Greetings, and apologies as usual for cross-posting.
FYI, the following multilevel/hierarchical modeling paper is available for
downloading in PostScript format (537K) at
http://www.bath.ac.uk/~masdd
Comments, either to me at [log in to unmask] or to Bill Browne at
[log in to unmask], would be welcome.
Browne WJ, Draper D (1999). A comparison of Bayesian and likelihood methods
for fitting multilevel models. Under review at JRSS-B.
Abstract
We use simulation studies to compare Bayesian and likelihood methods for
fitting variance-components and random-effects logistic regression (RELR)
models. The likelihood approaches we examine are based on iterative
generalised least squares (IGLS) and restricted IGLS (RIGLS) for Gaussian
outcomes, and marginal and penalised quasi-likelihood (MQL and PQL) for
Bernoulli outcomes; our Bayesian methods are based on Markov chain Monte
Carlo (MCMC) estimation (using adaptive hybrid Metropolis-Gibbs sampling for
RELR models) and a variety of prior distributions, both diffuse (inverse
gamma and uniform priors for variance components) and informative. For
evaluation criteria we consider bias of point estimates and nominal versus
actual coverage of interval estimates. We find that in both classes of models
(a) both likelihood and Bayesian approaches can be made to produce nearly
unbiased estimates, but (b) Bayesian diffuse-prior intervals have coverage as
good as or better than that of likelihood intervals, and Bayesian actual
coverage with the inverse gamma prior is close to nominal. In both model
classes we find (not surprisingly) that informative priors lead to either
better or worse performance than diffuse-Bayes approaches, depending on the
quality of the prior information. We therefore recommend the use of maximum
likelihood estimation (for its computational speed) during the model
exploration phase of a multilevel study, and Bayesian estimation using MCMC
to produce final publishable results, either with an appropriate diffuse
prior when little is known about the parameters a priori (to obtain good
calibration) or with an informative prior if there is good reason to believe
that the prior information will retrospectively be seen to be on target (to
obtain greater accuracy).
Keywords: Adaptive MCMC, bias, diffuse priors, hybrid Metropolis-Gibbs
sampling, IGLS, informative priors, interval coverage, MQL, PQL, RIGLS,
random-effects logistic regression, variance-components models
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Prof. David Draper
Statistics Group web http://www.bath.ac.uk/~masdd
Department of email [log in to unmask]
Mathematical Sciences phone UK (01225) 826 222, nonUK +44 1225 826 222
University of Bath fax UK (01225) 826 492, nonUK +44 1225 826 492
Claverton Down
Bath BA2 7AY England
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