An improved unrelated question randomized response model

Abstract

In this paper we restrict the design probabilities of Mahmood, Singh and Horn (1998) unrelated question randomized response model. Besides its simplicity, the resulted restricted model has two advantages over Mahmood et al. (1998) model with other design probabilities. First, the restricted model requires selecting only one simple random sample and not two which reduces the cost of survey. Second, the efficiency of the estimator of the proportion of the population bearing a sensitive characteristic is increased. In addition, efficiency comparisons showed that this estimator can be easily adjusted to be more efficient than other competitors that were developed after 1998. A simulation study is performed to determine the minimum sample size required for the estimator to lie inside the unit interval. Moreover, the restricted model is extended to stratified random sampling and the resulting estimator is shown to be more efficient than the Kim and Elam (2007) and Singh and Tarray (2016) estimators.