A Matrix--free Likelihood Method for Exploratory Factor Analysis of High-dimensional Gaussian Data
This is an incremental improvement for researchers analyzing high-dimensional data in fields like psychology, offering a faster method for factor analysis.
The paper tackles the problem of estimating covariance parameters in exploratory factor analysis for high-dimensional Gaussian data with fewer observations than variables, achieving substantially faster computation than expectation-maximization without losing accuracy.
This paper 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.