A Quantitative Optional Unrelated-Question Randomized Response Model
by
Tracy Spears Gill
University of North Carolina at Greensboro
Coauthors: Anna Tuck, Sat Gupta, Mary Crowe

Obtaining accurate information is essential in all surveys, but can be problematic when subjects face sensitive or incriminating questions. Despite assurances of anonymity, subjects often give untruthful responses, leading to serious response bias. One method of reducing this bias is the Unrelated Question Randomized Response Technique (RRT), in which a predetermined proportion of subjects are randomized to answer an innocuous unrelated question with known prevalence. Subjects are provided a higher level of anonymity because the researcher does not know which question (sensitive or innocuous) any individual answered, although the mean of the sensitive question can be estimated at the aggregate level.

We propose a generalization of the Unrelated Question RRT model, to be used with a quantitative question, which takes into account the fact that a question may be very sensitive to one person, but not at all sensitive to another. We estimate the Mean Prevalence of a sensitive behavior, as well as the Sensitivity Level of the underlying question (proportion of subjects who consider the question sensitive), and show that both are asymptotically normal and unbiased. Computer simulations validate these theoretical results, while a field test of the method is planned for fall 2012 using a survey topic sensitive to undergraduate students.

Date received: June 22, 2012