Structured prior distributions for the covariance matrix in latent factor models

Heaps, Sarah Elizabeth; Jermyn, Ian Hyla

Abstract

Factor models are widely used for dimension reduction in the analysis of multivariate data. This is achieved through decomposition of a p×p covariance matrix into the sum of two components. Through a latent factor representation, they can be interpreted as a diagonal matrix of idiosyncratic variances and a shared variation matrix, that is, the product of a p×k factor loadings matrix and its transpose. If k≪p, this defines a parsimonious factorisation of the covariance matrix. Historically, little attention has been paid to incorporating prior information in Bayesian analyses using factor models where, at best, the prior for the factor loadings is order invariant. In this work, a class of structured priors is developed that can encode ideas of dependence structure about the shared variation matrix. The construction allows data-informed shrinkage towards sensible parametric structures while also facilitating inference over the number of factors. Using an unconstrained reparameterisation of stationary vector autoregressions, the methodology is extended to stationary dynamic factor models. For computational inference, parameter-expanded Markov chain Monte Carlo samplers are proposed, including an efficient adaptive Gibbs sampler. Two substantive applications showcase the scope of the methodology and its inferential benefits.

Citation

Heaps, S. E., & Jermyn, I. H. (2024). Structured prior distributions for the covariance matrix in latent factor models. Statistics and Computing, 34(4), Article 143. https://doi.org/10.1007/s11222-024-10454-0

• Journal Article Type: Article
• Acceptance Date: Jun 11, 2024
• Online Publication Date: Jun 26, 2024
• Publication Date: Aug 1, 2024
• Deposit Date: Jul 15, 2024
• Publicly Available Date: Jul 15, 2024
• Journal: Statistics and Computing
• Print ISSN: 0960-3174
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 34
• Issue: 4
• Article Number: 143
• DOI: https://doi.org/10.1007/s11222-024-10454-0
• Keywords: Dimension reduction, Latent factor models, Structured prior distributions, Covariance matrix, 62J99, Intraday gas demand, 62M10, 62F15, Stationary dynamic factor models
• Public URL: https://durham-repository.worktribe.com/output/2512744