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.


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Last updated 19 June 2010