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A Logistic Regression Extension for the Randomized Response Simple and Crossed Models: Theoretical Results and Empirical Evidence

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  • Shu-Hui Hsieh
  • Pier Francesco Perri

Abstract

We propose some theoretical and empirical advances by supplying the methodology for analyzing the factors that influence two sensitive variables when data are collected by randomized response (RR) survey modes. First, we provide the framework for obtaining the maximum likelihood estimates of logistic regression coefficients under the RR simple and crossed models, then we carry out a simulation study to assess the performance of the estimation procedure. Finally, logistic regression analysis is illustrated by considering real data about cannabis use and legalization and about abortion and illegal immigration. The empirical results bring out certain considerations about the effect of the RR and direct questioning survey modes on the estimates. The inference about the sign and the significance of the regression coefficients can contribute to the debate on whether the RR approach is an effective survey method to reduce misreporting and improve the validity of analyses.

Suggested Citation

  • Shu-Hui Hsieh & Pier Francesco Perri, 2022. "A Logistic Regression Extension for the Randomized Response Simple and Crossed Models: Theoretical Results and Empirical Evidence," Sociological Methods & Research, , vol. 51(3), pages 1244-1281, August.
    • Handle: RePEc:sae:somere:v:51:y:2022:i:3:p:1244-1281
    DOI: 10.1177/0049124120914950
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    References listed on IDEAS

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    1. 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.
    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. Pier Francesco Perri & Elvira Pelle & Manuela Stranges, 2016. "Estimating Induced Abortion and Foreign Irregular Presence Using the Randomized Response Crossed Model," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 129(2), pages 601-618, November.
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    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.

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