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On Estimation and Prediction for Spatial Generalized Linear Mixed Models

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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.
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Keywords: EM algorithm; Generalized linear mixed models; Metropolis-Hastings algorithm; Spatial interpolation; Variogram

Document Type: Research Article

Affiliations: Program in Statistics, Washington State University, Pullman, Washington 99164-3144, U.S.A., Email: [email protected]

Publication date: 2002-03-01

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