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A Multivariate Randomized Response Model for Sensitive Binary Data

Author

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  • Chu, Amanda M.Y.
  • Omori, Yasuhiro
  • So, Hing-yu
  • So, Mike K.P.

Abstract

A new statistical method is proposed to combine the randomized response technique, probit modeling, and Bayesian analysis to analyze large-scale online surveys of multiple binary randomized responses. The proposed method is illustrated by analyzing sensitive dichotomous randomized responses on different types of drug administration error from nurses in a hospital cluster. A statistical challenge is that nurses’ true sensitive responses are unobservable because of a randomization scheme that protects their data privacy to answer the sensitive questions. Four main contributions of the paper are highlighted. The first is the construction of a generic statistical approach in modeling multivariate sensitive binary data collected from the randomized response technique. The second is studying the dependence of multivariate sensitive responses via statistical measures. The third is the calculation of an overall attitude score using sensitive responses. The last one is an illustration of the proposed statistical method for analyzing administration policies that potentially involve sensitive topics which are important to study but are not easily investigated via empirical studies. The particular healthcare example on drug administration policies demonstrated in this paper also presents a scientific way to elicit managerial strategies while protecting data privacy through analytics.

Suggested Citation

  • Chu, Amanda M.Y. & Omori, Yasuhiro & So, Hing-yu & So, Mike K.P., 2023. "A Multivariate Randomized Response Model for Sensitive Binary Data," Econometrics and Statistics, Elsevier, vol. 27(C), pages 16-35.
    • Handle: RePEc:eee:ecosta:v:27:y:2023:i:c:p:16-35
    DOI: 10.1016/j.ecosta.2022.01.003
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    References listed on IDEAS

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    1. Vivekananda Roy & James P. Hobert, 2007. "Convergence rates and asymptotic standard errors for Markov chain Monte Carlo algorithms for Bayesian probit regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 607-623, September.
    2. Jeongeun Kim & David W Bates, 2013. "Medication administration errors by nurses: adherence to guidelines," Journal of Clinical Nursing, John Wiley & Sons, vol. 22(3-4), pages 590-598, February.
    3. Celine Marielle Laffont & Marc Vandemeulebroecke & Didier Concordet, 2014. "Multivariate Analysis of Longitudinal Ordinal Data With Mixed Effects Models, With Application to Clinical Outcomes in Osteoarthritis," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 955-966, September.
    4. Daniele Durante, 2019. "Conjugate Bayes for probit regression via unified skew-normal distributions," Biometrika, Biometrika Trust, vol. 106(4), pages 765-779.
    5. Samuel S. K. Kwan & Mike K. P. So & Kar Yan Tam, 2010. "Research Note ---Applying the Randomized Response Technique to Elicit Truthful Responses to Sensitive Questions in IS Research: The Case of Software Piracy Behavior," Information Systems Research, INFORMS, vol. 21(4), pages 941-959, December.
    6. Sean M. O'Brien & David B. Dunson, 2004. "Bayesian Multivariate Logistic Regression," Biometrics, The International Biometric Society, vol. 60(3), pages 739-746, September.
    7. Nicholas G. Polson & James G. Scott & Jesse Windle, 2013. "Bayesian Inference for Logistic Models Using Pólya--Gamma Latent Variables," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(504), pages 1339-1349, December.
    8. McFadden, Daniel, 1980. "Econometric Models for Probabilistic Choice among Products," The Journal of Business, University of Chicago Press, vol. 53(3), pages 13-29, July.
    9. Doyle, Peter, 1977. "The application of probit, logit, and tobit in marketing: A review," Journal of Business Research, Elsevier, vol. 5(3), pages 235-248, September.
    10. Imai, Kosuke & van Dyk, David A., 2005. "A Bayesian analysis of the multinomial probit model using marginal data augmentation," Journal of Econometrics, Elsevier, vol. 124(2), pages 311-334, February.
    11. William Barcella & Maria De Iorio & James Malone‐Lee, 2018. "Modelling correlated binary variables: an application to lower urinary tract symptoms," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(4), pages 1083-1100, August.
    12. 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.
    13. Amemiya, Takeshi, 1981. "Qualitative Response Models: A Survey," Journal of Economic Literature, American Economic Association, vol. 19(4), pages 1483-1536, December.
    14. Berrett, Candace & Calder, Catherine A., 2012. "Data augmentation strategies for the Bayesian spatial probit regression model," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 478-490.
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