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Note on Convergence of Minres.

J Levin

    Multivariate Behavioral Research
    |January 19, 2016
    PubMed
    Summary
    This summary is machine-generated.

    Minres is an analytic procedure that minimizes residuals in correlation matrices. The alternating least-squares approach is recommended for reliable convergence in factor analysis.

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    Area of Science:

    • Psychometrics
    • Multivariate Statistics

    Background:

    • Factor analysis is a statistical method used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved variables called factors.
    • Minres is an iterative factor analytic procedure designed to minimize the sum-of-squares of off-diagonal residuals in a correlation matrix.

    Purpose of the Study:

    • To describe the Minres procedure for factor analysis.
    • To highlight the importance of the alternating least-squares approach for convergence.
    • To validate the original Comrey and Ahumada (1964) solution.

    Main Methods:

    • The Minres procedure iteratively solves for rows or elements of the factor pattern.
    • It minimizes the sum-of-squares of off-diagonal residuals.
    • Convergence is not guaranteed with immediate row replacement in some Minres versions.

    Main Results:

    • The alternating least-squares procedure is recommended for robust convergence.
    • The original Comrey and Ahumada (1964) solution is confirmed as correct.
    • Iterative solutions for factor patterns are central to the Minres method.

    Conclusions:

    • The alternating least-squares method ensures reliable convergence for the Minres procedure.
    • Accurate factor analysis relies on appropriate iterative techniques.
    • The foundational Comrey and Ahumada (1964) solution remains valid.