Approximate pairwise likelihood inference in SGLM models with skew normal latent variables

Abstract 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.