A new improved randomized response model with application to compulsory motor insurance

One of the challenges, when investigating sensitive attributes, or information that people tend not to disclose, through surveys is the ethical obligation to preserve the privacy of respondents. Although the randomized response method, originally suggested by Warner, allows estimating the proportion of such attributes within the population while maintaining confidentiality, the variance of the estimate consistently increases if the likelihood of selecting the question about sensitive attribute increases. The purpose of this research is to introduce a new three-stage RR model which provides an efficient alternative to Warner's model that allows more credibility from a practical perspective and apply the model to estimate noncompliance ratio in compulsory motor insurance. For the two models, a measure of privacy protection was calculated and a relation between this measure and the efficiency of both models was introduced. Efficiency comparisons indicate that the proposed model can always be made more efficient than both Warner's and Mangat & Singh's RR models. The proposed model, with specific parameter selection, was applied on a selected population and proved a practical reliability. The noncompliance ratio to obtain compulsory motor insurance was estimated by both a point and a confidence interval. This estimate provides a basis to predict third party motor insurance inclusion.