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Small-Sample Degrees of Freedom with Multiple Imputation

John Barnard and Donald B. Rubin
Biometrika
Vol. 86, No. 4 (Dec., 1999), pp. 948-955
Published by: Oxford University Press on behalf of Biometrika Trust
Stable URL: http://www.jstor.org/stable/2673599
Page Count: 8
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Small-Sample Degrees of Freedom with Multiple Imputation
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Abstract

An appealing feature of multiple imputation is he 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.

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