In spatio-temporal analysis, the effect of a covariate on the outcome usually varies across areas and time. The spatial configuration of the areas may potentially depend on not only the structured random intercept but also spatially varying coefficients of covariates. In addition, the normality assumption of the distribution of spatially varying coefficients could lead to potential biases of estimations. In this article, we propose a Bayesian semiparametric space-time model where the spatially-temporally varying coefficient is decomposed as fixed, spatially varying and temporally varying coefficients. The spatially varying coefficients of space-time covariates are modeled nonparametrically by using the area-specific Dirichlet process prior with weights transformed via a generalized transformation. Temporally varying coefficients of covariates are modeled through the dynamic model. Uncertainty of inclusion of the spatially-temporally varying coefficients is also taken into account by variable selection procedure through determining the probabilities of different effects for each covariate. The proposed semiparametric approach shows the improvement compared to the Bayesian spatial-temporal models with normality assumption on spatial random effects and the Bayesian model with the Dirichlet process prior on the random intercept. A simulation example is presented to evaluate the performance of the proposed approach with the competing models. An application to low birth weight data in South Carolina is used for an illustration.
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