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.

翻译：本文推导了一种新的多元回归模型，旨在拟合相关的二值数据。该多元分布源自基于边际方法的、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。指定补对数-对数函数以实现响应变量与随机效应之间的强共轭性。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分布进一步导出了MBerGLG回归（MBerGLGR）模型，为拟合非平衡及平衡的相关响应二值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、有效且渐近一致的。采用随机化分位数残差来识别可能偏离所提模型及数据的情况，并检测异常个体。最后，在数据分析部分展示了两个应用实例。