An alternative to unrelated randomized response techniques with logistic regression analysis

Area of Science:

• Statistics
• Survey Methodology
• Privacy-Preserving Data Analysis

Background:

• The randomized response technique (RRT) is crucial for addressing privacy concerns and response bias in surveys on sensitive topics.
• Existing RRT methods, like Greenberg et al.'s unrelated-question RRT and Warner's related-question RRT, have limitations regarding information gain on innocuous questions.

Purpose of the Study:

• To propose a novel approach combining unrelated-question RRT and related-question RRT to improve information collection on innocuous questions.
• To enhance the efficiency of the maximum likelihood estimator for sensitive characteristic prevalence estimation.
• To introduce a new design for RRT that improves upon existing methods.

Main Methods:

• Jointly applying the unrelated-question RRT (Greenberg et al., 1969) and related-question RRT (Warner, 1965).
• Developing a transformation method with large-sample properties for data analysis.
• Utilizing logistic regression for estimating the prevalence of sensitive characteristics.
• Employing a joint conditional likelihood method, demonstrated with two survey studies (extramarital relationships, cable TV).

Main Results:

• The proposed combined RRT approach provides more information on innocuous questions compared to existing unrelated-question RRT.
• The new method improves the efficiency of the maximum likelihood estimator.
• Simulation studies demonstrate the relative efficiencies of the proposed methods.
• Analysis of survey data under different scenarios highlights the practical utility of the approach.

Conclusions:

• The joint application of related- and unrelated-question RRT offers a more efficient and informative approach to sensitive surveys.
• The proposed transformation and joint conditional likelihood methods provide robust tools for analyzing data from this novel RRT design.
• This research advances privacy-preserving statistical methods, enhancing the reliability of survey findings on sensitive issues.