Evaluating Performance of Mean Estimators of Sensitive Variables under Measurement Errors with Respect to Efficiency and Respondent Privacy

RRT (Randomized Response Technique, Warner (1965), JASA) Models are commonly used in surveys where we ask sensitive questions. In an RRT model, a respondent is asked to provide a scrambled response. An Optional RRT model (Gupta et al. (2002), JSPI) is a variation of the usual RRT model where only those respondents provide a scrambled response who consider the question sensitive. Others provide a truthful response. However, the researcher does not who provided what kind of response. The principal idea here is that a question may be sensitive for one respondent but not for another, so why force everyone to provide a scrambled response.

In this study, our primary focus is on examining if using optional RRT models as opposed to non-optional RRT models for mean estimation of a sensitive variable when measurement errors are present, produces more efficient estimators. A unified measure of model efficiency and respondent privacy will be used in this comparison.