An alternative to unrelated randomized response techniques with logistic regression analysis

Shu Hui Hsieh, Shen Ming Lee, Chin-Shang Li, Su Hao Tu

Research output: Contribution to journalArticle

1 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)1-21
Number of pages21
JournalStatistical Methods and Applications
DOIs
StateAccepted/In press - Jan 25 2016

Keywords

  • Joint conditional likelihood method
  • Randomized response technique
  • Transformation method

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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