Bayesian Estimation of Spatio-Temporal Models with Covariates Measured with Spatio-Temporally Correlated Errors: Evidence from Monte Carlo Simulation

Abstract

Spatio-temporal data are susceptible to covariates measured with errors. However, little is known about the empirical effects of measurement error on the asymptotic biases in regression coefficients and variance components when measurement error is ignored. The purpose of this paper is to analyze Bayesian inference of spatio-temporal models in the case of a spatio-temporally correlated covariate measured with error by way of Monte Carlo simulation. We consider spatio-temporal model with spatio-temporal correlation structure corresponds to the Leroux conditional autoregressive (CAR) and the first order autoregressive priors. We apply different spatio-temporal dependence parameter of response and covariate. We use the relative bias (RelBias) and Root Mean Squared Error (RMSE) as valuation criteria. The simulation results show the Bayesian analysis considering measurement error show more accurate and efficient estimated regression coefficient and variance components compared with naïve analysis.