Exact REML Estimation Procedure in the Spatial Probit Normal Model for Binary Outcomes

• Activity Number: 353
• Type: Contributed
• Date/Time: Tuesday, August 3, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Cristian Meza*+ and Rolando De la Cruz and Susana Eyheramendy and Felipe Osorio
• Companies: Universidad de Valparaiso and Pontificia Universidad Católica de Chile and Pontificia Universidad Católica de Chile and Universidad de Valparaiso
• Keywords: Spatial GLMM ; Probit ; Binary outcomes ; REML ; Stochastic EM algorithm

Abstract

Generalized linear mixed models (GLMM) form a very general class of random effects models for discrete and continuous responses in the exponential family. A popular class of GLMM is the probit-normal model for analyzing binary data. A convenient way to model such data consists of discretizing a latent continuous distribution with a threshold. On the other hand, spatial GLMMs are commonly used for count or proportion data acquired over a continuous spatial domain. Non-Gaussian point-referenced spatial data are frequently modeled using GLMM with location-specific random effects where the spatial dependence is introduced in the covariance matrix of the random effects. In this work, it is showed how Restricted Maximum Likelihood (REML) estimates of the fixed effects and variance components can be computed in an exact way using a stochastic approximation of EM algorithm in this kind of model.