A Modified Forced Randomized Response Model

Abstract

In this paper, we proposed a new Randomized Response Model (RRM) that estimate proportion of people in a population (P) belonging to a sensitive group (S) under study. Simple random sampling with replacement and stratified simple random sampling scheme were adopted. Maximum likelihood and Bayesian estimation procedures of the proposed model were developed and compared. The sampling distribution (expectation and variance) of the proposed estimator under the two sampling techniques, efficiency comparison of the proposed model with some existing models, and numerical illustration of all the compared models were also explored. We found that the proposed model outperformed other existing RRMs in terms of efficiency and it proved to be more protective in designing survey for sensitive related issues.

Keywords

• randomized response, proportion, sensitive group, maximum likelihood estimator, sampling distribution