Abstract
An appealing feature of multiple imputation is the simplicity of the rules for combining the multiple complete-data inferences into a final inference, the repeated-imputation inference (Rubin, 1987). This inference is based on a t distribution and is derived from a Bayesian paradigm under the assumption that the complete-data degrees of freedom, νcom, are infinite, but the number of imputations, m, is finite. When νcom is small and there is only a modest proportion of missing data, the calculated repeated-imputation degrees of freedom, νm, for the t reference distribution can be much larger than νcom, which is clearly inappropriate. Following the Bayesian paradigm, we derive an adjusted degrees of freedom, ν̃m, with the following three properties: for fixed m and estimated fraction of missing information, ν̃m monotonically increases in νcom; ν̃m is always less than or equal to νcom; and ν̃m equals νm when νcom is infinite. A small simulation study demonstrates the superior frequentist performance when using ν̃m rather than νm.
Keywords
Imputation (statistics)Frequentist inferenceMathematicsDegrees of freedom (physics and chemistry)InferenceMissing dataStatisticsBayesian probabilityBayesian inferenceApplied mathematicsArtificial intelligenceComputer science
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Publication Info
- Year
- 1999
- Type
- article
- Volume
- 86
- Issue
- 4
- Pages
- 948-955
- Citations
- 769
- Access
- Closed
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Cite This
John Barnard
(1999).
Miscellanea. Small-sample degrees of freedom with multiple imputation.
Biometrika
, 86
(4)
, 948-955.
https://doi.org/10.1093/biomet/86.4.948
Identifiers
- DOI
- 10.1093/biomet/86.4.948