An alternative to unrelated randomized response techniques with logistic regression analysis

Abstract

The randomized response technique (RRT) is an important tool that is commonly used to protect a respondent’s privacy and avoid biased answers in surveys on sensitive issues. In this work, we consider the joint use of the unrelated-question RRT of Greenberg et al. (J Am Stat Assoc 64:520–539, 1969) and the related-question RRT of Warner (J Am Stat Assoc 60:63–69, 1965) dealing with the issue of an innocuous question from the unrelated-question RRT. Unlike the existing unrelated-question RRT of Greenberg et al. (1969), the approach can provide more information on the innocuous question by using the related-question RRT of Warner (1965) to effectively improve the efficiency of the maximum likelihood estimator of Scheers and Dayton (J Am Stat Assoc 83:969–974, 1988). We can then estimate the prevalence of the sensitive characteristic by using logistic regression. In this new design, we propose the transformation method and provide large-sample properties. From the case of two survey studies, an extramarital relationship study and a cable TV study, we develop the joint conditional likelihood method. As part of this research, we conduct a simulation study of the relative efficiencies of the proposed methods. Furthermore, we use the two survey studies to compare the analysis results under different scenarios.

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

“…For the unrelated-question technique, Hsieh, Lee, and Shen (2010) presented a logistic regression model in the presence of missing covariates. Recently, Hsieh et al (2016) used a logistic regression model based on an RR design which jointly considers the Warner method and unrelated-question technique and can effectively improve the efficiency of the maximum likelihood (ML) estimator of Scheers and Dayton (1998). Cruyff et al (2016) provided a review of regression procedures for RR data, including univariate and multivariate logistic regression.…”