Sparse Bayesian factor analysis when the number of factors is unknown

TL;DR

This paper introduces a Bayesian method for estimating the number of factors in sparse factor analysis models, combining model estimation, selection, and identification efficiently using MCMC techniques.

Contribution

It proposes a novel framework that simultaneously estimates and selects the number of factors in sparse Bayesian factor models with spike-and-slab priors.

Findings

Effective estimation of factor number via posterior summaries.

Integration of model selection and identification in a single framework.

Use of customized MCMC for efficient computation.

Abstract

There has been increased research interest in the subfield of sparse Bayesian factor analysis with shrinkage priors, which achieve additional sparsity beyond the natural parsimonity of factor models. In this spirit, we estimate the number of common factors in the highly implemented sparse latent factor model with spike-and-slab priors on the factor loadings matrix. Our framework leads to a natural, efficient and simultaneous coupling of model estimation and selection on one hand and model identification and rank estimation (number of factors) on the other hand. More precisely, by embedding the unordered generalized lower triangular loadings representation into overfitting sparse factor modelling, we obtain posterior summaries regarding factor loadings, common factors as well as the factor dimension via postprocessing draws from our efficient and customized Markov chain Monte Carlo scheme.