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A Two-stage Multilevel Randomized Response Technique With Proportional Odds Models and Missing Covariates

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  • Shu-Hui Hsieh
  • Shen-Ming Lee
  • Chin-Shang Li

Abstract

Surveys of income are complicated by the sensitive nature of the topic. The problem researchers face is how to encourage participants to respond and to provide truthful responses in surveys. To correct biases induced by nonresponse or underreporting, we propose a two-stage multilevel randomized response (MRR) technique to investigate the true level of income and to protect personal privacy. For a wide range of applications, we present a proportional odds model for two-stage MRR data and apply inverse probability weighting and multiple imputation methods to deal with covariates on some subjects that are missing at random. A simulation study is conducted to investigate the effects of missing covariates and to evaluate the performance of the proposed methods. The practicality of the proposed methods is illustrated with the regular monthly income data collected in the Taiwan Social Change Survey. Furthermore, we provide an estimate of personal regular monthly mean income.

Suggested Citation

  • 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.
    • Handle: RePEc:sae:somere:v:51:y:2022:i:1:p:439-467
    DOI: 10.1177/0049124120914954
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    References listed on IDEAS

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    1. Lillard, Lee & Smith, James P & Welch, Finis, 1986. "What Do We Really Know about Wages? The Importance of Nonreporting and Census Imputation," Journal of Political Economy, University of Chicago Press, vol. 94(3), pages 489-506, June.
    2. Corstange, Daniel, 2009. "Sensitive Questions, Truthful Answers? Modeling the List Experiment with LISTIT," Political Analysis, Cambridge University Press, vol. 17(1), pages 45-63, January.
    3. Paolo Righi & Stefano Falorsi & Andrea Fasulo, 2014. "Methods for variance estimation under random hot deck imputation in business surveys," Rivista di statistica ufficiale, ISTAT - Italian National Institute of Statistics - (Rome, ITALY), vol. 16(1-2), pages 45-64.
    4. 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.
    5. van den Hout, Ardo & van der Heijden, Peter G.M. & Gilchrist, Robert, 2007. "The logistic regression model with response variables subject to randomized response," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6060-6069, August.
    6. 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.
    7. Shen-Ming Lee & Mei-Jih Gee & Shu-Hui Hsieh, 2011. "Semiparametric Methods in the Proportional Odds Model for Ordinal Response Data with Missing Covariates," Biometrics, The International Biometric Society, vol. 67(3), pages 788-798, September.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    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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