Bayesian Estimation and Testing of a Beta Factor Model for Bounded Continuous Variables

The particularities of bounded data are often overlooked. This type of data is likely to display a pattern of skewness because of the existence of an upper and lower limit that cannot be exceeded. In the context of factor analysis, when variables are skewed in opposite directions, using normal-theory factor analysis might lead to over-factoring. We propose a Bayesian beta factor model to analyze doubly bounded data. A simulation study was conducted to evaluate the performance of the normal and beta factor models in the presence of skewed variables. Two Bayesian approaches to model evaluation methods are considered, posterior predictive checking and three information criterion measures (DIC, WAIC, and LOO). The number of estimated factors based on the Bayesian methods is compared for the normal and beta factor models. An application of the model using real data is also presented. We found that the beta factor model constitutes a suitable alternative to analyze data with a pattern of mixed skewness. Posterior predictive checking appears to be a viable option to select the optimal number of factors in Bayesian factor analysis.