Spatial models for non-Gaussian data with covariate measurement error

Spatial models have been widely used in the public health setup. In the case of continuous outcomes, the traditional approaches to model spatial data are based on the Gaussian distribution. This assumption might be overly restrictive to represent the data. The real data could be highly non-Gaussian and may show features like heavy tails and/or skewness. In spatial data modeling, it is also commonly assumed that the covariates are observed without errors, but for various reasons, such as measurement techniques or instruments used, uncertainty is inherent in spatial (especially geostatistics) data, and so, these data are susceptible to measurement errors in the covariates of interest. In this paper, we introduce a general class of spatial models with covariate measurement error that can account for heavy tails, skewness, and uncertainty of the covariates. A likelihood method, which leads to the maximum likelihood estimation approach, is used for inference through the Monte Carlo expectation-maximization algorithm. The predictive distribution at nonsampled sites is approximated based on the Markov chain Monte Carlo algorithm. The proposed approach is evaluated through a simulation study and by a real application (particulate matter data set).