In spatial generalized linear mixed models, spatial correlation is assumed by adding normal latent variables to the model. In these models because of the non-Gaussian spatial response and the presence of latent variables, the likelihood function cannot usually be given in a closed form, thus the maximum likelihood approach is very challenging. The main purpose of this paper is to introduce two new algorithms for the maximum likelihood estimations of parameters and to compare them in terms of speed and accuracy with existing algorithms. The presented algorithms are applied to a simulation study and their performances are compared.

Spatial generalized linear mixed models are used commonly for modeling discrete spatial responses. In this models the spatial correlation of the data is considered as spatial latent variables. For simplicity, it is usually assumed in these models that spatial latent variables are normally distributed. An incorrect normality assumption may leads to inaccurate results and is therefore erroneous. In this paper we model the spaial latent variables in a general random field, namely the closed skew Gaussian random field which is more flexible and includes the Gaussian random field. We propose a new algorithm for maximum likelihood estimates of the parameters. A key ingredient in our algorithm is using a Hamiltonian Monte Carlo version of the EM algorithm. The performance of the proposed model and algorithm is presented through a simulation study.

Spatial generalized linear mixed model is commonly used to model Non-Gaussian data and the spatial correlation of the data is modelled by latent variables. In this paper, latent variables are modeled using a stationary skew Gaussian random field and a new algorithm based on composite marginal likelihood is presented. The performance of this stationary random field in the model and the proposed algorithm is implemented in a simulation example.