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

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    Principal component analysis (PCA) and common factor analysis (CFA) yield different results, contrary to previous claims. Differences in pattern loadings depend on indicators per factor, not total variables, suggesting PCA is unsuitable for latent construct analysis.

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    Area of Science:

    • Psychometrics
    • Statistical Analysis
    • Multivariate Statistics

    Background:

    • Contrasting conclusions exist regarding the similarity between common factor analysis (CFA) and principal component analysis (PCA).
    • Velicer and Jackson (1990a) suggested solutions are similar and differences emerge only with excessive dimensions.
    • Snook and Gorsuch (1989) argued for dissimilar estimates, labeling PCA loadings as biased and CFA loadings as unbiased.

    Purpose of the Study:

    • To re-evaluate conclusions by Velicer and Jackson (1990a) on common factor analysis (CFA) versus principal component analysis (PCA).
    • To investigate the relationship between the number of indicators per factor and the discrepancy between CFA and PCA pattern loadings.
    • To explore the implications of these differences for parameter generalizability and the representation of latent constructs.

    Main Methods:

    • Replication of Snook and Gorsuch's (1989) findings on CFA and PCA pattern loadings.
    • Extension of the analysis to examine the influence of the number of indicators per factor.
    • Exploration of parameter differences under oblique factor solutions and varying data conditions (communality levels, variable placement).

    Main Results:

    • The difference between CFA and PCA pattern loadings is inversely related to the number of indicators per factor.
    • This discrepancy is not dependent on the total number of observed variables, challenging previous assertions.
    • PCA underrepresents intercorrelations among dimensions compared to CFA, particularly with oblique factors.

    Conclusions:

    • Principal component analysis (PCA) should be avoided when the goal is to obtain parameters that accurately reflect latent constructs.
    • Common factor analysis (CFA) provides more accurate parameter estimates for latent variables.
    • The number of indicators per factor is a critical determinant of the differences observed between PCA and CFA.