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Estimation of parameters of logistic regression for two-stage randomized response technique

Author

Listed:
  • Pei-Chieh Chang

    (Feng Chia University)

  • Kim-Hung Pho

    (Feng Chia University
    Ton Duc Thang University)

  • Shen-Ming Lee

    (Feng Chia University)

  • Chin-Shang Li

    (University at Buffalo)

Abstract

When a survey study is related to sensitive issues such as political orientation, sexual orientation, and income, respondents may not be willing to reply truthfully, which leads to bias results. To protect the respondents’ privacy and improve their willingness to provide true answers, Warner (J Am Stat Assoc 60:63–69, 1965) proposed the randomized response (RR) technique in which respondents select a question by means of a random device in order to ensure that they maintain privacy. Huang (Stat Neerl 58:75–82, 2004) extended the RR design of Warner (1965) to propose a two-stage RR design. Not only can this method be used to estimate the population proportion of persons with a sensitive characteristic, but also estimate the honest answer rate in the first stage. This work develops a covariate extension of the two-stage RR design of Huang (2004) by applying logistic regression to investigate the effects of covariates on a sensitive characteristic and an honest response. Simulation experiments are conducted to study the finite-sample performance of the maximum likelihood estimators of the logistic regression parameters. The proposed methodology is applied to analyze the survey data of sexuality of freshmen at Feng Chia University in Taiwan in 2016.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:compst:v:36:y:2021:i:3:d:10.1007_s00180-021-01068-5
    DOI: 10.1007/s00180-021-01068-5
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Shen-Ming Lee & Ter-Chao Peng & Jean de Dieu Tapsoba & Shu-Hui Hsieh, 2017. "Improved estimation methods for unrelated question randomized response techniques," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(16), pages 8101-8112, August.
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    Cited by:

    1. 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.
    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. 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.
    4. 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.
    5. 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.

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