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

Randomized response is an efficacious and effective survey method to collect subtle information. It entitles respondents to respond to over-sensitive issues and defensive questions (such as criminal behavior, gambling habits, addiction to drugs, 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, precautionary and Degroot loss functions. We have also expanded our proposal for the case of mixture of Beta priors under squared error loss function. The performance of the Bayes and maximum likelihood estimators is evaluated in terms of mean squared errors. Moreover, an application with real data set is also provided to explain the proposal for practical considerations.