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
Affiliated Institutions
Related Publications
Multiple Imputation of Missing Values
Following the seminal publications of Rubin about thirty years ago, statisticians have become increasingly aware of the inadequacy of “complete-case” analysis of datasets with m...
Multiple Imputation for Nonresponse in Surveys
Tables and Figures. Glossary. 1. Introduction. 1.1 Overview. 1.2 Examples of Surveys with Nonresponse. 1.3 Properly Handling Nonresponse. 1.4 Single Imputation. 1.5 Multiple Imp...
Imputing missing covariate values for the Cox model
Abstract Multiple imputation is commonly used to impute missing data, and is typically more efficient than complete cases analysis in regression analysis when covariates have mi...
Multiple Imputation in Practice
Missing data frequently complicates data analysis for scientific investigations. The development of statistical methods to address missing data has been an active area of resear...
Imputations of Missing Values in Practice: Results from Imputations of Serum Cholesterol in 28 Cohort Studies
Missing values, common in epidemiologic studies, are a major issue in obtaining valid estimates. Simulation studies have suggested that multiple imputation is an attractive meth...
Publication Info
- Year
- 1999
- Type
- article
- Volume
- 86
- Issue
- 4
- Pages
- 948-955
- Citations
- 769
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
769
OpenAlex
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