Spatial generalized linear mixed models are commonly employed for modeling discrete spatial responses that are acquired on a continuous area. A standard assumption in these models is that the latent variables are normally distributed, however skewed residuals appear in some spatial generalized linear mixed models. In this study, we consider a closed skew Gaussian random field for the spatial latent variables in the spatial generalized linear mixed models and present a new approximate pairwise likelihood approach to estimate parameters. In order to introduce a new algorithm to obtain the pairwise maximum likelihood estimates for the parameters, we use a linearization method in the composite marginal likelihood and EM algorithm. Also, techniques to calculate parameter estimates and spatial prediction in this class of skew models are proposed. The performance of the proposed model and method are illustrated through a simulation study, and applied the Tehran air quality index data set.

空间广义线性混合模型通常用于对在连续区域上获取的离散空间响应进行建模。这些模型中的一个标准假设是潜在变量是正态分布的，但是偏斜残差出现在一些空间广义线性混合模型中。在这项研究中，我们考虑了空间广义线性混合模型中空间潜在变量的闭合偏斜高斯随机场，并提出了一种新的近似成对似然方法来估计参数。为了引入一种新算法来获得参数的成对最大似然估计，我们在复合边际似然和EM算法中使用线性化方法。此外，还提出了在此类偏斜模型中计算参数估计和空间预测的技术。