A mixed randomized response model

To implement the privacy problem with the Moors (J. Amer. Statist. Assoc. 66 (1971) 627) model, Mangat et al. (Commun. Statist. Theory Methods 26(3) (1997) 243) and Singh et al. (J. Statist. Plann. Inference 83 (2000) 243) presented several strategies as an alternative to Moors model, but their models may lose a large portion of data information and require a high cost to obtain confidentiality of the respondents. Our proposed model has the advantage of simplicity over the previous models while protecting confidentiality. We extend the proposed model to stratified sampling.