Randomized response techniques for a multi-level attribute using a single sensitive question
type: Item
instance of: scholarly article
title: Randomized response techniques for a multi-level attribute using a single sensitive question
zbMATH Open document ID: 1393.62006
author: Shu-Hui Hsieh
author: S. M. Lee
author: Su-Hao Tu
published in: Statistical Papers
publication date: 2018-03-22T00:00:00Z
review text: 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.
reviewed by: T. J. Rao
Mathematics Subject Classification ID: 62D05
Mathematics Subject Classification ID: 62P25
zbMATH DE Number: 6852100
zbMATH Keywords: multiple categories
zbMATH Keywords: randomized response technique
zbMATH Keywords: Christofides model
zbMATH Keywords: Taiwan social change survey
zbMATH Keywords: sexual orientation
MaRDI profile type: Publication
full work available at URL: s00362-016-0764-9
OpenAlex ID: W2303043803
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DOI: 10.1007/S00362-016-0764-9
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description: scientific article; zbMATH DE number 6852100