Variance Estimation After Imputation

Abstract

Imputation is commonly used to compensate for item nonresponse. Variance estimation after imputation has generated considerable discussion and several variance estimators have been proposed. We propose a variance estimator based on a pseudo data set used only for variance estimation. Standard complete data variance estimators applied to the pseudo data set lead to consistent estimators for linear estimators under various imputation methods, including without­replacement hot deck imputation and with­replacement hot deck imputation. The asymptotic equivalence of the proposed method and the adjusted jackknife method of Rao and Sitter (1995) is illustrated. The proposed method is directly applicable to variance estimation for two­phase sampling.