Observed-data DIC for spatial panel data models

In spatial panel data modeling, researchers often need to choose a spatial weights matrix from a pool of candidates, and decide between static and dynamic specifications. We propose observed-data deviance information criteria to resolve these specification problems in a Bayesian setting. The presence of high dimensional latent variables (i.e., the individual and time fixed effects) in spatial panel data models invalidates the use of a deviance information criterion (DIC) formulated with the conditional and the complete-data likelihood functions of spatial panel data models. We first show how to analytically integrate out these latent variables from the complete-data likelihood functions to obtain integrated likelihood functions. We then use the integrated likelihood functions to formulate observed-data DIC measures for both static and dynamic spatial panel data models. Our simulation analysis indicates that the observed-data DIC measures perform satisfactorily to resolve specification problems in spatial panel data modeling. We also illustrate the usefulness of the proposed observed-data DIC measures using an application from the literature on spatial modeling of the house price changes in the US.