Sparse Bayesian Joint Modal Estimation for Exploratory Item Factor Analysis

Abstract

This study presents a scalable Bayesian estimation algorithm for sparse estimation in exploratory item factor analysis based on a classical Bayesian estimation method, namely Bayesian joint modal estimation (BJME). BJME jointly estimates the model parameters and factor scores by maximizing the complete-data joint posterior density. The proposed algorithm achieves scalability through an alternating optimization scheme that iteratively updates the model parameters and factor scores. Simulation studies show that the proposed algorithm has high computational efficiency and high accuracy in variable selection over latent factors and parameter recovery. Moreover, we provide a real data analysis using a large-scale dataset from a psychological assessment of the Big Five personality traits. The results indicate that the proposed algorithm extracts an interpretable factor loading structure in a computationally efficient manner.