Dataset for: Spatial models for non-Gaussian data with covariates measurement error

Spatial models have been widely used in the public health set-up. 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 error in the covariates of interest. In this paper, we introduce a general class of spatial models with covariates measurement error that can account for both heavy tails, skewness, and also uncertainty of the covariates. A likelihood method, which leads to maximum likelihood estimation approach, is used for the inference through Monte Carlo Expectation-Maximization algorithm. The predictive distribution at non-sampled sites is approximated based on Markov chain Monte Carlo algorithm. The proposed approach is evaluated through a simulation study and also by a real application (particulate matters dataset).