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The spatial generalized linear mixed models are often used, where the latent variables representing spatial correlations are modeled through a Gaussian random field to model the categorical spatial data. The violation of the Gaussian assumption affects the accuracy of predictions and parameter estimates in these models. In this paper, the spatial generalized linear mixed models are fitted and analyzed by utilizing a stationary skew Gaussian random field and employing an approximate Bayesian approach. The performance of the model and the approximate Bayesian approach is examined through a simulation example, and implementation on an actual data set is presented.