The Efficiency of the Multiple Trial Randomized Response Technique

Abstract

It has been proven theoretically that repeated administration of two-related-question randomized response technique (RRT) substantially increases the efficiency by reducing the variance of the estimate. The realtive efficiency of RRT to direct question with various number of trials per respondent under various degrees of truthful response and various conditions has also been examined. However, if the respondent becomes more concerned about his anonymity, then the mean square error may be larger. A field study of limited scope conducted in Taichung, Taiwan indicated that this multiple trial RRT model is at least as feasible as, if not more feasible than, the conventional single trial RRT. There was no sign suggesting cooperation of respondents had deteriorated because each was asked to repeat the procedures three times. If the number of trials did not exceed three, we believe that the increase in the cost of survey and "exhaustion" of respondents from repeated administration of the same set of questions would be negligible. Hence, we believe that this multiple trial technique is a feasible and useful survey method for study of various contemporary social problems of sensitive nature. More field testing, particularly in different socio-cultural settings, is necessary however, before a general conclusion may be drawn.

Investigating the Impact of Simple and Mixture Priors on Estimating Sensitive Proportion Through a General Class of Randomized Response Models

“…In order to give a detailed description of the suggested Bayesian method from a practical point of view, we consider the data collected by Liu and Chow [40] in which they estimated the incidence of induced abortion in Taiwan. Liu and Chow [40] carried out Warner [1] procedure with probability of sensitive question being equal to 0.7 for n = 150 married women in order to determine the proportion of women, who had experienced induced abortion.…”

“…Liu and Chow [40] carried out Warner [1] procedure with probability of sensitive question being equal to 0.7 for n = 150 married women in order to determine the proportion of women, who had experienced induced abortion. The number of yes responses in the sample is recorded as 60, yielding the sample proportion of yes responses (^ ) as 0.4.…”

“…The number of yes responses in the sample is recorded as 60, yielding the sample proportion of yes responses (^ ) as 0.4. Liu and Chow [40] obtained the maximum likelihood estimate as 0.25. Later on, Winkler and Franklin [17] and Bar-Lev et al [30] analyzed the same data through the Bayesian analysis using complete and conjugate prior distributions, respectively.…”

Bayesian randomized item response modeling for sensitive measurements

“…The forced response method is more efficient than traditional Warner's and unrelated-question methods. Texts on the efficiency of randomized response techniques can be found in Bhargava and Singh (2002), Dowling and Shachtman (1975), and Liu and Chow (1976a), among others. Moreover, all abovementioned designs require a physical randomizing device, e.g.…”

“…Horvitz et al (1967) and Liu and Chow (1976a) suggested that by multiple trials, performed on each respondent, a reduction in variance can be achieved. Other developments of Warner's method concerned extensions to multiple categories.…”