Small-sample degrees of freedom with multiple imputation

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 o n a t distribution and is derived from a Bayesian paradigm under the assump tion that the complete-data degrees of freedom, v(com), are infinite, but t he number of imputations, m, is finite. When v(com) is small and there is o nly a modest proportion of missing data, the calculated repeated-imputation degrees of freedom, v(m), for the t reference distribution can be much lar ger than v(com), which is clearly inappropriate. Following the Bayesian par adigm, we derive an adjusted degrees of freedom, (v) over tilde(m), with th e following three properties: for fixed m and estimated fraction of missing information, (v) over tilde(m) monotonically increases in v(com); (v) over tilde(m) is always less than or equal to v(com); and (v) over tilde(m) equ als v(m) when v(com) is infinite. A small simulation study demonstrates the superior frequentist performance when using (v) over tilde(m) rather than v(m).