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On Estimation and Prediction for Spatial Generalized Linear Mixed Models
Author(s) -
Zhang Hao
Publication year - 2002
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.0006-341x.2002.00129.x
Subject(s) - generalized linear mixed model , kriging , monte carlo method , mathematics , statistics , gaussian , random effects model , algorithm , computer science , medicine , meta analysis , physics , quantum mechanics
Summary. We use spatial generalized linear mixed models (GLMM) to model non‐Gaussian spatial variables that are observed at sampling locations in a continuous area. In many applications, prediction of random effects in a spatial GLMM is of great practical interest. We show that the minimum mean‐squared error (MMSE) prediction can be done in a linear fashion in spatial GLMMs analogous to linear kriging. We develop a Monte Carlo version of the EM gradient algorithm for maximum likelihood estimation of model parameters. A by‐product of this approach is that it also produces the MMSE estimates for the realized random effects at the sampled sites. This method is illustrated through a simulation study and is also applied to a real data set on plant root diseases to obtain a map of disease severity that can facilitate the practice of precision agriculture.