Pairwise likelihood inference in spatial generalized linear mixed models

Abstract

Spatial generalized linear mixed models are flexible models for a variety of applications, where spatially dependent and non-Gaussian random variables are observed. The focus is inference in spatial generalized linear mixed models for large data sets. Maximum likelihood or Bayesian Markov chain Monte Carlo approaches may in such cases be computationally very slow or even prohibitive. Alternatively, one may consider a composite likelihood, which is the product of likelihoods of subsets of data. In particular, a composite likelihood based on pairs of observations is adopted. In order to maximize the pairwise likelihood, a new expectation–maximization-type algorithm which uses numerical quadrature is introduced. The method is illustrated on simulated data and on data from air pollution effects for fish populations in Norwegian lakes. A comparison with alternative methods is given. The proposed algorithm is found to give reasonable parameter estimates and to be computationally efficient.