Iteration of Target Matrices in Exploratory Factor Analysis.

摘要

Exploratory factor analysis (EFA) almost always involves two unique steps: 1) initial extraction of m orthogonal, "unrotated" factors from a covariance matrix, followed by 2) rotation of said factors to an interpretable structure. The present research is focused entirely on the second step, rotation; specifically, a new, semi-analytic rotation algorithm called iterated target rotation (ITR) is developed and tested. The goal of ITR is to improve upon basic target rotation (Hurley & Cattell, 1962) by automatically searching for a viable target matrix. Whereas basic target rotation requires a user to specify a target matrix a priori, ITR uses an iterative search procedure to find a viable (often ideal) target matrix. Using Monte Carlo simulation of raw data (N = 250, 500, and 1000), the performance of ITR was tested in simple, complex, and highly complex population factor structures. Further, two characteristics of the ITR algorithm itself were varied, resulting in the following four simulation condition variables: sample size (three conditions), complexity of population factor structure (four conditions), method for iterating solutions (three conditions), and method for beginning the iterations (seven conditions). Performance was defined as the ability to accurately recover a true factor structure, as measured by the root mean-square error (RMSE) between the ITR solution and the population structure. Results suggest that, with few exceptions, ITR performs well even in highly complex structures. Limitations and future directions are discussed, and one potential improvement on the target-iteration algorithm is tested preliminarily.