Extensions of Mangat's randomized-response model

The randomized-response technique can be an effective survey method when collecting sensitive information. In this paper, we extend the model proposed by Mangat (J. Roy. Statist. Soc. Ser. B 56 (1994) 93) in two ways. First, we propose a Bayesian version of the model, which is applicable when prior information on π, the sensitive characteristic prevalence, is available. Our Bayesian approach can provide greatly-improved point estimators when compared to those obtained from maximum likelihood; furthermore, our approach provides estimators guaranteed to lie within the parameter space. Second, we extend Mangat's procedure to include data obtained from a stratified-sampling protocol and show that both of our new stratified procedures - one non-Bayesian and one Bayesian - are more efficient than the one initially proposed by Mangat (1994) for a single population.