A Hybrid of Randomized Response Techniques and Crosswise Design with Logistic Regression Analysis

Abstract

Randomized response techniques (RRT) are important tools which are commonly used to protect respondent's privacy and avoid biased answers in surveys on sensitive issues. In this paper, we introduce a randomized response technique with crosswise design (RRTCD), which is a hybrid of the unrelated questions RRT of Greenberg et al. (1969) and the crosswise design (Tian et al. 2007). The RRTCD has an advantage over the RRT of Greenberg et al. (1969) by gaining additional information to develop more efficient estimators. We establish two methods: validation likelihood method and joint conditional likelihood method to analyze data with missing outcome by extending RRTCD by the method of Hsieh et al. (2013). The third method is a transformation method by using available information from answers of survey to estimate. Large sample properties of the proposed estimators are provided. Also, a simulation study on the relative efficiencies of the methods has been conducted. Furthermore, the result of simulation study is supported by two real data examples. Key words: Missing data, randomized response techniques, validation likelihood method, joint conditional likelihood method, transformation method.