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Goldstein, Harvey; Carpenter, James; Kenward, Michael G.; Levin, Kate A.

Multilevel models with multivariate mixed response types. (English) Zbl 07257700

Stat. Model. 9, No. 3, 173-197 (2009).
Summary: 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.

Cited in 17 Documents

MSC:

62-XX Statistics

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

Software:

Matlab; GLLAMM; MLwiN; Mplus; WinBUGS; Stata
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Full Text: DOI

References:

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