On the identifiability of Bayesian factor analytic models

Abstract

A well known identifiability issue in factor analytic models is the invariance with respect to orthogonal transformations. This problem burdens the inference under a Bayesian setup, where Markov chain Monte Carlo (MCMC) methods are used to generate samples from the posterior distribution. We introduce a post-processing scheme in order to deal with rotation, sign and permutation invariance of the MCMC sample. The exact version of the contributed algorithm requires to solve $2^q$ assignment problems per (retained) MCMC iteration, where $q$ denotes the number of factors of the fitted model. For large numbers of factors two approximate schemes based on simulated annealing are also discussed. We demonstrate that the proposed method leads to interpretable posterior distributions using synthetic and publicly available data from typical factor analytic models as well as mixtures of factor analyzers. An R package is available online at CRAN web-page.

arXiv commentto appear in STCO

References in corpus (7)

• Model-based clustering based on sparse finite Gaussian mixtures
• label.switching: An R Package for Dealing with the Label Switching Problem in MCMC Outputs
• Identifying Mixtures of Mixtures Using Bayesian Estimation
• Infinite Mixtures of Infinite Factor Analysers
• Expandable Factor Analysis
• Overfitting Bayesian Mixtures of Factor Analyzers with an Unknown Number of Components
• Clustering Multivariate Data using Factor Analytic Bayesian Mixtures with an Unknown Number of Components

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