The Two Alternate Questions Randomized Response Model for Human Surveys

Abstract

The present model is applicable when $\pi_Y$, the population proportion with a nonsensitive attribute $Y$, is not known in advance and two samples are required to estimate $\pi_A$, the population proportion with a sensitive attribute $A$. It consists of using the sensitive question and two nonsensitive alternate questions in each sample, yielding two unbiased estimates of $\pi_A$. The optimum estimator, a weighted average of these two estimates, is described and its minimum variance calculated. The efficiency of this estimator is compared with Moors' optimized version of the standard two sample single alternate question model, and with the one sample single alternate question model when $\pi_Y$ is known