Downward calibration property of estimated response propensities

Abstract

We consider four methods for estimating response propensities: three traditional ones (linear, logistic, probit) and one more recent, a decision tree method. We show that some but not all the methods produce estimates that calibrate sample totals of auxiliary variables down to the response set totals. The downward calibration property reveals interesting relationships between estimated propensities, auxiliary variables, and true response probabilities. However, the property itself does not guarantee more accurate propensity estimation. Our simulation study shows that the accuracy of the estimation method depends primarily on the relationship nature between true response probabilities and auxiliary variables.