Joint distribution and marginal distribution methods for checking assumptions of generalized linear model
Joint distribution and marginal distribution methods for checking assumptions of generalized linear model
复制标题
检查广义线性模型假设的联合分布和边际分布方法
DOI：
10.1080/03610926.2019.1651860
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Qiqing Yu
中科院分区：
文献类型：
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作者：
J. Dong;Qiqing Yu
本文研究了广义线性模型的模型诊断图和检验问题。有几种常用的绘图方法和测试来检查回归模型的假设。然而，现有的图和检验需要对响应变量Y和协变量Z的联合累积分布函数进行某些约束，因此当真实的数据集不满足这些约束时，这些图和检验是无效的。特别是，在后一种情况下，这些检验提供的p值是假的。在这篇文章中，我们提出了一种新的方法来检查模型的假设。该方法比较了Y的边际分布（或（Y，Z）的联合分布）的两种估计：一种是非参数极大似然估计，另一种是基于零假设的估计。这种方法被称为边际分布（MD）方法或联合分布（JD）方法。研究了它们的渐近性质。仿真结果表明，无论是诊断图和假设检验使用新的方法提供了令人满意的结果和JD方法总是一致的，即使当现有的方法失败。
Abstract In this article, we consider the model diagnostic plot and test of the generalized linear model. There exist several commonly used plotting methods and tests for checking the regression model assumptions. However, the existing plots and tests require certain constraints on the joint cumulative distribution function of the response variable Y and the covariate Z and thus are invalid when the real data set does not satisfy those constraints. In particular, in the latter case, the p-values provided by these tests are false. In this article, we propose a new method to check the model assumptions. This method compares two estimators of the marginal distribution of Y (or the joint distribution of (Y, Z)): one is the non-parametric maximum likelihood estimator and the other is an estimator based on the null hypothesis. This method is called the marginal distribution (MD) method or the joint distribution (JD) method. Their asymptotic properties are studied. The simulation results suggest both the diagnostic plots and the hypothesis tests using the new methods provide satisfactory results and the JD method is always consistent even when the existing methods fail.