Statistical Modelling 9 (2009), 173197
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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