Randomized response techniques for a multi-level attribute using a single sensitive question
The model of \textit{T. C. Christofides} [Metrika 57, No. 2, 195--200 (2003; Zbl 1341.62041)] for estimating the proportion \(\theta\) of individuals possessing a single sensitive attribute \(A_1\) involves asking the respondent to select an integer at random from 1 to \(L\) with probabilities \(P_1,P_2,\dots,P_L\), \(\sum^L_{i=1}P_i=1\). The respondent is then asked how far away this number is from \(L+1\) if he/she has the attribute \(A_1\) or 0 otherwise, i.e. if the respondent possesses the complement of \(A_1\). In this paper, the authors extend the above model to the case of \(m>2\) possible mutually exclusive attributes \(A_1,A_2,\dots,A_m\). Let \(\theta_j\) be the proportion of individuals in a population with attribute \(A_j\), for \(j=1,2,\dots,m\). Then for a simple random sample of size \(n\), the true attribute \(X_j\) has the p.m.f. \(X_i=0\) with probability \(\theta_1\) \(X_i=L+1\) with probability \(\theta_2\) \(X_i=L+m-1\) with probability \(\theta_m\) with \(\sum^m_{j=1}\theta_j=1\). Next, they study the estimation of parameters of a primary model where at least one value of \(X\) is a non sensitive attribute and a combining model where all categories are sensitive. This extended technique is illustrated using the data from the 2012 Family and Gender Module of Taiwan Social Change Survey to estimate the proportion of individuals of different sexual orientations. They also compare their results with data obtained from direct questioning in the same survey.
scientific article; zbMATH DE number 6852100
scientific article