Combining answers to direct and indirect questions: An implementation of Kuk’s randomized response model

In this article, we propose a two folded approach for estimation of the population proportion of a sensitive attribute. The rationale of proposed technique is to give respondents choice if they want to avail randomized device or not. Thus, our technique is inherently capable of entertaining the responses attained through direct questioning and by employing randomization device, as well. We believe that free to choose policy will be helpful to develop a curtsy between interviewer and respondent (which is highly desirable, especially when sensitive issue is under consideration) and thus enhances the survey reliability. The proposed technique is developed for simple random sampling, at first, and then extended to stratified random sampling. The superior performance of proposed technique in comparison to the Kuk (1990) method is demonstrated throughout this article. We provide algebraic, graphical and numerical evidences in support of our proposed technique. Furthermore, we also offer cost analysis considering most commonly used cost functions in the literature of survey research.