Improved estimation methods for unrelated question randomized response techniques

ABSTRACT

The randomized response technique (RRT) is an important tool, commonly used to avoid biased answers in survey on sensitive issues by preserving the respondents’ privacy. In this paper, we introduce a data collection method for survey on sensitive issues combining both the unrelated-question RRT and the direct question design. The direct questioning method is utilized to obtain responses to a non sensitive question that is related to the innocuous question from the unrelated-question RRT. These responses serve as additional information that can be used to improve the estimation of the prevalence of the sensitive behavior. Furthermore, we propose two new methods for the estimation of the proportion of respondents possessing the sensitive attribute under a missing data setup. More specifically, we develop the weighted estimator and the weighted conditional likelihood estimator. The performances of our estimators are studied numerically and compared with that of an existing one. Both proposed estimators are more efficient than the Greenberg's estimator. We illustrate our methods using real data from a survey study on illegal use of cable TV service in Taiwan.

KEYWORDS:

• Randomized response techniques
• validation likelihood estimator
• weighted conditional likelihood estimator
• weighted estimator.

Acknowledgments

The authors are grateful to an associate editor and two referees for their helpful comments that improved the presentation. The research of S.M. Lee and S.H. Hsieh were supported by the Ministry of Science and Technology (MOST) of Taiwan, ROC (101-2118-M-035-004-MY2 and 100-2118-M-001-001-MY2, respectively).