A generalized approach to randomised response for quantitative variables

A generalized approach to randomised response for quantitative variables The methodology of randomised response (RR) has advanced considerably in recent years. Nevertheless, most research in this area has addressed the estimation of qualitative variables, and relatively little attention has been paid to the study of quantitative ones. Furthermore, most studies concern only simple random sampling. In this paper, we present a new model of RR aimed at determining a total that is valid for any sampling design. This general procedure includes several important RR techniques that constitute particular cases. We propose an unbiased estimator, with an analytic expression for its variance. Confidence intervals are also obtained for the parameter, applying analytical formulae such as those based on resampling technologies. A simulation study illustrates the behaviour of the estimator using diverse randomisation devices and for different scrambling distributions. To illustrate the advantages of this method, we obtained a stratified clustered sample of university students, who were questioned to determine the frequency with which they cheated in exams. Their responses to these questions were obtained via an RR technique, and also using a direct questionnaire. We conclude that estimates based on anonymous questionnaires may result in severe underestimation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quality & Quantity Springer Journals

A generalized approach to randomised response for quantitative variables

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Publisher
Springer Netherlands
Copyright
Copyright © 2014 by Springer Science+Business Media Dordrecht
Subject
Social Sciences, general; Methodology of the Social Sciences; Social Sciences, general
ISSN
0033-5177
eISSN
1573-7845
D.O.I.
10.1007/s11135-014-0046-3
Publisher site
See Article on Publisher Site

Abstract

The methodology of randomised response (RR) has advanced considerably in recent years. Nevertheless, most research in this area has addressed the estimation of qualitative variables, and relatively little attention has been paid to the study of quantitative ones. Furthermore, most studies concern only simple random sampling. In this paper, we present a new model of RR aimed at determining a total that is valid for any sampling design. This general procedure includes several important RR techniques that constitute particular cases. We propose an unbiased estimator, with an analytic expression for its variance. Confidence intervals are also obtained for the parameter, applying analytical formulae such as those based on resampling technologies. A simulation study illustrates the behaviour of the estimator using diverse randomisation devices and for different scrambling distributions. To illustrate the advantages of this method, we obtained a stratified clustered sample of university students, who were questioned to determine the frequency with which they cheated in exams. Their responses to these questions were obtained via an RR technique, and also using a direct questionnaire. We conclude that estimates based on anonymous questionnaires may result in severe underestimation.

Journal

Quality & QuantitySpringer Journals

Published: Jun 21, 2014

References

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