An Optimal Stratification Method for Addressing Nonresponse Bias in Bayesian Adaptive Survey Design

In a probability sampling survey, adaptive data collection strategies may be used to obtain a response set that minimizes nonresponse bias within budget constraints. Previous research has stratified the target population into subgroups defined by categories of auxiliary variables observed for the entire population, and tailored strategies to obtain similar response rates across subgroups. However, if the auxiliary variables are weakly correlated with the target survey variables, optimizing data collection for these subgroups may not reduce nonresponse bias and may actually increase the variance of survey estimates. In this paper, we propose a stratification method to identify subgroups by: (1) predicting values of target survey variables from auxiliary variables, and (2) forming subgroups with different response propensities based on the predicted values of target survey variables. By tailoring different data collection strategies to these subgroups, we can obtain a response set with less variation in response propensities across subgroups that are directly relevant to the target survey variables. Given this rationale, we also propose to measure nonresponse bias by the coefficient of variation of response propensities estimated from the predicted target survey variables. A case study using the Dutch Health Survey shows that the proposed stratification method generally produces less variation in response propensities with respect to the predicted target survey variables compared to traditional methods, thereby leading to a response set that better resembles the population.