Poverty is a multidimensional concept often comprising a monetary outcome and other welfare dimensions such as education, subjective well-being or health that are measured on an ordinal scale. In applied research, multidimensional poverty is ubiquitously assessed by studying each poverty dimension independently in univariate regression models or by combining several poverty dimensions into a scalar index. This approach inhibits a thorough analysis of the potentially varying interdependence between the poverty dimensions. We propose a multivariate copula generalized additive model for location, scale and shape (copula GAMLSS or distributional copula model) to tackle this challenge. By relating the copula parameter to covariates, we specifically examine if certain factors determine the dependence between poverty dimensions. Furthermore, specifying the full conditional bivariate distribution allows us to derive several features such as poverty risks and dependence measures coherently from one model for different individuals. We demonstrate the approach by studying two important poverty dimensions: income and education. Since the level of education is measured on an ordinal scale while income is continuous, we extend the bivariate copula GAMLSS to the case of mixed ordered-continuous outcomes. The new model is integrated into the GJRM package in R and applied to data from Indonesia. Particular emphasis is given to the spatial variation of the income–education dependence and groups of individuals at risk of being simultaneously poor in both education and income dimensions.

中文翻译：

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使用分布式 copula 模型对混合有序连续结果进行超越一维贫困分析

贫困是一个多维度的概念，通常包括货币结果和其他福利维度，如教育、主观幸福感或健康，这些维度是按顺序衡量的。在应用研究中，通过在单变量回归模型中独立研究每个贫困维度或将多个贫困维度组合成一个标量指数，多维贫困无处不在。这种方法阻碍了对贫困维度之间潜在变化的相互依存关系的彻底分析。我们提出了一个用于位置、尺度和形状的多变量 copula 广义加性模型（copula GAMLSS 或分布式 copula 模型）来应对这一挑战。通过将 copula 参数与协变量相关联，我们专门检查某些因素是否决定了贫困维度之间的依赖性。此外，指定完整的条件双变量分布使我们能够从不同个体的一个模型中连贯地推导出若干特征，例如贫困风险和依赖度量。我们通过研究两个重要的贫困维度来展示该方法：收入和教育。由于教育水平是按顺序衡量的，而收入是连续的，我们将双变量 copula GAMLSS 扩展到混合有序-连续结果的情况。新模型被集成到 由于教育水平是按顺序衡量的，而收入是连续的，我们将双变量 copula GAMLSS 扩展到混合有序-连续结果的情况。新模型被集成到 由于教育水平是按顺序衡量的，而收入是连续的，我们将双变量 copula GAMLSS 扩展到混合有序-连续结果的情况。新模型被集成到R 中的GJRM包并应用于来自印度尼西亚的数据。特别强调了收入-教育依赖的空间变化以及面临教育和收入方面同时处于贫困风险的个人群体。