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Multilevel models with multivariate mixed response types

University of Bristol. E-mail: h.goldstein{at}bristol.ac.uk

James Carpenter

London School of Hygiene and Tropical Medicine

Michael G Kenward

Kate A Levin

University of Edinburgh

We build upon the existing literature to formulate a class of models for multivariate mixtures of Gaussian, ordered or unordered categorical responses and continuous distributions that are not Gaussian, each of which can be defined at any level of a multilevel data hierarchy. We describe a Markov chain Monte Carlo algorithm for fitting such models. We show how this unifies a number of disparate problems, including partially observed data and missing data in generalized linear modelling. The two-level model is considered in detail with worked examples of applications to a prediction problem and to multiple imputation for missing data. We conclude with a discussion outlining possible extensions and connections in the literature. Software for estimating the models is freely available.

Key Words: Box–Cox transformation • data augmentation • data coarsening • latent Gaussian model • maximum indicant model • MCMC • missing data • mixed response models • multilevel • multiple imputation • multivariate • normalising transformations • partially known values • prediction • prior-informed imputation • probit model

Statistical Modelling, Vol. 9, No. 3, 173-197 (2009)
DOI: 10.1177/1471082X0800900301


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