A multiple imputation method using population information

Multiple imputation (MI) is effectively used to deal with missing data when the missing mechanism is missing at random. However, MI may not be effective when the missing mechanism is not missing at random (NMAR). In such cases, additional information is required to obtain an appropriate imputation. Pham et al. (2019) proposed the calibrated-<i>δ</i> adjustment method, which is a multiple imputation method using population information. It provides appropriate imputation in two NMAR settings. However, the calibrated-<i>δ</i> adjustment method has two problems. First, it can be used only when one variable has missing values. Second, the theoretical properties of the variance estimator have not been provided. This article proposes a multiple imputation method using population information that can be applied when several variables have missing values. The proposed method is proven to include the calibrated-<i>δ</i> adjustment method. It is shown that the proposed method provides a consistent estimator for the parameter of the imputation model in an NMAR situation. The asymptotic variance of the estimator obtained by the proposed method and its estimator are also given.