Fractional Regression Nearest Neighbor Imputation

Sample surveys typically gather information on a sample of units from a finite population and assign survey weights to the sampled units. Survey frequently have missing values for some variables for some units. Fractional regression imputation creates multiple values for each missing value by adding randomly selected empirical residuals to predicted values. Fractional imputation methods assign fractional survey weights to the imputed values. Fractional nearest neighbor imputation randomly selects multiple donors for each missing value from a set of nearest neighbors. The fractional regression nearest neighbor imputation method developed in this paper imputes more than one value for each missing item using donors that are neighbors selected by a distance calculation involving both regression model predictions and variables used in other nearest neighbor methods. Different distance function specifications, which can involve both observed and predicted values, produce alternative imputation procedures. In this paper, we compare the performance of fractional imputation methods, including fractional regression nearest neighbor imputation, in a simulation study. In addition, we examine empirically the performance of the imputation methods studied in this paper on a subset of data from the Iowa Family Transitions Project under different missing data assumptions.