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<p>Logistic regression is widely used to estimate the proportion of a population possessing sensitive characteristics. It is essential to validate the assumed model before making statistical inferences to avoid erroneous conclusions. We propose employing a suite of statistical tests to evaluate the goodness-of-fit of logistic regression when only probabilistic versions of the binary response variable are collected using randomized response techniques. We rigorously derive the asymptotic properties of the proposed test statistics under the null hypothesis and some assumptions. Through comprehensive simulation studies and real data analyses, we demonstrate the finite-sample performance of the tests in terms of size and power.</p>

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Goodness-of-fit test for logistic regression for sensitive data collected via randomized response techniques

  • 期刊论文

  • 发表日期：

    2026年4月2日

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  • Truong-Nhat Le,
  • Tzu-Ju Hsu,
  • Shen-Ming Lee,
  • Chin-Shang Li

摘要

Logistic regression is widely used to estimate the proportion of a population possessing sensitive characteristics. It is essential to validate the assumed model before making statistical inferences to avoid erroneous conclusions. We propose employing a suite of statistical tests to evaluate the goodness-of-fit of logistic regression when only probabilistic versions of the binary response variable are collected using randomized response techniques. We rigorously derive the asymptotic properties of the proposed test statistics under the null hypothesis and some assumptions. Through comprehensive simulation studies and real data analyses, we demonstrate the finite-sample performance of the tests in terms of size and power.