IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i2p345-d1029960.html
   My bibliography  Save this article

Prediction of a Sensitive Feature under Indirect Questioning via Warner’s Randomized Response Technique and Latent Class Model

Author

Listed:
  • Shen-Ming Lee

    (Department of Statistics, Feng Chia University, Taichung 40724, Taiwan)

  • Phuoc-Loc Tran

    (Department of Mathematics, College of Natural Science, Can Tho University, Can Tho, Vietnam)

  • Truong-Nhat Le

    (Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam)

  • Chin-Shang Li

    (School of Nursing, The State University of New York, University at Buffalo, Buffalo, NY 14214, USA)

Abstract

We investigate the association of a sensitive characteristic or latent variable with observed binary random variables by the randomized response (RR) technique of Warner in his publication (Warner, S.L. J. Am. Stat. Assoc. 1965 , 60 , 63–69) and a latent class model. First, an expectation-maximization (EM) algorithm is provided to easily estimate the parameters of the null and alternative/full models for the association between a sensitive characteristic and an observed categorical random variable under the RR design of Warner’s paper above. The likelihood ratio test (LRT) is utilized to identify observed categorical random variables that are significantly related to the sensitive trait. Another EM algorithm is then presented to estimate the parameters of a latent class model constructed through the sensitive attribute and the observed binary random variables that are obtained from dichotomizing observed categorical random variables selected from the above LRT. Finally, two classification criteria are conducted to predict an individual in the sensitive or non-sensitive group. The practicality of the proposed methodology is illustrated with an actual data set from a survey study of the sexuality of first-year students, except international students, at Feng Chia University in Taiwan in 2016.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:345-:d:1029960
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/2/345/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/2/345/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Heiko Groenitz, 2018. "Logistic regression analyses for indirect data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(16), pages 3838-3856, August.
    2. Shu-Hui Hsieh & Shen-Ming Lee & Su-Hao Tu, 2018. "Randomized response techniques for a multi-level attribute using a single sensitive question," Statistical Papers, Springer, vol. 59(1), pages 291-306, March.
    3. 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.
    4. Bengt Muthén & Kerby Shedden, 1999. "Finite Mixture Modeling with Mixture Outcomes Using the EM Algorithm," Biometrics, The International Biometric Society, vol. 55(2), pages 463-469, June.
    5. Graeme Blair & Kosuke Imai & Yang-Yang Zhou, 2015. "Design and Analysis of the Randomized Response Technique," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1304-1319, September.
    6. Shen‐Ming Lee & Truong‐Nhat Le & Phuoc‐Loc Tran & Chin‐Shang Li, 2022. "Investigating the association of a sensitive attribute with a random variable using the Christofides generalised randomised response design and Bayesian methods," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1471-1502, November.
    7. Shu-Hui Hsieh & Shen-Ming Lee & Chin-Shang Li, 2022. "A Two-stage Multilevel Randomized Response Technique With Proportional Odds Models and Missing Covariates," Sociological Methods & Research, , vol. 51(1), pages 439-467, February.
    8. 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.
    9. Kuo‐Chung Huang, 2004. "A survey technique for estimating the proportion and sensitivity in a dichotomous finite population," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(1), pages 75-82, February.
    10. 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.
    11. 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.
    12. Hsieh, S.H. & Lee, S.M. & Shen, P.S., 2009. "Semiparametric analysis of randomized response data with missing covariates in logistic regression," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2673-2692, May.
    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. 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.

    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. 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.
    2. Shen‐Ming Lee & Truong‐Nhat Le & Phuoc‐Loc Tran & Chin‐Shang Li, 2022. "Investigating the association of a sensitive attribute with a random variable using the Christofides generalised randomised response design and Bayesian methods," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1471-1502, November.
    3. 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.
    4. Asma Halim & Irshad Ahmad Arshad & Summaira Haroon & Waqas Shair, 2022. "A Comparative Study of Modified Hidden Logits Using Randomized Response Techniques," Journal of Policy Research (JPR), Research Foundation for Humanity (RFH), vol. 8(4), pages 447-461, December.
    5. Groenitz, Heiko, 2016. "A covariate nonrandomized response model for multicategorical sensitive variables," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 124-138.
    6. 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.
    7. 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.
    8. 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.
    9. Asma Halim & Irshad Ahmad Arshad & Summaira Haroon & Waqas Shair, 2022. "Effect of Misclassification on Test of Independence Using Different Randomized Response Techniques," Journal of Policy Research (JPR), Research Foundation for Humanity (RFH), vol. 8(4), pages 427-438, December.
    10. Shu-Hui Hsieh & Shen-Ming Lee & Chin-Shang Li, 2022. "A Two-stage Multilevel Randomized Response Technique With Proportional Odds Models and Missing Covariates," Sociological Methods & Research, , vol. 51(1), pages 439-467, February.
    11. Kim-Hung Pho & Michael McAleer, 2021. "Specification and Estimation of a Logistic Function, with Applications in the Sciences and Social Sciences," Advances in Decision Sciences, Asia University, Taiwan, vol. 25(2), pages 74-104, June.
    12. 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.
    13. Balgobin Nandram & Yuan Yu, 2019. "Bayesian Analysis of Sparse Counts Obtained From the Unrelated Question Design," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 8(5), pages 66-84, September.
    14. Ivar Krumpal & Thomas Voss, 2020. "Sensitive Questions and Trust: Explaining Respondents’ Behavior in Randomized Response Surveys," SAGE Open, , vol. 10(3), pages 21582440209, July.
    15. Ó Ceallaigh, Diarmaid & Timmons, Shane & Robertson, Deirdre & Lunn, Pete, 2023. "Problem gambling: A narrative review of important policy-relevant issues," Research Series, Economic and Social Research Institute (ESRI), number SUSTAT119, June.
    16. Marco Guerra & Francesca Bassi & José G. Dias, 2020. "A Multiple-Indicator Latent Growth Mixture Model to Track Courses with Low-Quality Teaching," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 147(2), pages 361-381, January.
    17. Michael Prendergast & David Huang & Yih-Ing Hser, 2008. "Patterns of Crime and Drug Use Trajectories in Relation to Treatment Initiation and 5-Year Outcomes," Evaluation Review, , vol. 32(1), pages 59-82, February.
    18. Silvia Bacci & Francesco Bartolucci & Giulia Bettin & Claudia Pigini, 2017. "A mixture growth model for migrants' remittances: An application to the German Socio-Economic Panel," Mo.Fi.R. Working Papers 145, Money and Finance Research group (Mo.Fi.R.) - Univ. Politecnica Marche - Dept. Economic and Social Sciences.
    19. Carlos Barros, 2012. "Sustainable Tourism in Inhambane-Mozambique," CEsA Working Papers 105, CEsA - Centre for African and Development Studies.
    20. Sylvain Chassang & Christian Zehnder, 2019. "Secure Survey Design in Organizations: Theory and Experiments," Working Papers 2019-22, Princeton University. Economics Department..

    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:gam:jmathe:v:11:y:2023:i:2:p:345-:d:1029960. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.