The Correlation Thresholding Algorithm for Exploratory Factor Analysis

Exploratory factor analysis is often used in the social sciences to estimate potential measurement models. To do this, several important issues need to be addressed: (1) determining the number of factors, (2) learning constraints in the factor loadings, and (3) selecting a solution amongst rotationally equivalent choices. Traditionally, these issues are treated separately. This work examines the Correlation Thresholding (CT) algorithm, which uses a graph-theoretic perspective to solve all three simultaneously, from a unified framework. Despite this advantage, it relies on several assumptions that may not hold in practice. We discuss the implications of these assumptions and assess the sensitivity of the CT algorithm to them for practical use in exploratory factor analysis. This is examined over a series of simulation studies, as well as a real data example. The CT algorithm shows reasonable robustness against violating these assumptions and very competitive performance in comparison to other methods.