Beta spatial linear mixed model with variable dispersion using Monte Carlo maximum likelihood

Abstract

We propose a beta spatial linear mixed model with variable dispersion using Monte Carlo maximum likelihood. The proposed method is useful for those situations where the response variable is a rate or a proportion. An approach to the spatial generalized linear mixed models using the Box–Cox transformation in the precision model is presented. Thus, the parameter optimization process is developed for both the spatial mean model and the spatial variable dispersion model. All the parameters are estimated using Markov chain Monte Carlo maximum likelihood. Statistical inference over the parameters is performed using approximations obtained from the asymptotic normality of the maximum likelihood estimator. Diagnosis and prediction of a new observation are also developed. The method is illustrated with the analysis of one simulated case and two studies: clay and magnesium contents. In the clay study, 147 soil profile observations were taken from the research area of the Tropenbos Cameroon Programme, with explanatory variables: elevation in metres above sea level, agro‐ecological zone, reference soil group and land cover type. In the magnesium content, the soil samples were taken from 0‐ to 20‐cm‐depth layer at each of the 178 locations, and the response variable is related to the spatial locations, altitude and sub‐region.