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Randomized response techniques for a multi-level attribute using a single sensitive question

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  • Shu-Hui Hsieh

    (Academia Sinica)

  • Shen-Ming Lee

    (Feng Chia University)

  • Su-Hao Tu

    (Academia Sinica)

Abstract

Collecting reliable responses to sensitive survey questions is challenging, since respondents may be more likely to refuse to respond or to provide biased responses. To address these challenges, Warner (J Am Stat Assoc 60:63–69, 1965) pioneered the randomized response (RR) technique to estimate proportions of individuals in a population with either of two possible attributes. The RR technique can overcome non-response and underreporting biases because it doesn’t reveal the respondent’s attribute, and a generalization of the random component of the response by Christofides (Metrika 57:195–200, 2003) improves estimation properties. In this study, we develop a new RR model to estimate proportions of individuals with each of multiple categories of an attribute using a single sensitive question by means of only one randomization device based on Christofides’s (Metrika 57:195–200, 2003) model. Under the proposed model, a respondent reports the absolute difference between an integer associated with his or her attribute and a random integer. In a part of this research, we conduct a simulation study of the relative efficiency of the proposed methods. The technique is illustrated using data from the 2012 Family and Gender Module of the Taiwan Social Change Survey to estimate the proportions of individuals of different sexual orientations, and the results are compared with the results of direct inquiry from the same survey.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:59:y:2018:i:1:d:10.1007_s00362-016-0764-9
    DOI: 10.1007/s00362-016-0764-9
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    References listed on IDEAS

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    1. Gerty J. L. M. Lensvelt-Mulders & Joop J. Hox & Peter G. M. van der Heijden & Cora J. M. Maas, 2005. "Meta-Analysis of Randomized Response Research," Sociological Methods & Research, , vol. 33(3), pages 319-348, February.
    2. Lee, Cheon-Sig & Sedory, Stephen A. & Singh, Sarjinder, 2013. "Estimating at least seven measures of qualitative variables from a single sample using randomized response technique," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 399-409.
    3. Lucio Barabesi & Sara Franceschi & Marzia Marcheselli, 2012. "A randomized response procedure for multiple-sensitive questions," Statistical Papers, Springer, vol. 53(3), pages 703-718, August.
    4. 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.
    5. Tasos Christofides, 2005. "Randomized response technique for two sensitive characteristics at the same time," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 62(1), pages 53-63, September.
    6. Seil, K.S. & Desai, M.M. & Smith, M.V., 2014. "Sexual orientation, adult connectedness, substance use, and mental health outcomes among adolescents: Findings From the 2009 New York city youth risk behavior survey," American Journal of Public Health, American Public Health Association, vol. 104(10), pages 1950-1956.
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    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. 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.
    3. Hua Xin & Jianping Zhu & Tzong-Ru Tsai & Chieh-Yi Hung, 2021. "Hierarchical Bayesian Modeling and Randomized Response Method for Inferring the Sensitive-Nature Proportion," Mathematics, MDPI, vol. 9(19), pages 1-12, October.
    4. 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.

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