Bayesian models for weighted data with missing values: a bootstrap approach. Issue 4 (18th January 2018)

• Record Type: Journal Article
• Authors: Goldstein, Harvey; Carpenter, James; Kenward, Michael G.
• Is Part Of: Journal of the Royal Statistical Society. Volume 67:Issue 4(2018:Aug.)
• Page Start: 1071
• Page End: 1081
• Publication Date: 2018-01-18
• Subjects: Markov chain Monte Carlo sampling -- Millennium Cohort Study -- Missing data -- Weighted bootstrap; Statistics -- Periodicals; 519.5
• DOI: 10.1111/rssc.12259
• Languages: English
• ISSNs: 0035-9254

Abstract

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.