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Applications of Multilevel Structured Additive Regression Models to Insurance Data

机译：多级结构化添加剂模型对保险数据的应用

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Models with structured additive predictor provide a very broad and rich framework for complex regression modeling. They can deal simultaneously with nonlinear covariate effects and time trends, unit- or cluster specific heterogeneity, spatial heterogeneity and complex interactions between covariates of different type. In this paper, we discuss a hierarchical version of regression models with structured additive predictor and its applications to insurance data. That is, the regression coefficients of a particular nonlinear term may obey another regression model with structured additive predictor. The proposed model may be regarded as a an extended version of a multilevel model with nonlinear covariate terms in every level of the hierarchy. We describe several highly efficient MCMC sampling schemes that allow to estimate complex models with several hierarchy levels and a large number of observations typically within a couple of minutes. We demonstrate the usefulness of the approach with applications to insurance data.
机译：具有结构化添加剂预测器的模型为复杂的回归建模提供了一种非常广泛和丰富的框架。它们可以同时处理非线性协变量和时间趋势，单位或簇特异性异质性，不同类型的协变量之间的空间异质性和复杂的相互作用。在本文中，我们讨论了具有结构化添加剂预测器的回归模型的分层版本及其在保险数据中的应用。也就是说，特定非线性术语的回归系数可以用结构化添加剂预测器遵循另一个回归模型。所提出的模型可以被视为具有在层次结构的每个级别的非线性协变量的多级模型的扩展版本。我们描述了几种高效的MCMC采样方案，允许估计具有多个层级水平的复杂模型，并且通常在几分钟内具有大量观察。我们展示了对保险数据应用的方法的有用性。

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