On the construction of imputation classes in surveys

This paper explores the problem of the construction of imputation classes using the score method, sometimes called predictive mean stratification or response propensity stratification, depending on the context. This method was studied in Thomsen (1973), Little (1986) and Eltinge & Yansaneh (1997). We use a different framework to evaluate the properties of the resulting imputed estimator of a population mean. In our framework, we condition on the realized sample. This enables us to considerably simplify our theoretical developments in the frequent situation where the boundaries and the number of classes are sample-dependent. We find that the key factor for reducing the non-response bias is to form classes homogeneous with respect to the response probabilities and/or the conditional expectation of the variable of interest. In the latter case, the non-response/imputation variance is also reduced. Finally, we performed a simulation study to fully evaluate various versions of the score method and to compare them with a cross-classification method, which is frequently used in practice. The results showed the superiority of the score method in general.