A Matrix-Free Likelihood Method for Exploratory Factor Analysis of High-Dimensional Gaussian Data

Abstract

<p>This technical note proposes a novel profile likelihood method for estimating the covariance parameters in exploratory factor analysis of high-dimensional Gaussian datasets with fewer observations than number of variables. An implicitly restarted Lanczos algorithm and a limited-memory quasi-Newton method are implemented to develop a matrix-free framework for likelihood maximization. Simulation results show that our method is substantially faster than the expectation-maximization solution without sacrificing accuracy. Our method is applied to fit factor models on data from suicide attempters, suicide ideators, and a control group. <a href="https://doi.org/10.1080/10618600.2019.1704296" target="_blank">Supplementary materials</a> for this article are available online.</p>