On estimation and prediction for spatial generalized linear mixed models.
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.
Zhang
Hao
H
Program in Statistics, Washington State University, Pullman 99164-3144, USA. zhanghao@wsu.edu
D000465:Algorithms; D003198:Computer Simulation; D001467:Hordeum / Q000382:microbiology; D015233:Models, Statistical; D009010:Monte Carlo Method; D009181:Mycoses / Q000453:epidemiology / Q000382:microbiology; D010935:Plant Diseases / Q000382:microbiology; D018517:Plant Roots / Q000382:microbiology; D011237:Predictive Value of Tests