Estimation of correlation in randomized response - ARCHIVED

Stanley Warner’s contributions to randomized response are reviewed. Following this review, a linear model, based on random permutation models, is developed to include many known randomized response designs as special cases. Under this model optimal estimators for finite population variances and covariances are obtained within a general class of quadratic design-unbiased estimators. From these results an estimator of the finite population correlation is obtained. Three randomized response designs are examined in particular: (i) the unrelated questions model of Greenberg et al. (1969); (ii) the additive constants model of Pollock and Bek (1976); and (iii) the multiplicative constants model of Pollock and Bek (1976). Simple models for response bias are presented to illustrate the effect of this bias on estimation of the correlation.