A novel Bayesian approach for latent variable modeling from mixed data with missing values

Abstract

We consider the problem of learning parameters of latent variable models from mixed (continuous and ordinal) data with missing values. We propose a novel Bayesian Gaussian copula factor (BGCF) approach that is proven to be consistent when the data are missing completely at random (MCAR) and that is empirically quite robust when the data are missing at random, a less restrictive assumption than MCAR. In simulations, BGCF substantially outperforms two state-of-the-art alternative approaches. An illustration on the ‘Holzinger & Swineford 1939’ dataset indicates that BGCF is favorable over the so-called robust maximum likelihood.