Common Factor Analysis Versus Principal Component Analysis: Differential Bias in Representing Model Parameters?

Abstract

The aim of the present article was to reconsider several conclusions by Velicer and Jackson (1990a) in their review of issues that arise when comparing common factor analysis and principal component analysis. Specifically, the three conclusions by Velicer and Jackson that are considered in the present article are: (a) that common factor and principal component solutions are similar, (b) that differences between common factor and principal component solutions appear only when too many dimensions are extracted, and (c) that common factor and principal component parameters are equally generalizable. In contrast, Snook and Gorsuch (1989) argued recently that principal component analysis and common factor analysis led to different, dissimilar estimates of pattern loadings, terming the principal component loadings biased and the common factor loadings unbiased. In the present article, after replicating the Snook and Gorsuch results, an extension demonstrated that the difference between common factor and principal component pattern loadings is inversely related to the number of indicators per factor, not to the total number of observed variables in the analysis, countering claims by both Snook and Gorsuch and Velicer and Jackson. Considering the more general case of oblique factors, one concomitant of overrepresentation of pattern loadings is an underrepresentation of intercorrelations among dimensions represented by principal component analysis, whereas comparable values obtained using factor analysis are accurate. Differences in parameters deriving from principal component analysis and common factor analysis were explored in relation to several additional aspects of population data, such as variation in the level of communality of variables on a given factor and the moving of a variable from one battery of measures to another. The results suggest that principal component analysis should not be used if a researcher wishes to obtain parameters reflecting latent constructs or factors.