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

Harvey Goldstein*, James Carpenter, Michael Kenward

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

3 Citations (Scopus)
288 Downloads (Pure)


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.

Original languageEnglish
Pages (from-to)1071-1081
Number of pages11
JournalJournal of the Royal Statistical Society: Series C
Issue number4
Early online date18 Jan 2018
Publication statusPublished - 1 Aug 2018


  • Markov chain Monte Carlo sampling
  • Millennium Cohort Study
  • Missing data
  • Weighted bootstrap


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