A Theory of Higher Order Interactions Between Sensitive Variables: Empirical Evidences and an Application to a Variety of Smoking

In carrying out surveys involving sensitive characteristics, randomized response models have been considered among the best techniques since they provide the maximum privacy protection to the respondents and procure honest responses. Over the years, researchers have carried out studies on the estimation of proportions of the population possessing sensitive characteristics. However, there is a paucity of research studies that have addressed higher order interactions between these sensitive characters. In this article, we develop a new theory based on three proposed randomized response models which we name as: simple model, semi-crossed model, and fully crossed model. Twenty-one new unbiased estimators of seven parameters are introduced, their variance expressions are derived, and unbiased estimators of variances are developed. The three models are compared under various values of the parameters by computing the percent relative efficiency of one model over another model. The most efficient model is then applied to study the population proportions of three varieties of smoking habits among students, and their first- and second-order interactions. The last four sections (Ninth to Twelfth) are verifications of theoretical results using the Cramer-Rao lower bounds of variances for the developed 21 new estimators in randomized response sampling.

Automated summary

Randomized response models are considered the best technique for surveys involving sensitive characteristics as they provide maximum privacy protection and honest responses. However, there is a lack of research on higher order interactions between these characteristics. In this article, a new theory based on three proposed randomized response models is developed, and unbiased estimators and variance expressions are introduced. The models are compared and the most efficient one is applied to study smoking habits and interactions among students.