Semiparametric Fractional Imputation Using Gaussian Mixture Models for Handling Multivariate Missing Data

Abstract

Item nonresponse is frequently encountered in practice. Ignoring missing data can lose efficiency and lead to misleading inference. Fractional imputation is a frequentist approach of imputation for handling missing data. However, the parametric fractional imputation may be subject to bias under model misspecification. In this article, we propose a novel semiparametric fractional imputation (SFI) method using Gaussian mixture models. The proposed method is computationally efficient and leads to robust estimation. The proposed method is further extended to incorporate the categorical auxiliary information. The asymptotic model consistency and $\sqrt{n}$-consistency of the SFI estimator are also established. Some simulation studies are presented to check the finite sample performance of the proposed method. Supplementary materials for this article are available online.

Acknowledgments

The authors wish to thank the editor, the associate editor, and three anonymous referees for very constructive comments.

Funding

The research of the second author was partially supported by a grant from US National Science Foundation (1733572).