Computational Statistics

, Volume 15, Issue 3, pp 391–420

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

  • William J. Browne
  • David Draper

DOI: 10.1007/s001800000041

Cite this article as:
Browne, W. & Draper, D. Computational Statistics (2000) 15: 391. doi:10.1007/s001800000041

Summary

We use simulation studies (a) to compare Bayesian and likelihood fitting methods, in terms of validity of conclusions, in two-level ramdom-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.

Keywords: Adaptive Metropolis Sampling, Diffuse Prior Distributions, Educational Data, Gibbs Sampling, Hierarchical Modeling, IGLS, Markov Chain Monte Carlo (MCMC), MCMC Efficiency, Maximum Likelihood Methods, Random-Effects Logistic Regression, Random-Slopes Regression, RIGLS, Variance Components.

Copyright information

© Physica-Verlag, Heidelberg 2000

Authors and Affiliations

  • William J. Browne
    • 1
  • David Draper
    • 2
  1. 1.Institute of Education, University of London, 20 Bedford Way, London WC1H 0AL, EnglandGB
  2. 2.Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, EnglandGB