We propose a versatile joint regression framework for count responses. The method is implemented in the R add-on package GJRM and allows for modelling linear and non-linear dependence through the use of several copulae. Moreover, the parameters of the marginal distributions of the count responses and of the copula can be specified as flexible functions of covariates. Motivated by competitive settings, we also discuss an extension which forces the regression coefficients of the marginal (linear) predictors to be equal via a suitable penalisation. Model fitting is based on a trust region algorithm which estimates simultaneously all the parameters of the joint models. We investigate the proposal’s empirical performance in two simulation studies, the first one designed for arbitrary count data, the other one reflecting competitive settings. Finally, the method is applied to football data, showing its benefits compared to the standard approach with regard to predictive performance.

中文翻译：

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计数数据的广义联合回归：竞争环境的惩罚性扩展

我们提出了用于计数响应的通用联合回归框架。该方法在R附加程序包GJRM中实现并允许通过使用多个copulae对线性和非线性相关性进行建模。此外，可以将计数响应和语系的边际分布的参数指定为协变量的灵活函数。受竞争环境的影响，我们还讨论了一种扩展，该扩展通过适当的惩罚迫使边际（线性）预测变量的回归系数相等。模型拟合基于信任区域算法，该算法同时估计联合模型的所有参数。我们在两项模拟研究中研究了该提案的经验表现，第一项研究是针对任意计数数据设计的，另一项研究反映了竞争环境。最后，该方法应用于足球数据，