文档介绍：JSS Journal of Statistical Software
January 2010, Volume 33, Issue 2. /
MCMC Methods for Multi-Response Generalized
Linear Mixed Models: The MCMCglmm R Package
Jarrod D. Hadfield
University of Edinburgh
Abstract
Generalized linear mixed models provide a flexible framework for modeling a range of
data, although with non-Gaussian response variables the likelihood cannot be obtained
in closed form. Markov chain Monte Carlo methods solve this problem by sampling
from a series of simpler conditional distributions that can be evaluated. The R package
MCMCglmm implements such an algorithm for a range of model fitting problems. More
than one response variable can be analyzed simultaneously, and these variables are allowed
to follow Gaussian, Poisson, multi(bi)nominal, exponential, zero-inflated and censored dis-
tributions. A range of variance structures are permitted for the random effects, including
interactions with categorical or continuous variables (., random regression), and more
complicated variance structures that arise through shared ancestry, either through a pedi-
gree or through a phylogeny. Missing values are permitted in the response variable(s) and
data can be known up to some level of measurement error as in meta-analysis. All simu-
lation is done in C/ C++ using the CSparse library for sparse linear systems.
Keywords: MCMC, linear mixed model, pedigree, phylogeny, animal model, multivariate,
sparse, R.
Due to their flexibility, linear mixed models are now widely used across the sciences (Brown
and Prescott 1999; Pinheiro and Bates 2000; Demidenko 2004). However, generalizing these
models to non-Gaussian data has proved difficult because integrating over the random effects
is intractable (McCulloch and Searle 2001). Although techniques that approximate these
integrals (Breslow and Clayton 1993) are now popular, Markov chain Monte Carlo (MCMC)
methods provide an alternative strategy for marginalizing the random effects