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几何回归模型是处理计数数据的有效工具，但该类数据往往包含大量零值，正确识别零膨胀特征对于选择合适的模型至关重要，过量的零值会导致几何回归模型出现推断偏差，而不必要地采用复杂的零膨胀几何回归模型可能会导致解释和计算上的困难，从而影响模型的实用性和准确性。为此，本文提出一种新的检验方法，用于判断几何回归模型中是否存在零膨胀特征。该方法的核心在于比较实际观察到的零值与几何回归模型预测的零值的差异，进而基于估计方程得到检验统计量的显式表达式及其渐近性质。通过新检验方法与Wald、Likelihood Ratio(LR)和Score检验进行模拟研究对比，结果表明新检验方法在多数情况下具有显著优势，特别是在控制第一类错误方面。最后，本文通过实证分析验证本文方法的有效性和实用性。
Abstract：Geometric regression models are effective for modeling count data, which often contain an excess of zero values. Correctly identifying zero inflation is crucial for selecting an appropriate model, as excessive zeros can lead to bias in the inference of the geometric model, and the unnecessary adoption of a complex zero-inflated geometric regression model may lead to interpretative and computational difficulties, which may affect the practicality and accuracy of the model. To address this, we propose a novel test for detecting zero-inflation within geometric regression models. The core of our method involves comparing the number of observed zeros with the number predicted by the geometric regression model. Based on estimating equations, we derive the explicit expression of the test statistic and its asymptotic properties. Simulation studies comparing the new test with Wald, Likelihood Ratio(LR), and Score tests demonstrate that the proposed method offers significant advantages in most cases, particularly in controlling the Type I error rate. Finally, an empirical analysis validates the effectiveness and practical utility of our approach.
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(1)因篇幅所限，定理1~3证明以附件1展示，见《统计研究》网站所列附件。下同。
(1)因篇幅所限，几何回归模型下不同样本量时，无协变量的QQ图、协变量服从正态分布的QQ图、协变量服从均匀分布的QQ图分别以附图1~3展示。
(1)因篇幅所限，无协变量时ZIGR模型零膨胀检验功效结果以附图4展示。
(1)因篇幅所限，均值的协变量服从正态分布，零膨胀参数φ无协变量和依赖协变量时ZIGR模型零膨胀检验功效分别以附图5~6展示。
(2)因篇幅所限，均值的协变量服从均匀分布，零膨胀参数φ无协变量和依赖协变量时ZIGR模型零膨胀检验功效分别以附图7~8展示。
(1)数据来源为CHARLS数据库，相关网址为https://charls.charlsdata.com/pages/Data/2020-charls-wave5/zh-CN.html。
基本信息:
DOI：10.19343/j.cnki.11-1302/c.2025.08.011
中图分类号:O212.1
引用信息:
[1]张丽平,田茂再.几何回归模型中的零膨胀检验及应用[J].统计研究,2025,42(08):135-146.DOI:10.19343/j.cnki.11-1302/c.2025.08.011.
基金信息:
新疆维吾尔自治区研究生科研创新项目“零膨胀几何回归的统计推断及应用研究”(XJ2025G219); 北京市自然科学基金项目“函数型分层分位回归建模理论方法及应用”(1242005)
2024-06-14
2024
2025-07-25
2025
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2025-08-25
2025-08-25