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Practical likelihood analysis for spatial generalized linear mixed models
Author(s) -
Bonat Wagner Hugo,
Ribeiro Paulo Justiniano
Publication year - 2016
Publication title -
environmetrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.68
H-Index - 58
eISSN - 1099-095X
pISSN - 1180-4009
DOI - 10.1002/env.2375
Subject(s) - laplace's method , mathematics , markov chain monte carlo , generalized linear mixed model , laplace transform , monte carlo method , generalized linear model , mathematical optimization , marginal likelihood , algorithm , statistics , maximum likelihood , mathematical analysis
We investigate an algorithm for maximum likelihood estimation of spatial generalized linear mixed models based on the Laplace approximation. We compare our algorithm with a set of alternative approaches for two datasets from the literature. The Rhizoctonia root rot and the Rongelap are, respectively, examples of binomial and count datasets modeled by spatial generalized linear mixed models. Our results show that the Laplace approximation provides similar estimates to Markov Chain Monte Carlo likelihood, Monte Carlo expectation maximization, and modified Laplace approximation. Some advantages of Laplace approximation include the computation of the maximized log‐likelihood value, which can be used for model selection and tests, and the possibility to obtain realistic confidence intervals for model parameters based on profile likelihoods. The Laplace approximation also avoids the tuning of algorithms and convergence analysis, commonly required by simulation‐based methods. Copyright © 2015 John Wiley & Sons, Ltd.