Approximate likelihood inference in spatial generalized linear mixed models with closed skew normal latent variables

Abstract

Spatial generalized linear mixed models are used commonly for modeling discrete spatial responses, where spatial correlation of the data is considered via latent variables which follow the normal distribution. From a computational point of view, the normal assumption for latent variables are considered just for the convenience of calculations. In this paper, the closed skew normal distribution which is more flexible and includes the normal distribution is considered for the spatial latent variables. A new approximate algorithm is introduced to obtain maximum likelihood estimates of the parameters. Prediction of the latent variables at a new unsampled location is obtained using a new approximation minimum mean square error method. The performance of the proposed method is illustrated on a simulation study and on a real data set.