Classic Factor Analysis

In this chapter we explore the classic factor analytical model. Factor analysis is extremely important in its scientific historical role in explicitly recognizing measurement error in behavioral research,. and in providing a rigorous means of conceptualizing unobservable constructs and the theoretical nomological networks in which the constructs are embedded. More recently its importance is also in its foundational role as a predecessor to the currently enormously popular structural equations modeling techniques. Finally, classic factor analysis is also still commonly used today as an exploratory method. This chapter is organized as follows: First. the concepts of unobservable constructs and measurement error are reviewed. Second, factor analysis is distinguished from principal components analysis — these terms are often mistakenly used interchangeably even though these models have very different theoretical bases (if not empirical performances). Third, the decisions that must be made in the process of conducting a factor analysis are addressed. These issues include the "number of factors to retain" and the method of "rotation" to facilitate interpretation of the results. Finally, several advanced topics (e.g. higher-order factor analysis, multi-mode factor analysis, etc.) are discussed briefly. Several small data sets are analyzed throughout the chapter to provide examples, and the SAS and SPSSX commands necessary to run simple jobs are provided in Appendix A.