A common conjugate prior structure for several randomized response models

In this paper we present a common Bayesian approach to four randomized response models, including Warner's (1965) and other modification for it that appeared thereafter in the literature. Suitable truncated beta distributions are used throughout in a common conjugate prior structure to obtain the Bayes estimates for the proportion of a "sensitive" attribute in the population of interest. The results of this common conjugate prior approach are contrasted with those of Winkler and Franklin's (1979), in which non-conjugate priors have been used in the context of Warner's model. The results are illustrated numerically in several cases and exemplified further with data reported in Liu and Chow (1976) concerning incidents of induced abortions.