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 robust form of DIC, denoted as RDIC, is advocated 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 applied to several popular models in economics and finance. While DIC is very sensitive to the nonlinear transformations of latent variables in these models, RDIC is robust to these transformations. As a result, substantial discrepancy has been found between DIC and RDIC.