Logistic regression for data acquired via two-stage generalized randomized response technique

Shen-Ming Lee, Truong-Nhat Le, Phuoc-Loc Tran and Chin-Shang Li

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 21, 6711-6734

Abstract: We propose a two-stage generalized randomized response (GRR) design, incorporating the first-stage design of Huang’s two-stage RR design as the first-stage design and Christofides’ GRR design as the second-stage design. Our design allows estimation of the proportion of the population with a sensitive attribute and the population proportion of sensitive attribute respondents providing a truthful response to a directly asked sensitive question in the first stage. We derive the large-sample properties of the maximum likelihood (ML) estimators for logistic regression parameters and assess the finite-sample performance of the ML estimators via Monte Carlo experiments. The practical application of our methodology is illustrated by using the 2016 survey data on the sexuality of local freshmen of Feng Chia University in Taiwan.

Date: 2025
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DOI: 10.1080/03610926.2025.2461611

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