Bayesian models for weighted data with missing values: a bootstrap approach

Many data sets, especially from surveys, are made available to users with weights. Where the derivation of such weights is known, this information can often be incorporated in the user's substantive model (model of interest). When the derivation is unknown, the established procedure is to carry...

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Bibliographic Details
Published in:Journal of the Royal Statistical Society Series C: Applied Statistics 2018-08, Vol.67 (4), p.1071-1081
Main Authors: Goldstein, Harvey, Carpenter, James, Kenward, Michael G.
Format: Article
Language:English
Subjects:
Bayesian analysis
Bias
Cohort analysis
Computer simulation
Derivation
Markov analysis
Markov chain Monte Carlo sampling
Markov chains
Millennium Cohort Study
Missing data
Monte Carlo simulation
Simulation
Weighted bootstrap
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Summary:Many data sets, especially from surveys, are made available to users with weights. Where the derivation of such weights is known, this information can often be incorporated in the user's substantive model (model of interest). When the derivation is unknown, the established procedure is to carry out a weighted analysis. However, with non-trivial proportions of missing data this is inefficient and may be biased when data are not missing at random. Bayesian approaches provide a natural approach for the imputation of missing data, but it is unclear how to handle the weights. We propose a weighted bootstrap Markov chain Monte Carlo algorithm for estimation and inference. A simulation study shows that it has good inferential properties. We illustrate its utility with an analysis of data from the Millennium Cohort Study.
ISSN:0035-9254
1467-9876
DOI:10.1111/rssc.12259