A data cloning algorithm for computing maximum likelihood estimates in spatial generalized linear mixed models

Non-Gaussian spatial data are common in many sciences such as environmental sciences, biology and epidemiology. Spatial generalized linear mixed models (SGLMMs) are flexible models for modeling these types of data. Maximum likelihood estimation in SGLMMs is usually made cumbersome due to the high-dimensional intractable integrals involved in the likelihood function and therefore the most commonly used approach for estimating SGLMMs is based on the Bayesian approach. This paper proposes a computationally efficient strategy to fit SGLMMs based on the data cloning (DC) method suggested by Lele et al. (2007). This method uses Markov chain Monte Carlo simulations from an artificially constructed distribution to calculate the maximum likelihood estimates and their standard errors. In this paper, the DC method is adapted and generalized to estimate SGLMMs and some of its asymptotic properties are explored. Performance of the method is illustrated by a set of simulated binary and Poisson count data and also data about car accidents in Mashhad, Iran. The focus is inference in SGLMMs for small and medium data sets.