Maximum Likelihood Estimation for Spatial GLM Models

Spatial generalized linear mixed models are usually used for modelling non-Gaussian and discrete spatial responses. In these models, spatial correlation of the data is usually modelled by spatial latent variables. Although, it is a standard assumption that the latent variables have normal distribution, in practice this assumption may not be valid. The first purpose of this paper is to use a closed skew normal distribution for the spatial latent variables which is more flexible distribution and also includes normal and skew normal distributions. The second is to develop Monte Carlo EM gradient algorithm for maximum likelihood estimation of the model parameters. Then, the performance of the proposed model is illustrated through a simulation study. Finally, the model and algorithm are applied to a case study on a temperature data.