BAYESIAN STRUCTURED ADDITIVE DISTRIBUTIONAL REGRESSION WITH AN APPLICATION TO REGIONAL INCOME INEQUALITY IN GERMANY
BAYESIAN STRUCTURED ADDITIVE DISTRIBUTIONAL REGRESSION WITH AN APPLICATION TO REGIONAL INCOME INEQUALITY IN GERMANY
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DOI：
10.1214/15-aoas823
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发表时间：
2015-06-01
影响因子：
1.8
通讯作者：
Sohn, Alexander
中科院分区：
文献类型：
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作者：
Klein, Nadja;Kneib, Thomas;Sohn, Alexander
我们提出了一个通用的贝叶斯框架，在分布回归模型中，一个潜在的复杂的响应分布，而不仅仅是平均值的每个参数的推断是一个结构化的添加剂预测。后者是由各种不同的功能效应类型，如非线性效应，空间效应，随机系数，相互作用表面或其他（可能是非标准的）基函数表示相加。为了增强函数效应的特定属性，例如平滑度，将信息多元高斯先验分配给基函数系数。然后，推理可以基于计算效率高的马尔可夫链蒙特卡罗模拟技术，其中一个通用的程序使用特定于分布的迭代加权最小二乘近似的完整条件。分布回归的框架包括许多与处理非标准响应结构相关的特殊情况，例如高度偏斜的非负响应，过度分散和零膨胀的计数或份额，包括零膨胀和一膨胀的可能性。我们讨论了分布回归沿着劳动收入的决定因素在德国的全职工作男性的研究，特别注重德国统一后的地区差异。控制年龄，教育，工作经验和地方差异，我们估计完整的条件收入分布，使我们能够在一个联合模型中以一致的方式研究各种分布量，如矩，分位数或不平等措施。模型选择的实际方面的详细指导，包括劳动收入的几个竞争性分布的选择和收入分配的不同协变量的影响的考虑完成分布回归分析。我们发现，在其他条件相同的情况下，除了预期收入较低之外，东德德国的全职工作男性还面临着比西德男性更不平等的收入分配。
We propose a generic Bayesian framework for inference in distributional regression models in which each parameter of a potentially complex response distribution and not only the mean is related to a structured additive predictor. The latter is composed additively of a variety of different functional effect types such as nonlinear effects, spatial effects, random coefficients, interaction surfaces or other (possibly nonstandard) basis function representations. To enforce specific properties of the functional effects such as smoothness, informative multivariate Gaussian priors are assigned to the basis function coefficients. Inference can then be based on computationally efficient Markov chain Monte Carlo simulation techniques where a generic proceduremakes use of distribution-specific iteratively weighted least squares approximations to the full conditionals. The framework of distributional regression encompasses many special cases relevant for treating nonstandard response structures such as highly skewed nonnegative responses, overdispersed and zero-inflated counts or shares including the possibility for zero-and one-inflation. We discuss distributional regression along a study on determinants of labour incomes for full-time working males in Germany with a particular focus on regional differences after the German reunification. Controlling for age, education, work experience and local disparities, we estimate full conditional income distributions allowing us to study various distributional quantities such as moments, quantiles or inequality measures in a consistent manner in one joint model. Detailed guidance on practical aspects of model choice including the selection of several competing distributions for labour incomes and the consideration of different covariate effects on the income distribution complete the distributional regression analysis. We find that next to a lower expected income, full-time working men in East Germany also face a more unequal income distribution than men in the West, ceteris paribus.