A degrees-of-freedom approximation in multiple imputation. (English) Zbl 0995.62006

Lipsitz, Stuart R.; Parzen, Michael; Zhao, Lue Ping

J. Stat. Comput. Simulation 72, No. 4, 309-318 (2002).

Summary: When using multiple imputation to form confidence intervals with missing data, D.B. Rubin and N. Schenker [J. Am. Stat. Assoc. 81, 366-374 (1986; Zbl 0615.62011)] proposed using a \(t\)-distribution with approximate degrees-of-freedom which is a function of the number of multiple imputations and the within and between imputation variance. In this \(t\)-approximation, Rubin and Schenker assume there are a finite number of multiple imputations, but an infinite number of observations in the sample. We propose a further degrees-of-freedom approximation which is a function of the within and between imputation variance, the number of multiple imputations, and the number of observations in the sample. When the number of observations in the sample is small, our approximate degrees-of-freedom may be more appropriate, as seen in our simulations.

MSC:

62D05

Sampling theory, sample surveys

Keywords:

Bayesian bootstrap; ignorable non-response