Mixtures of Quantile-Based Factor Analyzers

In this work, we introduce a mixture of factor analyzers model where component-specific latent factors are modeled via independent quantile-based distributions. These are flexible and parsimonious distributions defined via their quantile function. Bayesian inference is carried out both via a Metropolis-within-Gibbs algorithm and via Stan, also exploiting its variational inference algorithm. In contrast to the Gaussian mixture of factor analyzers model, the proposed model is not a Gaussian mixture, thus being able to describe flexible non-elliptical shapes, which is highlighted via illustrations from simulated data. Quantile-based MFA models are compared in terms of classification accuracy with Gaussian and non-Gaussian MFA on some real datasets, where the extra flexibility of the quantile-based distributed factors clearly helps in achieving good results.