Analyzing efficiency for the multi-category parallel method
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Analyzing efficiency for the multi-category parallel method Heiko Groenitz1
Received: 19 December 2016 / Accepted: 28 November 2017 © Sapienza Università di Roma 2017
Abstract Survey data play an important role in many areas. The surveys typically consist of a list of direct questions. However, if survey data on sensitive topics (tax evasion, fraud, discrimination) are desired, direct questions lead to problems in data quality by answer refusal and untruthful answers. For this reason, there is a need for clever questioning procedures which protect the privacy of the respondents and yield data that allow statistical inference. One interesting procedure for categorical sensitive characteristics is the parallel method (PM). To apply the PM, the survey agency must choose certain parameters of the PM. So far, it has been not analyzed how these PM parameters influence the estimation efficiency corresponding to the PM. This paper addresses this important issue. Our investigations result in recommendations for survey agencies on appropriate PM parameters. Keywords Central limit theorem · Complex sample survey · Data protection · Estimation of proportions · Optimization · Sensitive characteristic
1 Introduction When respondents in surveys are asked directly for sensitive topics (income, tax evasion, fraud, cheating in examinations, discrimination and so on), the data quality causes great anxiety. The reason is that respondents may refuse to respond or provide an untruthful answer to protect their privacy. Statistical inference based on data obtained by direct questioning will often be seriously biased here. Therefore, indirect questioning methods have been developed in the literature. There are different groups of indirect questioning techniques. In randomized response techniques, the interviewee gives an indirect answer which depends on the result of a random experiment conducted by the interviewee. For example, Fox and Tracy [6], Chaudhuri [2], Chaudhuri and Christofides [3], and Chaudhuri et al. [4] give overviews on
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Heiko Groenitz [email protected] School of Business and Economics, Working Group Statistics, Philipps-University Marburg, Universitätsstraße 25, 35032 Marburg, Germany
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H. Groenitz
randomized response designs. In item count techniques, the respondent receives a list with questions on a sensitive and some nonsensitive attributes and answers the total sum of his or her values of these attributes. Interesting articles on item count approaches are, e.g., Imai [11], Petroczi et al. [15], Blair and Imai [1], and Groenitz [8]. In nonrandomized response procedures, the indirect answer depends on the sensitive variable and one or more nonsensitive scrambling variables where random experiments conducted by the respondents are avoided. Among others, some recommendable contributions on nonrandomized response methods are Yu et al. [20], Tang et al. [16], Liu and Tian [12–14], Tian [17], Tian and Tang [18], and Groenitz [7,9,10]. In the group of nonrandomized response techniques, Liu and Tian [
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