Bayesian and likelihood methods for fitting multilevel models with complex level-1 variation

Authors
Browne, W. J., Draper, D., Goldstein, H. and Rasbash, J.
Year
2002
Journal
Computational Statistics and Data Analysis, 39:2, 203-225
DOI
10.1016/S0167-9473(01)00058-5
Abstract

In multilevel modelling it is common practice to assume constant variance at level 1 across individuals. In this paper we consider situations where the level-1 variance depends on predictor variables. We examine two cases using a dataset from educational research; in the first case the variance at level 1 of a test score depends on a continuous “intake score” predictor, and in the second case the variance is assumed to differ according to gender. We contrast two maximum-likelihood methods based on iterative generalised least squares with two Markov chain Monte Carlo (MCMC) methods based on adaptive hybrid versions of the Metropolis-Hastings (MH) algorithm, and we use two simulation experiments to compare these four methods. We find that all four approaches have good repeated-sampling behaviour in the classes of models we simulate. We conclude by contrasting raw- and log-scale formulations of the level-1 variance function, and we find that adaptive MH sampling is considerably more efficient than adaptive rejection sampling when the heteroscedasticity is modelled polynomially on the log scale.

Number of levels
2
Model data structure
Response types
Multivariate response model?
No
Longitudinal data?
No
Further model keywords
Substantive discipline
Substantive keywords
Impact

Paper describes MCMC algorithms for complex level 1 variation

Paper submitted by
William Browne, Bristol Veterinary School, University of Bristol, william.browne@bristol.ac.uk
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