一种面向非平衡二元数据的新型多元回归模型：随机效应方法下的强共轭性
A novel multivariate regression model for unbalanced binary data : a strong conjugacy under random effect approach
AI总结：
本文提出MBerGLG分布及MBerGLGR回归模型，利用广义对数伽马随机效应与互补双对数函数实现强共轭，为平衡及非平衡相关二元数据提供有效拟合方法。
摘要：
本文推导了一种新的多元回归模型，用于拟合相关的二元数据。该多元分布源自边际方法下具有非正态随机截距的伯努利混合模型。通过考虑特定的参数设置，假设随机效应分布为广义对数伽马（GLG）分布。指定互补双对数函数以在响应变量与随机效应之间建立强共轭性。这种新的离散多元分布被命名为MBerGLG分布，具有位置参数和离散参数。MBerGLG分布导出了MBerGLG回归（MBerGLGR）模型，为拟合非平衡和平衡的相关响应二元数据提供了一种替代方法。蒙特卡洛模拟研究表明，其最大似然估计量是无偏的、有效的，并且具有渐近一致性。采用随机化分位数残差来识别所提出模型与数据之间可能存在的偏离，并检测非典型个体。最后，在数据分析部分给出了两个应用实例。
英文摘要：
In this paper, we deduce a new multivariate regression model designed to fit correlated binary data. The multivariate distribution is derived from a Bernoulli mixed model with a nonnormal random intercept on the marginal approach. The random effect distribution is assumed to be the generalized log-gamma (GLG) distribution by considering a particular parameter setting. The complement log-log function is specified to lead to strong conjugacy between the response variable and random effect. The new discrete multivariate distribution, named MBerGLG distribution, has location and dispersion parameters. The MBerGLG distribution leads to the MBerGLG regression (MBerGLGR) model, providing an alternative approach to fitting both unbalanced and balanced correlated response binary data. Monte Carlo simulation studies show that its maximum likelihood estimators are unbiased, efficient, and consistent asymptotically. The randomized quantile residuals are performed to identify possible departures from the proposal model and the data and detect atypical subjects. Finally, two applications are presented in the data analysis section.
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