# Modified binary randomized response technique models

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
Jeong Sep Sihm (Creator)
Institution
The University of North Carolina at Greensboro (UNCG )
Web Site: http://library.uncg.edu/
Sat Gupta

Abstract: Social Desirability Bias (SDB) is the tendency in respondents to answer questions untruthfully in the hope of giving good impression to others. SDB occurs when the survey question is highly sensitive or personal, and responses cause sample statistics to systematically overestimate or underestimate corresponding population parameters. The Randomized Response Technique (RRT) is one of several methods to get around SDB in surveys involving sensitive questions in a face-to-face interview. We first review some of the well-established binary response RRT models including the two-parameter models such as the two-stage RRT model and the optional RRT model. Then, we examine an optional RRT model based on the unrelated question RRT as presented by Gupta, Tuck, Spears Gill, and Crowe (2013). Also, we show another optional RRT model based on the two-stage RRT. Next, we carry out efficiency comparisons between these models and show simulation results. While these two models are all based on the split-sample approach to estimate two unknown parameters of interest ( $\pi$ and $\omega$—the prevalence of sensitive characteristic and the sensitivity level of the underlying question respectively), the next two models utilize the two-question approach instead. One of them relies on the unrelated question RRT model. And the other relies on the two-stage optional RRT model. Again, efficiencies of estimators are compared and simulation results are provided. In the end, simulation results and figures are presented and some conclusions are made regarding which estimator performs better. It turns out that the two-stage optional indirect RRT model with two-question approach performs better than other binary optional RRT models.