Multiple Auxiliary Variables in Nonresponse Adjustment

Prior work has shown that effective survey nonresponse adjustment variables should be highly correlated with both the propensity to respond to a survey and the survey variables of interest. In practice, propensity models are often used for nonresponse adjustment with multiple auxiliary variables as predictors. These auxiliary variables may be positively or negatively associated with survey participation, they may be correlated with each other, and can have positive or negative relationships with the survey variables. Yet the consequences for nonresponse adjustment of these conditions are not known to survey practitioners. Simulations are used here to examine the effects of multiple auxiliary variables with opposite relationships with survey participation and the survey variables. The results show that bias and mean square error of adjusted respondent means are substantially different when the predictors have relationships of the same directions compared to when they have opposite directions with either propensity or the survey variables. Implications for nonresponse adjustment and responsive designs will be discussed.