Bayesian estimation of a quantile-based factor model

Probability distributions defined via their quantile functions, called quantile-based distributions, allow for flexible density shapes with few parameters. In this article we consider the quantile-based flattened generalized logistic distribution, which accommodates for skewness and flat shapes, and we show that it can be effectively estimated in a Bayesian framework via MCMC algorithms. Building on this, we introduce a factor model with mutually independent latent variables modelled with the same flexible distribution; for its estimation we develop an MCMC algorithm that also takes into account identifiability constraints. The novel factor model is illustrated with data from the European Social Survey, where its results are shown to be more flexible compared to the classical factor analysis and more parsimonious than the closely related independent factor analysis model, which employs univariate Gaussian mixtures for the latent factors.