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    Area of Science:

    • Multivariate statistics
    • Data analysis methodology

    Background:

    • Lack of standardized methods for assessing goodness-of-fit in principal components analysis (PCA) pattern comparison.
    • Need for objective criteria to evaluate congruence between factor structures derived from different datasets.

    Purpose of the Study:

    • To develop a standard for evaluating the goodness-of-fit of patterns from principal components analysis.
    • To provide a guideline for determining the congruence of factor structures between two datasets.

    Main Methods:

    • Developed an empirical sampling distribution for the average trace statistic (E'E) using a Monte Carlo approach.
    • Utilized the orthogonal Procrustes problem for analyzing various orders of A matrices.

    Main Results:

    • Established a method based on the average trace statistic distribution.
    • Demonstrated the utility of the method for assessing factor structure congruence.

    Conclusions:

    • The presented method serves as a guideline for congruence assessment in principal components analysis.
    • Addresses the identified gap in statistical evaluation standards for comparing PCA results.