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

Categorical variableMissing dataMultivariate statisticsMarkov chain Monte CarloComputer scienceImputation (statistics)GaussianGeneralized linear mixed modelData miningMathematicsAlgorithmArtificial intelligenceBayesian probabilityMachine learning

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Publication Info

Year
2009
Type
article
Volume
9
Issue
3
Pages
173-197
Citations
220
Access
Closed

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Harvey Goldstein, James R. Carpenter, Michael G. Kenward et al. (2009). Multilevel models with multivariate mixed response types. Statistical Modelling , 9 (3) , 173-197. https://doi.org/10.1177/1471082x0800900301

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DOI
10.1177/1471082x0800900301