2018 Volume 47 Issue 1 Pages 1-16
Multiple imputation is one of the most popular methods to deal with missing data, and its use has been increasing in various fields, such as medical studies and social studies. Although multiple imputation is rather appealing in practice since it is possible to use ordinary statistical methods for complete dataset once the missing values are fully imputed, the method of imputation is still problematic. If the missing values are imputed from some parametric model, the validity of imputation is not necessarily ensured and the final estimate for a parameter of interest can be biased unless the parametric model is correctly specified. In this paper, we propose a method for multiple imputation to obtain a consistent (or asymptotically unbiased) final regression estimate even if the imputation model is misspecified when the response variable is missing. The key idea is to use an imputation model from which the imputation values are easily produced and to make a proper adjustment in likelihood function after the imputation by using the density ratio between the imputation model and the true conditional density function for the missing variable as a weight. We also propose a new method to improve our estimation using a cross-validation. The performance of our method is evaluated by both theory and simulation studies.
