Statistical Modelling 5 (2005), 229–242
Two slice-EM algorithms for ļ¬tting generalized linear
mixed models with binary response
Florin Vaida
Division of Biostatistics and Bioinformatics
Department of Familz and Preventive Medicine
School of Medicine
University of California at San Diego
La Jolla, CA 92093-0717
U.S.A.
vaida@ucsd.edu
Xiao-Li Meng
Department of Statistics
Harvard University
Cambridge, MA 02138
U.S.A.
Abstract:
The celebrated simplicity of the EM algorithm is
somewhat lost in its common use for
generalized linear mixed models (GLMMs) because of
its analytically intractable E-step. A natural and
typical strategy in practice is to implement the E-step
via Monte Carlo by drawing the unobserved random
effects from their conditional distribution as
specified by the E-step. In this paper, we show that further
augmenting the missing data (e.g., the random effects)
used by the M-step leads to a quite attractive and
general slice sampler for implementing the Monte Carlo
E-step. The slice sampler scheme is straightforward
to implement, and it is neither restricted to the
particular choice of the link function (e.g., probit) nor to the
distribution of the random effects (e.g., normal). We
apply this scheme to the standard EM algorithm as
well as to an alternative EM algorithm which treats
the variance-standardized random effects, rather than
the random effects themselves, as missing data. The
alternative EM algorithm does not only have faster
convergence, but also leads to generalized linear model-like
variance estimation, because it converts the
random-effect standard deviations into linear regression
parameters. Using the well-known salamander
mating problem, we compare these two algorithms with each
other, as well as with a variety of methods
given in the literature in terms of the resulting point
and interval estimates.
Keywords:
auxiliary variables; data augmentation;
EM algorithm; Markov chain Monte Carlo; mixed
effect; random effect; slice sampler
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