The Correlation Thresholding Algorithm for Exploratory Factor Analysis

TL;DR

This paper introduces the Correlation Thresholding algorithm, a unified graph-theoretic approach for addressing key issues in exploratory factor analysis, demonstrating its robustness and competitive performance through simulations and real data.

Contribution

It presents a novel unified algorithm that simultaneously solves factor number determination, loadings constraints, and solution selection in exploratory factor analysis.

Findings

The CT algorithm is robust to assumption violations.

It performs competitively compared to existing methods.

Simulation and real data validate its effectiveness.

Abstract

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.