We introduce a bivariate bidimensional mixed-effects regression model, motivated by the analysis of ${\text{CO}}_2$ emission levels and growth on OECD countries from 1990 to 2018. The model is able to capture heterogeneity across countries and allows for a full association structure among outcomes, assuming a discrete distribution for the random terms with a possibly different number of support points in each univariate profile. We test the behavior of the proposed approach via a simulation study, considering several factors such as the number of observed units, times, and levels of heterogeneity in the data. Empirically, we define an extended version of the STIRPAT model where all model parameters, and not only the mean, vary according to a regression model. Our empirical findings provide evidence of heterogeneous behaviors across countries and suggest the need of a flexible approach to properly reflect the heterogeneity in both the emission levels and the growth processes.

中文翻译：

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二氧化碳排放和增长：双变量二维均值-方差随机效应模型

我们引入了一个双变量二维混合效应回归模型，其动机是分析${\text{一氧化碳}}_2$1990 年至 2018 年 OECD 国家的排放水平和增长。该模型能够捕捉各国之间的异质性，并允许结果之间的完整关联结构，假设随机项呈离散分布，每个单变量中的支持点数量可能不同轮廓。我们通过模拟研究来测试所提出方法的行为，考虑了几个因素，例如观察到的单元的数量、时间和数据中的异质性水平。根据经验，我们定义了 STIRPAT 模型的扩展版本，其中所有模型参数（而不仅仅是平均值）根据回归模型而变化。