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A generalized approach to randomised response for quantitative variables

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  • Antonio Arcos
  • María del Rueda
  • Sarjinder Singh

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. Copyright Springer Science+Business Media Dordrecht 2015

Suggested Citation

  • Antonio Arcos & María del Rueda & Sarjinder Singh, 2015. "A generalized approach to randomised response for quantitative variables," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(3), pages 1239-1256, May.
    • Handle: RePEc:spr:qualqt:v:49:y:2015:i:3:p:1239-1256
    DOI: 10.1007/s11135-014-0046-3
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    References listed on IDEAS

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    5. J.-P. Fox & Cheryl Wyrick, 2008. "A Mixed Effects Randomized Item Response Model," Journal of Educational and Behavioral Statistics, , vol. 33(4), pages 389-415, December.
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    9. Oluseun Odumade & Sarjinder Singh, 2010. "An Alternative to the Bar-Lev, Bobovitch, and Boukai Randomized Response Model," Sociological Methods & Research, , vol. 39(2), pages 206-221, November.
    10. Christopher R. Gjestvang & Sarjinder Singh, 2006. "A new randomized response model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 523-530, June.
    11. van den Hout, Ardo & van der Heijden, Peter G.M. & Gilchrist, Robert, 2007. "The logistic regression model with response variables subject to randomized response," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6060-6069, August.
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    Cited by:

    1. María del Mar Rueda & Beatriz Cobo & Antonio Arcos, 2021. "Regression Models in Complex Survey Sampling for Sensitive Quantitative Variables," Mathematics, MDPI, vol. 9(6), pages 1-13, March.
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    3. Priyanka Kumari & Trisandhya Pidugu, 2019. "Modelling Sensitive Issues On Successive Waves," Statistics in Transition New Series, Statistics Poland, vol. 20(1), pages 41-65, March.
    4. María del Mar García Rueda & Pier Francesco Perri & Beatriz Rodríguez Cobo, 2018. "Advances in estimation by the item sum technique using auxiliary information in complex surveys," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(3), pages 455-478, July.

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