Statistical Modelling 12 (2012), 145–164

Bayesian latent structure models with space-time dependent covariates

Bo Cai
Department of Epidemiology and Biostatistics,
University of South Carolina
Columbia, SC
USA
eMail: bcai@sc.edu

Andrew B Lawson
Division of Biostatistics and Epidemiology
Medical University of South Carolina
Charleston, SC
USA

Md Monir Hossain
Center for Clinical and Translational Sciences,
The University of Texas
Houston, TX
USA

Jungsoon Choi
Division of Biostatistics and Epidemiology
Medical University of South Carolina
Charleston, SC
USA

Abstract:

Spatial-temporal data requires flexible regression models which can model the dependence of responses on space- and time-dependent covariates. In this paper, we describe a semiparametric space-time model from a Bayesian perspective. Nonlinear time dependence of covariates and the interactions among the covariates are constructed by local linear and piecewise linear models, allowing for more flexible orientation and position of the covariate plane by using time-varying basis functions. Space-varying covariate linkage coefficients are also incorporated to allow for the variation of space structures across the geographical location. The formulation accommodates uncertainty in the number and locations of the piecewise basis functions to characterize the global effects, spatially structured and unstructured random effects in relation to covariates. The proposed approach relies on variable selection-type mixture priors for uncertainty in the number and locations of basis functions and in the space-varying linkage coefficients. A simulation example is presented to evaluate the performance of the proposed approach with the competing models. A real data example is used for illustration.

Keywords:

Bayesian regression; latent structure model; piecewise linear splines; space-time models; variable selection

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