Statistical Modelling 2 (2002), 23–38
Fitting exponential family mixed models
Juni Palmgren
Mathematical Statistics, Stockholm University,
S–10691 Stockholm
Sweden
e-mail: juni@mathematik.su.se
and
Medical Epidemiology, Karolinska Institutet,
Sweden
Samuli Ripatti,
Mathematical Statistics, Stockholm University,
Sweden
and
Medical Epidemiology, Karolinska Institutet,
Sweden
Abstract:
The generalized
linear model (McCullagh and Nelder, 1972) and the semiparametric multiplicative
hazard model (Cox, 1972) have significantly influenced the way in which
statistical modelling is taught and practized. Common for the two model
families is the assumption that conditionally on covariate information
(including time) the observations are independent. The obvious difficulty in
identifying and measuring all relevant covariates has pushed for methods that
can jointly handle both mean and dependence structures. The early 1990s saw a
myriad of approaches for dealing with multivariate generalized linear models.
More recently, the hazard models have been extended to multivariate settings.
Here we review (i) penalized likelihoods, (ii) Monte Carlo EM, and (iii)
Bayesian Markov chain Monte Carlo methods for fitting the generalized linear
mixed models and the frailty models, and we discuss the rationale for choosing
between the methods. The similarities of the toolboxes for these two
multivariate model families open up for a new level of generality both in
teaching and applied research. Two examples are used for illustration,
involving censored failure time responses and Poisson responses,
repectively.
Keywords:
Frailty; Generalized linear mixed model; Markov chain Monte Carlo;
Monte Carlo EM;
Penalized likelihood; Random effects.
Downloads:
Data and Software in
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Software uses R,
a (free) language and environment for statistical computing and graphics. For
more on the R-system refer to:
http://www.r-project.org
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