A hot deck imputation procedure for multiply imputing nonignorable missing data: The proxy pattern-mixture hot deck

Hot deck imputation is a common method for handling item nonresponse in surveys, but most implementations assume data are missing at random (MAR). A new hot deck method for imputation of a continuous partially missing outcome variable that harnesses the power of available covariates but does not assume data are MAR is proposed. A parametric model is used to create predicted means for both donors and donees under varying assumptions on the missing data mechanism, ranging from MAR to missing not at random (MNAR). For a given assumption on the missingness mechanism, the predicted means are used to define distances between donors and donees and probabilities of selection proportional to those distances. Multiple imputation using the hot deck is performed to create a set of completed data sets, using an approximate Bayesian bootstrap to ensure “proper” imputations. This new hot deck method creates an intuitive sensitivity analysis where imputations may be performed under MAR and under varying MNAR mechanisms, and the resulting impact on inference can be evaluated. In addition, a donor quality metric is proposed to help identify situations where close matches of donor to donee are not available, which can occur under strong MNAR assumptions. Bias and coverage of estimates from the proposed method are investigated through simulation and the method is applied to estimation of income in the Ohio Medicaid Assessment Survey. Results show that the method performs best when covariates are at least moderately predictive of the partially missing outcome, and without such covariates it effectively reduces to a simple random hot deck for all missingness assumptions.