A Matrix-free Likelihood Method for Exploratory Factor Analysis of High-dimensional Gaussian Data.

Area of Science:

• Statistics
• Psychometrics
• Computational Statistics

Background:

• Exploratory factor analysis (EFA) is crucial for understanding latent structures in high-dimensional data.
• Estimating covariance parameters in EFA is challenging with high-dimensional datasets where observations are fewer than variables.
• Existing methods like expectation-maximization can be computationally intensive.

Purpose of the Study:

• To propose a novel and efficient profile likelihood method for covariance parameter estimation in EFA.
• To address the challenges of high-dimensional Gaussian datasets with N < p.
• To develop a matrix-free computational framework for likelihood maximization.

Main Methods:

• Implementation of an implicitly restarted Lanczos algorithm.
• Utilizing a limited-memory quasi-Newton method for optimization.
• Development of a matrix-free framework for likelihood maximization.

Main Results:

• The proposed profile likelihood method demonstrates substantial speed advantages over the expectation-maximization solution.
• Accuracy of the novel method is comparable to the expectation-maximization approach.
• The method was successfully applied to fit factor models on real-world data.

Conclusions:

• The novel profile likelihood method provides an efficient and accurate solution for covariance parameter estimation in high-dimensional EFA.
• The matrix-free computational framework enhances scalability for large datasets.
• This approach has practical implications for analyzing complex psychological data, such as in studies of suicide ideation.