, should the analyst use ML (maximum likelihood), PAF (principal axis factoring), or some other method? What are the differences? What is the point of factor rotation? Which is better for a particular purpose, orthogonal or oblique rotation, and given the choice, how does the analyst choose among the many rotation methods available? Which method for determining the number of factors has the most support in the literature? And importantly, for results to be reproducible, how should the analysis be described and results be presented? In the final chapter, Professor Finch discusses factor scores and the problems that can arise using them, determining appropriate sample size, and how to handle missing data as well as introducing some more advanced topics. A strength of the volume is that it clearly differentiates EFA not only from Confirmatory Factor Analysis (chapters 1 and 2), but also Principal Components Analysis (chapter 3), discriminant analysis, partial least squares, and canonical correlation (chapter 6).
Two examples enliven the explanations. The first involves achievement motivation. This very simple example, based on four subscales, is used to demonstrate calculations and interpretation in the context. The other example is the Adult Temperament Scale. This is a very “real” example in that it reveals some of the challenges associated with EFA. In EFA, there are many mathematically plausible solutions: what criteria does the analyst use to make choices between them? Professor Finch uses the ATS example to demonstrate how comparisons of results based on different approaches to extraction and rotation can serve as robustness checks. However, it is also sometimes the case that the different methods do not point to a single, unified conclusion. In the ATS example, different methods provide inconsistent guidance on factor retention. This can happen, and Professor Finch comments on how the analyst might respond. Data and software code for both examples are contained in a companion website at study.sagepub.com/researchmethods/qass/finch-exploratory-factor-analysis.
As Professor Finch explains, there is a continuum of factor analysis models, ranging from purely exploratory models which incorporate no a priori information to confirmatory models in which all aspects of the model are specified by the researcher as hypotheses about measurement structure. The approach taken in Exploratory Factor Analysis puts it somewhere in the middle of this continuum. Throughout, Professor Finch stresses the importance of theoretical expectations in making choices and assessing results. Although formal hypotheses about measurement structure are not tested in EFA, theory nevertheless guides the application of this data analytic technique.
Barbara Entwisle
Series Editor
About the Author
W. Holmes Finch (Ph.D. South Carolina) is the George and Frances Ball Distinguished Professor of Educational Psychology in the Department of Educational Psychology at Ball State University. Prior to coming to Ball State, he worked as a consultant in the Statistics Department at the University of South Carolina for 12 years advising faculty and graduate students on the appropriate statistical methods for their research. Dr. Finch teaches courses in statistical and research methodology as well as psychometrics and educational measurement. His research interests involve issues in psychometrics, including dimensionality assessment, differential item functioning, generalizability theory and unfolding models. In addition, he pursues research in multivariate statistics, particularly those involving nonparametric techniques. He is the co-author of Multilevel Modeling Using R (with Holden, J.E., & Kelley, K., CRC Press, 2014); Applied Psychometrics Using SAS (with French, B.F. & Immekus, J., Information Age, 2014); and Latent Variable Models in R (with French, B.F., Routledge, 2015).
Acknowledgments
I would like to acknowledge several folks for their help with this book. First, Barbara Entwistle and Helen Salmon were invaluable sources of encouragement, guidance, and editorial ideas throughout the writing of the book. In addition, I would like to acknowledge the many great teachers and mentors with whom I’ve had the pleasure to work over the years, in particular John Grego, Brian Habing, and Huynh Huynh. Finally, I would like to acknowledge Maria, without whose love and support none of this work would be possible.
I would like to thank the following reviewers for their feedback:
Damon Cann, Utah State University
Stephen G. Sapp, Iowa State University
Michael D. Biderman, University of Tennessee at Chattanooga
Chapter 1 Introduction to Factor Analysis
Factor analysis is perhaps one of the most widely used statistical procedures in the social sciences. An examination of the PsycINFO database for the period between January 1, 2000, and September 19, 2018, revealed a total of approximately 55,000 published journal articles indexed with the keyword factor analysis. Similar results can be found by examining the ERIC database for education research and JSTOR for other social sciences. Thus, it is not an exaggeration to state that