Investigating the impact of simple and mixture priors on estimating sensitive proportion through a general class of randomized response models

Randomized response is an effective survey method to collect subtle information. It facilitates responding to over-sensitive issues and defensive questions (such as criminal behavior, gambling habits, drug addictions, abortions, etc.) while maintaining confidentiality. In this paper, we conducted a Bayesian analysis of a general class of randomized response models by using different prior distributions, such as Beta, Uniform, Jeffreys, and Haldane, under squared error loss, and precautionary and DeGroot loss functions. We have also expanded our proposal to the case of mixture of Beta priors under squared error loss function. The performance of the Bayes and maximum likelihood estimators has been evaluated in terms of mean squared errors. Moreover, an application with real dataset has been also provided to explain the proposal for practical considerations.