Factor analysis is a dimension reduction technique designed to express the actual observed variables (possibly many in number) using a smaller number of underlying latent (unobserved) variables. In this chapter, we shall discuss the SAS® implementation of exploratory factor analysis, which involves identifying factors, determining which factors are needed to satisfactorily describe the original data, interpreting the meaning of these factors, and so on. Confirmatory factor analysis goes further and involves techniques for testing hypotheses to confirm theories, and so on. Although SAS contains procedures for running confirmatory factor analysis, we shall only discuss exploratory factor analysis in this chapter.
17.1 FACTOR ANALYSIS BASICS
The typical steps in performing an exploratory factor analysis are the following:
- a. Compute a correlation (or covariance) matrix for the observed variables.
- b. Extract the factors (this involves deciding how many factors to extract, the method to use, and the values to use for the prior communality estimates).
- c. Rotate the factors to improve interpretation.
- d. Compute factor scores (if needed).