Bayesian semiparametric model with spatially–temporally varying coefficients selection

Abstract

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.

Hierarchical spatially varying coefficient and temporal dynamic process models usingspTDyn

“…It is also possible to perform the MCMC diagnostics using the coda package; see details in spTDyn for further specifications. We obtain the MCMC summary statistics using the summary argument: The coefficient estimates of the terms soi and grid in the above R output are for the fixed β j0 , j = 1, 2 coefficients of the explanatory variables, as defined in Equation (19). We also observe from the summary output that, as expected, the spatial variance σ 2 η is much higher than the nugget effect σ 2 .…”

“…Note that the formula argument also uses the intercept term α and the nonspatially varying effects β j0 , j = 1, 2 for the covariates defined in model (19). It is also possible to omit the intercept term from the model using '-1' in the formula argument.…”

Nonparametric Bayesian Inference in Biostatistics

“…For example Cai et al (2013) generalize the logit link in the ARSB model for Poisson data of to allow for spatially varying regression coefficients, and apply their model to the spatial assessment of low birth-weight across South Carolina counties. Since the CAR marginals have support over the entire real line, we introduce a transformation logit(w ik ) = z ik and take the (z 1k ,... ,z nk ) to be distributed as CAR yielding a MRF on the location weights and encouraging smoothing across neighbors.…”

A hybrid hierarchical Bayesian model for spatiotemporal surveillance data

“…Compared with other clustering algorithms, the most salient advantage of a Dirichlet process is the automatic selection of the number of clusters. Bayesian nonparametric and semiparametric spatial modeling has seen rapid development recently, especially with applications of Dirichlet processes to spatiotemporal data analysis . Spatial scan statistics have been applied to a wide variety of epidemiological studies for disease hotspot detection.…”