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Matched Determiners Vs. Factor Invariance: A Reply To Korth.

R B Cattell

    Multivariate Behavioral Research
    |January 27, 2016
    PubMed
    Summary

    This study enhances understanding of factor matching in personality research, demonstrating its broader applicability across cultures. It introduces a novel distribution for Monte Carlo methods and emphasizes real base factor analysis for accurate determiner matching.

    Area of Science:

    • Psychometrics
    • Personality Psychology
    • Cross-Cultural Psychology

    Background:

    • Factor matching is crucial for personality research, as noted by Korth (1978).
    • Existing methods may underestimate the success of factor matching within and across cultures.
    • The significance of "diagonalization" in matching matrices requires further evaluation.

    Purpose of the Study:

    • To reassess the scope and significance of factor matching in personality research.
    • To propose a more accurate distribution for Monte Carlo determinations of r[SUBc] coefficients.
    • To refine the criteria for establishing factor invariance and demonstrating determiner matching.

    Main Methods:

    • Critique of Korth's (1978) factor matching evaluation.
    • Development of a special distribution for Monte Carlo analyses of factor loadings.

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  • Application of real base factor analysis principles to assess determiner matching.
  • Numerical illustration comparing congruence coefficients for real base vs. ordinary factor analysis patterns.

    • Main Results:

    • Factor matching is more successful within and between cultures than previously suggested.
    • Treating factor loadings as random normal deviates is inappropriate for Monte Carlo studies.
    • A specific distribution is required for accurate Monte Carlo determinations of r[SUBc] distributions.
    • Ordinary factor analysis patterns may not reflect perfect congruence even when real base patterns are identical.

    Conclusions:

    • Factor invariance, as commonly defined, is insufficient proof of determiner identity.
    • Real base factor analysis provides a more rigorous method for demonstrating the degree of determiner matching.
    • The congruence coefficient has limitations; decisions should integrate r[SUBc] and the salient variable similarity index (delta).