Likelihood Inference in A Multivariate Spatial GLMM with Skew Gaussian Random Effects Using the Slice-SAB Algorithm

Abstract

This paper introduces a multivariate skew Gaussian process and uses it to extend the family of multivariate spatial generalized linear mixed models to include skew Gaussian random effects. In this setting, the param- eter estimation encounters problems because the likelihood function involves high dimensional integrations which are computationally intensive. For estimating parameters of the complicated model structure, this article proposes an algorithm which is a combination of boosting with a variant of stochastic approximation. This algorithm which known as stochastic approximation boosting (SAB) algorithm, uses the Markov chain Monte Carlo method based on slice sampling to obtain simulations from full conditional distribution of random effects. A simulation study is conducted to assess the performance of our method. The proposed methodology is further illustrated through an application to a data set of soil pollution in a province of Iran.

Keywords

• Multivariate spatial data; Random effects; Maximum likelihood estimates; Boosting; Stochastic approximation; Skew normal.