Sparse Bayesian joint modal estimation for exploratory item factor analysis

TL;DR

This paper introduces a scalable Bayesian algorithm for sparse exploratory item factor analysis, demonstrating high efficiency and accuracy in simulations and real psychological data.

Contribution

It proposes a novel Bayesian joint modal estimation algorithm with an alternating optimization scheme for scalable sparse factor analysis.

Findings

High computational efficiency in simulations

Accurate variable selection for latent factors

Effective extraction of interpretable factor loadings in real data

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 estimates the model parameters and factor scores that maximize the complete-data joint posterior density. The algorithm's scalability is achieved through an alternating optimization scheme that iteratively updates model parameters and latent variables. Simulation studies show that the proposed algorithm has high computational efficiency and accuracy in variable selection over latent factors and the recovery of the model parameters. Moreover, we conducted a real data analysis using large-scale data from a psychological assessment that targeted the Big Five personality traits. This result indicates that the proposed algorithm achieves computationally efficient parameter estimation and extracts the interpretable factor loading structure.