Principal Components and Factor Analysis

• General Purpose
• Basic Idea of Factor Analysis as a Data Reduction Method
• Factor Analysis as a Classification Method
• Miscellaneous Other Issues and Statistics

General Purpose

The main applications of factor analytic techniques are: (1) to reduce the number of variables and (2) to detect structure in the relationships between variables, that is to classify variables. Therefore, factor analysis is applied as a data reduction or structure detection method (the term factor analysis was first introduced by Thurstone, 1931). The topics listed below will describe the principles of factor analysis, and how it can be applied towards these two purposes. We will assume that you are familiar with the basic logic of statistical reasoning as described in Elementary Concepts. Moreover, we will also assume that you are familiar with the concepts of variance and correlation; if not, we advise that you read the Basic Statistics topic at this point.
There are many excellent books on factor analysis. For example, a hands-on how-to approach can be found in Stevens (1986); more detailed technical descriptions are provided in Cooley and Lohnes (1971); Harman (1976); Kim and Mueller, (1978a, 1978b); Lawley and Maxwell (1971); Lindeman, Merenda, and Gold (1980); Morrison (1967); or Mulaik (1972). The interpretation of secondary factors in hierarchical factor analysis, as an alternative to traditional oblique rotational strategies, is explained in detail by Wherry (1984).
Confirmatory factor analysis. Structural Equation Modeling (SEPATH) allows you to test specific hypotheses about the factor structure for a set of variables, in one or several samples (e.g., you can compare factor structures across samples).
Correspondence analysis. Correspondence analysis is a descriptive/exploratory technique designed to analyze two-way and multi-way tables containing some measure of correspondence between the rows and columns. The results provide information which is similar in nature to those produced by factor analysis techniques, and they allow you to explore the structure of categorical variables included in the table. For more information regarding these methods, refer to Correspondence Analysis.

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