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Introducing some efficient model selection criteria for mixed models is a substantial challenge; Its source is indeed fitting the model and computing the maximum likelihood estimates of the parameters. Data cloning is a new method to fit mixed models efficiently in a likelihood-based approach. This method has been popular recently and avoids the main problems of other likelihood-based methods in mixed models. A disadvantage of data cloning is its inability of computing the maximum of likelihood function of the model. This value is a key quantity in proposing and calculating information criteria. Therefore, it seems that we can not, directly, define an appropriate information criterion by data cloning approach. In this paper, this believe is broken and a criterion based on data cloning is introduced. The performance of the proposed model selection criterion is also evaluated by a simulation study.

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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.