Binomial regression models are commonly applied to proportion data such as those relating to the mortality and infection rates of diseases. However, it is often the case that the responses may exhibit excessive zeros; in such cases a zero-inflated binomial (ZIB) regression model can be applied instead. In practice, it is essential to test if there are excessive zeros in the outcome to help choose an appropriate model. The binomial models can yield biased inference if there are excessive zeros, while ZIB models may be unnecessarily complex and hard to interpret, and even face convergence issues, if there are no excessive zeros. In this paper, we develop a new test for testing zero inflation in binomial regression models by directly comparing the amount of observed zeros with what would be expected under the binomial regression model. A closed form of the test statistic, as well as the asymptotic properties of the test, is derived based on estimating equations. Our systematic simulation studies show that the new test performs very well in most cases, and outperforms the classical Wald, likelihood ratio, and score tests, especially in controlling type I errors. Two real data examples are also included for illustrative purpose.

中文翻译：

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在二项式回归模型中测试膨胀的零

二项式回归模型通常应用于比例数据，例如与疾病死亡率和感染率相关的数据。然而，通常情况下，响应可能会出现过多的零；在这种情况下，可以改用零膨胀二项式 (ZIB) 回归模型。在实践中，必须测试结果中是否存在过多的零以帮助选择合适的模型。如果有过多的零，二项式模型会产生有偏的推理，而 ZIB 模型可能会不必要地复杂且难以解释，如果没有过多的零，甚至会面临收敛问题。在本文中，我们通过直接比较观察到的零值与二项式回归模型下的预期值，开发了一种新的测试，用于测试二项式回归模型中的零通胀。检验统计量的封闭形式以及检验的渐近特性是基于估计方程推导出来的。我们的系统模拟研究表明，新测试在大多数情况下都表现良好，并且优于经典的 Wald、似然比和分数测试，尤其是在控制 I 类错误方面。出于说明目的，还包括两个真实数据示例。