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Why, When, and How to Weight When Imputing (308015)

Keywords: prediction model, selection model, ignorable, remainder weight

There are two weights to consider when weighting for nonresponse: the sampling weight (which here includes adjustments for unit nonresponse) and the item-nonresponse weight. When imputing with a predicted value based on a model, if the prediction model holds in the population and the sampling and weighting item response mechanisms are ignorable (i.e., neither are functions of the variable being imputed after being conditioning on this explanatory variables of the prediction model), then weights need not be used in the imputation. Otherwise, they are needed. Alternatively, even when the prediction model does not hold in the population, incorporating weights when fitting the prediction model can still result in the near unbiasedness of estimates in some sense if the sampling weight of a unit is approximately equal to the inverse of the probability of the unit being in the unit-respondent sample and the item-probability weight is approximately equal to the inverse of the conditional probability of item response minus 1. We will see why and how to use this remainder weight (so-called because we are predicting values in what remains in the population after item response of the remaining sample) in practice and propose a method for estimating variances with imputed values.