Bayesian estimation in alternative tripartite randomized response techniques

Abstract

ABSTRACT: In this work, a new method of Bayesian estimation for the Alternative Tripartite randomized response technique used in obtaining the proportion of people that belongs to sensitive character was proposed. The proposed approach accommodates other intrinsic parameter constraints in the posterior to improve statistical precision. The efficiency of the newly proposed Bayesian estimators was established for a wide interval of the values of the population proportion of the sensitive character (π). It was discovered that for any preset probabilities, the developed Bayesian estimators became better in capturing responses from respondents than any other classical estimators. Therefore, as the sample size increases and the proposed Bayesian models capture more and more sensitive characters, the Kumaraswamy prior estimator becomes more efficient while the Generalized beta prior estimator performs better when there are fewer people involved in the sensitive character. Applying the Bayesian methods to data on drug use disorder also confirmed their efficiency over the classical methods.

Keywords

• Bayesian Estimation
• Randomized Response
• Marginal Probability Density Function
• Relative Efficiency
• Sensitive Character