Statistical Modelling 9 (2009), 173–197

Multilevel models with multivariate mixed response types

Harvey Goldstein
Graduate School of Education
University of Bristol
Bristol, BS8 1JA
U.K.
eMail: h.goldstein@bristol.ac.uk

James Carpenter
London School of Hygiene and Tropical Medicine

Michael kenward and Kate A Levin
University of Edinburgh

Abstract:

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.

Keywords:

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

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