Flexible non-randomized response models for survey with sensitive question

Non-randomized response (NRR) models have recently been developed for analyzing sensitive questions. Unlike traditional randomized response models, NRR models do not require a randomizing device, which limits the survey format and reproductivity of results. On the other hand, NRR models introduce a non-sensitive question with binary outcomes in the questionnaire in order to protect privacy and encourage cooperation from respondents. Unfortunately, the proportion of subjects who possess the non-sensitive characteristic is assumed to be known, and the non-sensitive and sensitive questions are assumed to be independent. In this manuscript, we propose three new NRR models, which relax the aforementioned assumptions. Parameter and confidence interval estimates for the sensitive proportion will be developed. Optimal sample size allocations will be investigated. Performance of the proposed NRR models will be studied. A real survey on premarital sexual activity among college/university students in China is conducted to illustrate the proposed methodologies.