Randomized Response Techniques for Multiple Sensitive Attributes

Some randomized response techniques for investigating t ≧ 2 sensitive attributes are reviewed. A new technique is proposed that has the advantage of requiring only r trials per respondent (r ≦ t) if estimation of up to r-variate joint proportions is desired. The case of r = 2 is analyzed in detail. A procedure for deriving the restricted maximum likelihood estimators (MLE's) of the proportions and a test of independence between any set of pairs of attributes are given. The notion of measure of respondent jeopardy is extended to our setup. Keeping this measure fixed, we make numerical comparisons for the t = 2 case between competing techniques in terms of the trace of the asymptotic variance-covariance matrix of the estimator vector. Finally, a practical application of the new technique is described.