[R] summary: Generalized linear mixed model software
Jason Liao
jg_liao at yahoo.com
Fri Apr 12 16:42:53 CEST 2002
Thanks to those who responded to my inquiry about generalized linear
mixed models on R and S-plus. Before I summarize the software, I note
that there are several ways of doing statistical inference for
generalized linear mixed models:
(1)Standard maximum likelihood estimation, computationally intensive
due to intractable likelihood function
(2) Penalized quasi likelihood or similar approximations (Breslow &
Clayton, 1993; Lee & Nelder, 1999, Schall 1991). This method is not
good for binomial outcomes in particular. Theoretically, it is
consistent when the cluster size increases. It is not consistent when
the number of clusters increases while the size of each cluster remain
constant. The standard MLE (1) is consistent under either increasing
cluster size or the number of clusters. For theoretical result, see
Lin, X. & Breslow N.E. (1996) in JASA. For empirical demonstartion, see
Carlin et al (2001) in Biostatistics.
(3)Bayesian approach. See for example, Clayton, D. G. (1996).
Generalized linear mixed models. In Markov Chain Monte Carlo in
Practice, Ed W.R. Gilks, S. Richardson & D.J. Spiegelhalter, pp.
275-301. London: Chapman and Hall.
(4)REML estimation in GLMM. I will have a paper in June issue of
Bioemtrika. REML estimation has the same asymptotic property as
standard MLE but less bias for finite samples. Of course, one can argue
that Bayesian formulation automatically generates REML for variance
components.
Now the software.
PQL and variations: GLME in beta by José Pinheiro, reglm by Gordon
Smyth, glmmPQL in package MASS by Venables & Ripley
Bayesian method: GLMMgibbs and BUGS (not a R or S-plus package).
Standard MLE: glmm (only a random intercept) in one of Jim Lindsey's
packages?
Ok, this still leaves us without a good way of doing standard MLE. I
have programmed standard MLE using R. It takes 6 minutes for a
clustered binary outcome dataset, with 50 clusters and each cluster
with 10 binary responses, 6 fixed effects and two random effects for
each cluster.
=====
Jason G. Liao, Ph.D.
Division of Biometrics
University of Medicine and Dentistry of New Jersey
335 George Street, Suite 2200
New Brunswick, NJ 08903-2688
phone (732) 235-9748, fax (732) 235-9777
http://www.geocities.com/jg_liao
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