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 understanding factor analysis is key to understanding much published research in the fields of psychology, education, sociology, political science, anthropology, and the health sciences. The purpose of this book is to provide you with a solid foundation in exploratory factor analysis, which, along with confirmatory factor analysis, represents one of the two major strands within this broad field. Indeed, a portion of this first chapter will be devoted to comparing and contrasting these two ways of conceptualizing factor analysis. However, before getting to that point, we first need to describe what, exactly, factors are and the differences between latent and observed variables. We will then turn our attention to the importance of having strong theory to underpin the successful use of factor analysis, and how this theory should serve as the basis upon which we understand the latent variables that this method is designed to describe. We will then conclude the chapter with a brief discussion of the software available for conducting factor analysis and an outline of the book itself. My hope in writing this book is to provide you, the reader, with a sufficient level of background in the area of exploratory factor analysis so that you can conduct analyses of your own, delve more deeply into topics that might interest you, and confidently read research that has used factor analysis. If this book achieves these goals, then I will count it as a success.
Latent and Observed Variables
Much research in fields such as psychology is focused on variables that cannot be directly measured. These variables are often referred to as being latent, and include such constructs as intelligence, personality, mood, affect, and aptitude. These latent variables are frequently featured in social science research and are also the focus for clinicians who want to gain insights into the psychological functioning of their clients. For example, a researcher might be interested in determining whether there is a relationship between extraversion and job satisfaction, whereas a clinician may want to know whether her client is suffering from depression. In both cases, the variables of interest (extraversion, job satisfaction, and depression) are conceived of as tangible, real constructs, though they cannot be directly measured or observed. We talk about an individual as being an extravert or we conclude that a person is suffering from depression, yet we have no direct way of observing either of those traits. However, as we will see in this book, these latent variables can be represented in the statistical model that underlies factor analysis.
If latent variables are, by their very nature, not observable, then how can we hope to measure them? We make inferences about these latent variables by using variables that we can measure, and which we believe are directly impacted by the latent variables themselves. These observed variables can take the form of items on a questionnaire, a test, or some other score that we can obtain directly, such as behavior ratings made by a researcher of a child’s behavior on the playground. We generally conceptualize the relationship between the latent and observed variables as being causal, such that one’s level on the latent variable will have a direct impact on scores that we obtain on the observed variable. This relationship can take the form of a path diagram, as in Figure 1.1.
