Exact estimation procedures in a spatial mixed–effects probit model with binary outcomes

Abstract Generalized linear mixed models form a general class of random effects models for discrete and continuous response in the exponential family. Spatial GLMM are an extension of such models that allows us to fit spatial-dependent data. A popular model in this class is the probit-normal model. In this study we develop a novel exact algorithm to estimate a probit spatial generalized linear mixed models (GLMM) that fits binary point-reference spatial data. The spatial dependence in this model is taking into account in the covariance matrix of the location-specific random effects. GLMM are generally hard to estimate due to the high-dimensional integrals involved. Popular methods such as PQL, Laplace, etc. overcome this problem by approximating these integrals from which biased estimators can be obtained. In this study we implement a stochastic version of the EM algorithm that allows to obtain the ML and REML estimates of the parameters in the model without incurring into any kind of approximations, therefore allowing us to obtain more reliable estimators.