Abstract
In this paper, the scrambled and forced response method was used as the randomized response technique to maximize the efficiency of randomized response designs. When randomized response designs become more efficient their value as a tool to study sensitive topics will increase. An overview of the literature shows that when sensitive or incriminating topics are studied, the overall results of randomized response studies are more valid than the results of direct question designs. We propose a set of alternative estimators for probability proportional to size with replacement (PPSWR) corresponding to multi-character survey that elicit simultaneous information on many sensitive study variables. The estimators proposed are all biased but it is expected that the extent of bias will be smaller, since the proposed estimators are suitable for situations in between those optimum for the usual estimators and the estimators based on multi-characters for no correlation. The Mean Square Error (MSE) expressions are derived for the proposed estimators. The behavior of the proposed estimator has been examined under super population model. Numerical illustrations are carried out to show the performance of the proposed estimator model under forced response model.