Iteration of Partially Specified Target Matrices: Application to the Bi-Factor Case

Area of Science:

• Psychometrics
• Statistical Modeling
• Factor Analysis

Background:

• Bi-factor rotation methods are crucial for analyzing complex data structures with general and specific factors.
• Existing methods like Schmid-Leiman (SL) and SL with target rotation (SLt) have limitations with cross-loadings or near-zero loadings.
• Analytic bi-factor rotations such as bi-quartimin and bi-geomin also show performance variability.

Purpose of the Study:

• To introduce and evaluate a novel bi-factor rotation method, Schmid-Leiman with iterative target rotation (SLi).
• To compare the performance of SLi against established bi-factor rotation techniques.
• To identify optimal conditions for applying SLi in factor analysis.

Main Methods:

• A Monte Carlo simulation was employed to assess the performance of SLi, SL, SLt, bi-quartimin, and bi-geomin.
• The simulation manipulated factors such as cross-loadings, near-zero loadings, and sample size.
• Performance was evaluated based on the accuracy of bi-factor structure recovery.

Main Results:

• SLi demonstrated superior accuracy in recovering bi-factor structures across most simulated conditions.
• SLi showed significant improvements over SL and SLt when dealing with cross-loadings and pure general factor indicators.
• Bi-quartimin and bi-geomin exhibited inconsistent performance across different factor structures.

Conclusions:

• Schmid-Leiman with iterative target rotation (SLi) is a robust method for analyzing complex bi-factor structures.
• SLi is recommended over existing methods, particularly when factor structures include cross-loadings or pure general factor indicators.
• Adequate sample sizes (N ≥ 500) are essential for reliable bi-factor structure recovery, especially with low specific factor loadings.