Implementation and performance issues in the Bayesian and likelihood fitting of multilevel models

Browne, W. J. and Draper, D.
Computational Statistics, 15:3, 391-420

We use simulation studies (a) to compare Bayesian and likelihood fitting methods, in terms of validity of conclusions, in two-level random-slopes regression (RSR) models, and (b) to compare several Bayesian estimation methods based on Markov chain Monte Carlo, in terms of computational efficiency, in random-effects logistic regression (RELR) models. We find (a) that the Bayesian approach with a particular choice of diffuse inverse Wishart prior distribution for the (co)variance parameters performs at least as well-in terms of bias of estimates and actual coverage of nominal 95% intervals-as maximum likelihood methods in RSR models with medium sample sizes (expressed in terms of the number J of level-2 units), but neither approach performs as well as might be hoped wit small J; and (b) that an adaptive hybrid Metropolis-Gibbs sampling method we have developed for use in the multilevel modeling package MlwiN outperforms adaptive rejection Gibbs sampling in the RELR models we have considered, sometimes by a wide margin.

Number of levels
Model data structure
Response types
Multivariate response model?
Longitudinal data?
Further model keywords
Substantive discipline
Substantive keywords

Paper looks at choice of default priors in RSR models and also contains details of adapting Metropolis approach

Paper submitted by
William Browne, Bristol Veterinary School, University of Bristol,
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