Statistical Modelling 1 (2001), 103–124
Multiple membership multiple classification (MMMC) models
William J.Browne, Harvey Goldstein and JonRasbash
Institute of Education, University of London,
20 Bedford Way, London,
WC1H 0AL, UK
email: W.Browne@sta02.ioe.ac.uk
Abstract:
In the social and
other sciences many data are collected with a known but
complex underlying structure. Over the past two decades there has been
an increase in the use of multilevel modelling techniques that account
for nested data structures. Often however the underlying data
structures are more complex and cannot be fitted into a nested structure.
First there are cross-classified models where the classifications in the data
are not nested. Secondly we consider multiple membership models where
an observation does not belong simply to one member of a
classification. These two extensions when combined allow us to
fit models to a large array of underlying structures. Existing frequentist
modelling approaches to fitting such data have some important computational
limitations. In this paper we consider ways of overcoming such
limitations using Bayesian methods, since Bayesian model fitting is
easily accomplished using Monte Carlo Markov chain (MCMC) techniques.
In examples where we have been able to make direct comparisons,
Bayesian methods in conjunction with suitable `diffuse' prior
distributions lead to similar inferences to existing frequentist techniques.
In this paper we illustrate our techniques with examples in the fields
of education, veterinary epidemiology, demography, and public health
illustrating the diversity of models that fit into our
framework.
Keywords:
Multilevel Modelling,
Hierarchical Modelling,
Markov Chain Monte Carlo (MCMC),
Cross classified models,
multiple membership models,
complex data structures,
Bayesian GLMM modelling
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