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A note on randomized response models for quantitative data

Author

Listed:
  • Shaul K. Bar-Lev
  • Elizabeta Bobovitch
  • Benzion Boukai

Abstract

Standard randomized response (RR) models deal primarily with surveys which usually require a ‘yes’ or a ‘no’ response to a sensitive question, or a choice for responses from a set of nominal categories. As opposed to that, Eichhorn and Hayre (1983) have considered survey models involving a quantitative response variable and proposed an RR technique for it. Such models are very useful in studies involving a measured response variable which is highly ‘sensitive’ in its nature. Eichhorn and Hayre obtained an unbiased estimate for the expectation of the quantitative response variable of interest. In this note we propose a procedure which uses a design parameter (controlled by the experimenter) that generalizes Eichhorn and Hayre’s results. Such a procedure yields an estimate for the desired expectation which has a uniformly smaller variance. Copyright Springer-Verlag 2004

Suggested Citation

  • Shaul K. Bar-Lev & Elizabeta Bobovitch & Benzion Boukai, 2004. "A note on randomized response models for quantitative data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 60(3), pages 255-260, November.
    • Handle: RePEc:spr:metrik:v:60:y:2004:i:3:p:255-260
    DOI: 10.1007/s001840300308
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    Citations

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    Cited by:

    1. Giancarlo Diana & Pier Perri, 2011. "A class of estimators for quantitative sensitive data," Statistical Papers, Springer, vol. 52(3), pages 633-650, August.
    2. Singh, Sarjinder & Kim, Jong-Min, 2011. "A pseudo-empirical log-likelihood estimator using scrambled responses," Statistics & Probability Letters, Elsevier, vol. 81(3), pages 345-351, March.
    3. 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.
    4. Zawar Hussain & Mashail M Al-Sobhi & Bander Al-Zahrani, 2014. "Additive and Subtractive Scrambling in Optional Randomized Response Modeling," PLOS ONE, Public Library of Science, vol. 9(1), pages 1-11, January.
    5. Christopher Gjestvang & Sarjinder Singh, 2007. "Forced quantitative randomized response model: a new device," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 66(2), pages 243-257, September.
    6. 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.
    7. Kuo-Chung Huang, 2010. "Unbiased estimators of mean, variance and sensitivity level for quantitative characteristics in finite population sampling," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 71(3), pages 341-352, May.
    8. 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.
    9. Giancarlo Diana & Saba Riaz & Javid Shabbir, 2014. "Hansen and Hurwitz estimator with scrambled response on the second call," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(3), pages 596-611, March.
    10. 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.
    11. Giancarlo Diana & Pier Francesco Perri, 2010. "New scrambled response models for estimating the mean of a sensitive quantitative character," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(11), pages 1875-1890.
    12. Kumari Priyanka & Pidugu Trisandhya, 2019. "Modelling Sensitive Issues On Successive Waves," Statistics in Transition New Series, Polish Statistical Association, vol. 20(1), pages 41-65, March.
    13. Amitava Saha, 2011. "An optional scrambled randomized response technique for practical surveys," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 73(2), pages 139-149, March.
    14. Pier Francesco Perri & Beatriz Cobo Rodríguez & María del Mar Rueda García, 2018. "A mixed-mode sensitive research on cannabis use and sexual addiction: improving self-reporting by means of indirect questioning techniques," Quality & Quantity: International Journal of Methodology, Springer, vol. 52(4), pages 1593-1611, July.
    15. Muhammad Azeem & Sundus Hussain & Musarrat Ijaz & Najma Salahuddin, 2024. "An improved quantitative randomized response technique for data collection in sensitive surveys," Quality & Quantity: International Journal of Methodology, Springer, vol. 58(1), pages 329-341, February.
    16. 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.
    17. Zawar Hussain & Mashail M. Al-Sobhi & Bander Al-Zahrani & Housila P. Singh & Tanveer A. Tarray, 2016. "Improved randomized response in additive scrambling models," Mathematical Population Studies, Taylor & Francis Journals, vol. 23(4), pages 205-221, October.

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