Model selection in randomized response techniques for binary responses

Surveying Sensitive Topics with Indirect Questioning

“…There have been many different RRTs developed since Warner's original method, such as in Greenberg et al [36,37], Gupta [38], Gupta et al [39][40][41], Yu et al [42], Sihm et al [43], Gupta and Shabbir [44], and so on. Efforts specifically have been made to improve the efficiency of the technique by reducing the variance and thus the confidence intervals, because, the primary disadvantage of the Warner's model, and in fact of all RRTs, is that the variances of the estimators are higher than the ones that could be obtained from DQ [35,45]; for a comprehensive review of RRTs, interested readers are referred to Chaudhuri and Mukerjee [35], Chaudhuri [46], and Chaudhuri and Christofides [47]. In the next subsection, we will review some real-life applications of RRTs and their comparisons with other surveying techniques.…”

“…Unfortunately, once an RRT is incorporated within a survey, even if the question of interest turns out to be not sensitive after collecting the data, one has to proceed with the inefficient estimate obtained from the RRT. Motivated by the fact that if researchers do not have a priori knowledge about the sensitivity level of a question in a specific population, then they should be able to select between the estimators from an RRT and the DQ ; Ardah and Oral [45] proposed a novel two-stage RRT for a binary response where they utilized Warner's RRT in the second stage. Their model provides unbiased estimators of both prevalence of the sensitive characteristic and the proportion of cheating in the population simultaneously and allows one to obtain better estimates by avoiding the unnecessary penalty, i.e., the inflated variance, if the question of interest turns out to be significantly not sensitive.…”

“…Ardah and Oral [45] denoted the unknown true proportion of population members that have the sensitive characteristic A by π A , where 0 ≤ π A ≤ 1. They showed that, in a self-protective no-saying model (i.e., when a respondent cheats, s/he always answers in favor of the least stigmatizing category (see [53])) if one uses the DQ , the proportion of respondents who have the sensitive characteristic A becomes…”

“…Unfortunately, the SDB, i.e., the proportion of cheaters, cannot be measured using the DQ. Ardah and Oral's [45] proposed model, however, allows one to both estimate it and select the unbiased estimator with the minimum variance depending on the sensitivity level of the question (or proportion of cheating in the population). Ardah and Oral [45] utilized unrelated question RRT in the second stage of their model as well; in fact, their model can easily be extended to any desired RRT [45].…”