Pseudo-likelihood Inference for Discrete Spatial Response (A Case Study of the Semnan rainfall data)

Non-Gaussian spatial responses are usually modeled using spatial generalized linear mixed models، such that the spatial correlation of the data can be introduced via normal latent variables. The model parameters and the prediction of the latent variables at unsampled locations are of the most important interest in SGLMM by estimating of the latent variables at sampled locations. In these models، since there are the latent variables and non-Gaussian spatial response variables، likelihood function cannot usually be given in a closed form and maximum likelihood estimations may be computationally prohibitive. In this paper، a new algorithm is introduced for maximum likelihood estimation of the model parameters and predictions، that is faster than the former method. This algorithm obtains to combine the pseudo maximum likelihood method، the Expectation maximization Gradient algorithm and an approximate method. The performance and accuracy of the proposed model are illustrated through a simulation study. Finally، the model and the algorithm are applied to a case study on rainfall data observed in the weather stations of Semnan in 2012.