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<p>This research explores the application of the well-regarded Cauchy process in modeling self-reported discrete choice data. The advantages of this proposed approach are elucidated on two fronts. Firstly, it is demonstrated that the devised mechanism adeptly addresses the presence of contamination in self-reported data, particularly when the social desirability phenomenon is active. Secondly, the utility of the suggested scheme is discussed as a privacy protection strategy, capable of preserving the privacy of respondents, especially in studies involving tabooed behaviors. The flexibility of the Cauchy model is achieved by introducing a masking parameter as a proxy for the degree of prevailing desirability bias. The applicability of the proposed model is demonstrated through thorough numerical evaluations and detailed empirical assessments. The simulation-based investigations utilize the adaptive Metropolis–Hastings algorithm of Markov Chain Monte Carlo. The generality of the approach is enhanced by incorporating diverse parametric settings into the numerical environment. The validity of the masking parameter is assessed within the permissible range of 0–1. Furthermore, asymptotic considerations are explored by varying sample sizes, such as n = 50, 100, 500, and 1000. The numerical results are then validated by analyzing data on classical crimes' sensitivity. The legitimacy of the proposed model in maintaining the comparative hierarchy among competing choices is detailed throughout the article. The encouraging outcomes of this research are substantiated by reporting various relevant summaries, including estimated utility, preference probabilities, associated 95% credible intervals, and absolute estimated deviations.</p>

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An improved randomized response model based on cauchy stochastic process

  • 期刊论文

  • 发表日期：

    2026年1月27日

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  • Salman Arif Cheema,
  • Tanveer Kifayat,
  • Muhammad Abid,
  • Mahmoud E Bakr

摘要

This research explores the application of the well-regarded Cauchy process in modeling self-reported discrete choice data. The advantages of this proposed approach are elucidated on two fronts. Firstly, it is demonstrated that the devised mechanism adeptly addresses the presence of contamination in self-reported data, particularly when the social desirability phenomenon is active. Secondly, the utility of the suggested scheme is discussed as a privacy protection strategy, capable of preserving the privacy of respondents, especially in studies involving tabooed behaviors. The flexibility of the Cauchy model is achieved by introducing a masking parameter as a proxy for the degree of prevailing desirability bias. The applicability of the proposed model is demonstrated through thorough numerical evaluations and detailed empirical assessments. The simulation-based investigations utilize the adaptive Metropolis–Hastings algorithm of Markov Chain Monte Carlo. The generality of the approach is enhanced by incorporating diverse parametric settings into the numerical environment. The validity of the masking parameter is assessed within the permissible range of 0–1. Furthermore, asymptotic considerations are explored by varying sample sizes, such as n = 50, 100, 500, and 1000. The numerical results are then validated by analyzing data on classical crimes' sensitivity. The legitimacy of the proposed model in maintaining the comparative hierarchy among competing choices is detailed throughout the article. The encouraging outcomes of this research are substantiated by reporting various relevant summaries, including estimated utility, preference probabilities, associated 95% credible intervals, and absolute estimated deviations.