Factor analysis versus PCA

These techniques are typically used to analyze groups of correlated variables representing one or more common domains; for example, indicators of socioeconomic status, job satisfaction, health, self-esteem, political attitudes or family values. Principal components analysis is used to find optimal ways of combining variables into a small number of subsets, while factor analysis may be used to identify the structure underlying such variables and to estimate scores to measure latent factors themselves. The main applications of these techniques can be found in the analysis of multiple indicators, measurement and validation of complex constructs, index and scale construction, and data reduction. These approaches are particularly useful in situations where the dimensionality of data and its structural composition are not well known.

When an investigator has a set of hypotheses that form the conceptual basis for her/his factor analysis, the investigator performs a confirmatory, or hypothesis testing, factor analysis. In contrast, when there are no guiding hypotheses, when the question is simply what are the underlying factors the investigator conducts an exploratory factor analysis. The factors in factor analysis are conceptualized as "real world" entities such as depression, anxiety, and disturbed thought. This is in contrast to principal components analysis (PCA), where the components are simply geometrical abstractions that may not map easily onto real world phenomena.

Another difference between the two approaches has to do with the variance that is analyzed. In PCA, all of the observed variance is analyzed, while in factor analysis it is only the shared variances that is analyzed.

LINKS

LISREL - The SSI homepage for LISREL 8. LISREL is the pre-eminent statistical package for use in structural equation modeling. This program has been around for many years, and it can be thought of as the industry standard. Based on my limited experience, I would recommend LISREL over SAS. I find that I have much more control over the model than I do in SAS. This page provides links to FAQ's for LISREL, PRELIS, and SIMPLIS, as well as examples, references, and links.

Basic Concepts and Procedures of Confirmatory Factor Analysis - This paper by Connie Stapleton presents a brief comparison between exploratory and confirmatory factor analytic techniques.
Exploratory Factor Analysis - An online book manuscript by Ledyard Tucker and Robert MacCallum that provides an extensive technical treatment of the factor analysis model as well as methods for conducting exploratory factor analysis.
The Six Two-Mode Factor Analytic Models - This paper is perhaps a more technical paper than the average reader would want by Amy Minke
Confirmatory factor analysis using SAS - an explanation and code from Statistical Services at the University of Texas
Exploratory and Confirmatory Rotation Strategies in Exploratory Factor Analysis - This paper by Kimberly Rennie reviews the various rotation choices in EFA studies, including confirmatory rotation, and presents criteria useful in selecting rotation methods in various analytic situations.

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Last updated 19 June 2010