Robust Deviance Information Criterion for Latent Variable Models

It is shown in this paper that the data augmentation technique undermines the theoretical underpinnings of the deviance information criterion (DIC), a widely used information criterion for Bayesian model comparison, although it facilitates parameter estimation for latent variable models via Markov chain Monte Carlo (MCMC) simulation. Data augmentation makes the likelihood function non-regular and hence invalidates the standard asymptotic arguments. A new information criterion, robust DIC (RDIC), is proposed for Bayesian comparison of latent variable models. RDIC is shown to be a good approximation to DIC without data augmentation. While the later quantity is difficult to compute, the expectation - maximization (EM) algorithm facilitates the computation of RDIC when the MCMC output is available. Moreover, RDIC is robust to nonlinear transformations of latent variables and distributional representations of model specification. The proposed approach is illustrated using several popular models in economics and finance.