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    Area of Science:

    • Psychometrics
    • Multivariate Statistics

    Background:

    • Orthogonal confirmatory factor analysis (CFA) has a long history, with foundational work by Green (1952).
    • Subsequent research refined solutions using least-squares criteria, notably by Fischer, Roppert, Kristof, and Schonemann.
    • Related problems include orthonormalization of oblique matrices and fitting partially specified targets.

    Purpose of the Study:

    • To provide a comprehensive overview of the historical development of orthogonal confirmatory factor analysis techniques.
    • To synthesize various solutions and criteria used for orthogonal matrix transformations in CFA.
    • To highlight advancements in handling matrices of different ranks and fitting targets.

    Main Methods:

    • Review and synthesis of seminal papers in orthogonal confirmatory factor analysis.
    • Analysis of least-squares and other criteria (e.g., Procrustean) for matrix fitting.
    • Examination of solutions for full and less-than-full column rank matrices.

    Main Results:

    • Green's (1952) work established early solutions for orthogonal CFA.
    • Schonemann's (1966) solution offered greater generality by accommodating less-than-full rank matrices.
    • Cliff's (1966) work provided a practical, though non-least-squares, criterion that aligned with least-squares outcomes.

    Conclusions:

    • The field has evolved significantly, with increasing generality in solutions for orthogonal confirmatory factor analysis.
    • Least-squares criteria remain central, but alternative approaches have also contributed.
    • Techniques exist for various scenarios, including partially specified targets and different matrix rank conditions.