Optimizing randomized response surveys: A new adaptive nonlinear scrambling approach for sensitive data collection

Abstract

This study introduces an adaptive nonlinear optional randomized response technique that advances the trade-off between privacy and estimation efficiency in sensitive surveys. The model employs a nonlinear transformation function and a beta-distributed scrambling variable, allowing the perturbation mechanism to adapt dynamically to each question’s inherent sensitivity. This adaptability ensures stronger privacy guarantees without proportionally sacrificing the accuracy of population estimates. Theoretical derivations confirm the estimator’s unbiasedness, while also quantifying its improved variance and a robust privacy measure. A key innovation is an optimization framework that selects model parameters to minimize a combined efficiency–privacy metric, systematically enhancing overall performance. Validation through extensive simulation, a comprehensive survey of randomized response techniques for data privacy, and a data illustration show that an adaptive nonlinear optional randomized response Technique achieves significant reductions in estimator variance and gains in perceived privacy protection across a wide range of sensitivity probabilities. Compared to conventional optional randomized response techniques, it provides superior, balanced performance. Consequently, an adaptive nonlinear optional randomized response technique emerges as a flexible, reliable tool for collecting sensitive data in education, social sciences, and public health, where respondent trust and data accuracy are paramount.

Keywords

• Adaptive estimation
• nonlinear scrambling
• randomized response technique
• sensitive data collection
• survey privacy.

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