EFFICIENT ESTIMATION IN A TWO-STAGE RANDOMIZED RESPONSE MODEL

A two-stage randomized response model is devised to circumvent the lack of answers to a sensitive question. Respondents who have not answered the sensitive question in the first stage are requested in the second stage to either answer the sensitive question (second attempt then) or to draw a card indicating yes or no. In the latter case, they are required to report the outcome. This apparently innocent device helps to build a more efficient estimator of the proportion of the population having a given sensitive attribute. The procedure also increases the respondents' cooperation. As other estimators of the proportion of the population having a given sensitive attribute using randomized response models, this estimator can formally take values outside the unit interval, a possibility which should not be allowed. The minimum sample size for which the frequency of estimates outside [0,1] is small enough is obtained by simulation.