Inconsistent Regression and Nonresponse Bias: Exploring Their Relationship as a Function of Response Imbalance

One objective of adaptive data collection is to secure a better balanced survey response. Methods exist for this purpose, including balancing with respect to selected auxiliary variables. Such variables are also used at the estimation stage for (calibrated) nonresponse weighting adjustment. Earlier research has shown that the use of auxiliary information at the estimation stage can reduce bias, perhaps considerably, but without eliminating it. The question is: would it have contributed further to bias reduction if, prior to estimation, that information had also been used in data collection, to secure a more balanced set of respondents? If the answer is yes, there is clear incentive, from the point of view of better accuracy in the estimates, to practice adaptive survey design, otherwise perhaps not. A key question is how the regression relationship between the survey variable and the auxiliary vector presents itself in the sample as opposed to the response. Strength in the relationship is helpful but is not the only consideration. The dilemma with nonresponse is one of inconsistent regression: a regression model appropriate for the sample often fails for the responding subset, because nonresponse is selective, non-random. In this article, we examine how nonresponse bias in survey estimates depends on regression inconsistency, both seen as functions of response imbalance. As a measure of bias we use the deviation of the calibration adjusted estimator from the unbiased estimate under full response. We study how the deviation and the regression inconsistency depend on the imbalance. We observe in empirical work that both can be reduced, to a degree, by efforts to reduce imbalance by an adaptive data collection.