Bayesian analysis of generalized linear mixed models with spatial correlated and unrestricted skew normal errors

Existing studies on spatial linear mixed models typically assume a normal distribution for the random error components. However, such an assumption may not be appropriate in many applications. This work relaxes the normality assumption of a generalized linear mixed model with spatial correlated by using an unrestricted multivariate skew-normal distribution, which includes the normal distribution as a special case. For parameter estimation, a Bayesian inference algorithm is developed. A simulation study and the analysis of a real data set of cigarette consumption observed between 1963 and 1992 located in 46 states of the US are conducted to compare the proposed skew normal spatial mixed model with the normal spatial mixed model.