Efficient Bayesian Model Averaging in Factor Analysis

Although factor analytic models have proven useful for covariance structure modeling and dimensionality reduction in a wide variety of applications, a challenging problem is uncertainty in the number of latent factors. This article proposes an efficient Bayesian approach for model selection and averaging in hierarchical models having one or more factor analytic components. In particular, the approach relies on a method for embedding each of the smaller models within the largest possible model. Bayesian computation can proceed within the largest model, while moving between sub-models based on posterior model probabilities. The approach represents a type of parameter expansion, as one always samples within an encompassing model, incorporating extra parameters and latent variables when a smaller model is true. This results in a highly efficient stochastic search factor selection algorithm (SSFS) for identifying good factor models and performing model-averaged inferences. The approach is illustrated using simulated examples and a toxicology application.