PROCEDURES FOR WEIGHTING FACTORS AND VARIABLES IN ORTHOGONAL CONFIRMATORY FACTOR ANALYSIS

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.