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    Area of Science:

    • Multivariate statistics
    • Data analysis techniques

    Background:

    • Factor analysis, image component analysis, and principal component analysis are commonly used for similar data reduction purposes.
    • Factor analysis was historically preferred, but theoretical issues like factor indeterminacy have emerged.
    • Computational ease has made other methods attractive approximations.

    Purpose of the Study:

    • To compare the similarity of patterns generated by maximum likelihood factor analysis, rescaled image analysis, and principal component analysis.
    • To quantitatively assess the agreement between these three dimensionality reduction techniques across diverse datasets.

    Main Methods:

    • Comparison of factor loading patterns from maximum likelihood factor analysis, rescaled image analysis, and principal component analysis.
    • Utilized direct loading-by-loading comparison and a summary statistic based on difference matrices.
    • Employed orthogonal and oblique rotations, with Procrustes analysis to find maximum pattern similarity.

    Main Results:

    • All three methods produced remarkably similar patterns.
    • Image component analysis and maximum likelihood factor analysis demonstrated the highest degree of similarity.
    • Principal component analysis and maximum likelihood factor analysis showed the greatest dissimilarity, often in the final extracted factor.

    Conclusions:

    • The three methods, despite theoretical differences, yield largely comparable results in practice.
    • Rescaled image analysis offers a viable alternative to maximum likelihood factor analysis with high agreement.
    • Discrepancies may arise from the extraction of an excessive number of factors, particularly affecting later factors.