IDEAS home Printed from https://ideas.repec.org/a/spr/metrik/v77y2014i2p211-224.html
   My bibliography  Save this article

A new privacy-protecting survey design for multichotomous sensitive variables

Author

Listed:
  • Heiko Groenitz

Abstract

In this paper, we propose the diagonal model (DM), a survey technique for multicategorical sensitive variables. The DM is a nonrandomized response method; that is, the DM avoids the use of any randomization device. Thus, both survey complexity and study costs are reduced. The DM does not require that at least one outcome of the sensitive variable is nonsensitive. Thus, the model can even be applied to characteristics like income which are sensitive as a whole. We describe the maximum likelihood estimation for the distribution of the sensitive variable and show that the EM algorithm is beneficial to calculate the estimates. Subsequently, we present asymptotic as well as bootstrap confidence intervals. Applying properties of circulant matrices, we show the connection between efficiency loss and the degree of privacy protection (DPP). Here, we prove that the efficiency loss has a lower bound that depends on the DPP. Moreover, for any desired DPP, we derive model parameters that ensure the largest possible efficiency. Copyright Springer-Verlag 2014

Suggested Citation

  • Heiko Groenitz, 2014. "A new privacy-protecting survey design for multichotomous sensitive variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(2), pages 211-224, February.
    • Handle: RePEc:spr:metrik:v:77:y:2014:i:2:p:211-224
    DOI: 10.1007/s00184-012-0406-8
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00184-012-0406-8
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00184-012-0406-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Tan, Ming T. & Tian, Guo-Liang & Tang, Man-Lai, 2009. "Sample Surveys With Sensitive Questions: A Nonrandomized Response Approach," The American Statistician, American Statistical Association, vol. 63(1), pages 9-16.
    2. Jun-Wu Yu & Guo-Liang Tian & Man-Lai Tang, 2008. "Two new models for survey sampling with sensitive characteristic: design and analysis," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 67(3), pages 251-263, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Pei-Chieh Chang & Kim-Hung Pho & Shen-Ming Lee & Chin-Shang Li, 2021. "Estimation of parameters of logistic regression for two-stage randomized response technique," Computational Statistics, Springer, vol. 36(3), pages 2111-2133, September.
    2. Andreas Lagerås & Mathias Lindholm, 2020. "How to ask sensitive multiple‐choice questions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(2), pages 397-424, June.
    3. Truong-Nhat Le & Shen-Ming Lee & Phuoc-Loc Tran & Chin-Shang Li, 2023. "Randomized Response Techniques: A Systematic Review from the Pioneering Work of Warner (1965) to the Present," Mathematics, MDPI, vol. 11(7), pages 1-26, April.
    4. Guo-Liang Tian, 2014. "A new non-randomized response model: The parallel model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 68(4), pages 293-323, November.
    5. Shen-Ming Lee & Phuoc-Loc Tran & Truong-Nhat Le & Chin-Shang Li, 2023. "Prediction of a Sensitive Feature under Indirect Questioning via Warner’s Randomized Response Technique and Latent Class Model," Mathematics, MDPI, vol. 11(2), pages 1-21, January.
    6. Groenitz, Heiko, 2016. "A covariate nonrandomized response model for multicategorical sensitive variables," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 124-138.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Andreas Lagerås & Mathias Lindholm, 2020. "How to ask sensitive multiple‐choice questions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(2), pages 397-424, June.
    2. Raghunath Arnab & Dahud Kehinde Shangodoyin & Antonio Arcos, 2019. "Nonrandomized Response Model For Complex Survey Designs," Statistics in Transition New Series, Polish Statistical Association, vol. 20(1), pages 67-86, March.
    3. Liu, Yin & Tian, Guo-Liang, 2013. "A variant of the parallel model for sample surveys with sensitive characteristics," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 115-135.
    4. Heiko Groenitz, 2015. "Using prior information in privacy-protecting survey designs for categorical sensitive variables," Statistical Papers, Springer, vol. 56(1), pages 167-189, February.
    5. Truong-Nhat Le & Shen-Ming Lee & Phuoc-Loc Tran & Chin-Shang Li, 2023. "Randomized Response Techniques: A Systematic Review from the Pioneering Work of Warner (1965) to the Present," Mathematics, MDPI, vol. 11(7), pages 1-26, April.
    6. Guo-Liang Tian, 2014. "A new non-randomized response model: The parallel model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 68(4), pages 293-323, November.
    7. Qiu, Shi-Fang & Zou, G.Y. & Tang, Man-Lai, 2014. "Sample size determination for estimating prevalence and a difference between two prevalences of sensitive attributes using the non-randomized triangular design," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 157-169.
    8. Carlos Barros, 2012. "Sustainable Tourism in Inhambane-Mozambique," CEsA Working Papers 105, CEsA - Centre for African and Development Studies.
    9. Burgstaller, Lilith & Feld, Lars P. & Pfeil, Katharina, 2022. "Working in the shadow: Survey techniques for measuring and explaining undeclared work," Journal of Economic Behavior & Organization, Elsevier, vol. 200(C), pages 661-671.
    10. Kazuo Yamaguchi, 2016. "Cross-sectional and Panel Data Analyses of an Incompletely Observed Variable Derived From the Nonrandomized Method for Surveying Sensitive Questions," Sociological Methods & Research, , vol. 45(1), pages 41-68, February.
    11. Pavel Dietz & Anne Quermann & Mireille Nicoline Maria van Poppel & Heiko Striegel & Hannes Schröter & Rolf Ulrich & Perikles Simon, 2018. "Physical and cognitive doping in university students using the unrelated question model (UQM): Assessing the influence of the probability of receiving the sensitive question on prevalence estimation," PLOS ONE, Public Library of Science, vol. 13(5), pages 1-12, May.
    12. Horng-Jinh Chang & Mei-Pei Kuo, 2012. "Estimation of population proportion in randomized response sampling using weighted confidence interval construction," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(5), pages 655-672, July.
    13. Thorben C. Kundt & Florian Misch & Birger Nerré, 2017. "Re-assessing the merits of measuring tax evasion through business surveys: an application of the crosswise model," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 24(1), pages 112-133, February.
    14. Pier Francesco Perri & Eleni Manoli & Tasos C. Christofides, 2023. "Assessing the effectiveness of indirect questioning techniques by detecting liars," Statistical Papers, Springer, vol. 64(5), pages 1483-1506, October.
    15. Marc Höglinger & Ben Jann, 2018. "More is not always better: An experimental individual-level validation of the randomized response technique and the crosswise model," PLOS ONE, Public Library of Science, vol. 13(8), pages 1-22, August.
    16. Heiko Groenitz, 2018. "Analyzing efficiency for the multi-category parallel method," METRON, Springer;Sapienza Università di Roma, vol. 76(2), pages 231-250, August.
    17. Carlos Barros & Vera Barros & Peter Dieke, 2012. "Tourism and Human Development in Mozambique: an analysis for Inhambane province," CEsA Working Papers 100, CEsA - Centre for African and Development Studies.
    18. Ó Ceallaigh, Diarmaid & Timmons, Shane & Robertson, Deirdre & Lunn, Pete, 2023. "Measures of problem gambling, gambling behaviours and perceptions of gambling in Ireland," Research Series, Economic and Social Research Institute (ESRI), number RS169.
    19. Shen-Ming Lee & Phuoc-Loc Tran & Truong-Nhat Le & Chin-Shang Li, 2023. "Prediction of a Sensitive Feature under Indirect Questioning via Warner’s Randomized Response Technique and Latent Class Model," Mathematics, MDPI, vol. 11(2), pages 1-21, January.
    20. Shi-Fang Qiu & Man-Lai Tang & Ji-Ran Tao & Ricky S. Wong, 2022. "Sample Size Determination for Interval Estimation of the Prevalence of a Sensitive Attribute Under Randomized Response Models," Psychometrika, Springer;The Psychometric Society, vol. 87(4), pages 1361-1389, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metrik:v:77:y:2014:i:2:p:211-224. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.