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Applications of Multilevel Structured Additive Regression Models to Insurance Data

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  • Stefan Lang
  • Nikolaus Umlauf

Abstract

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 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.

Suggested Citation

  • Stefan Lang & Nikolaus Umlauf, 2010. "Applications of Multilevel Structured Additive Regression Models to Insurance Data," Working Papers 2010-01, Faculty of Economics and Statistics, Universität Innsbruck, revised Jan 2010.
    • Handle: RePEc:inn:wpaper:2010-01
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    References listed on IDEAS

    as
    1. Belitz, Christiane & Lang, Stefan, 2008. "Simultaneous selection of variables and smoothing parameters in structured additive regression models," Computational Statistics & Data Analysis, Elsevier, vol. 53(1), pages 61-81, September.
    2. Brezger, Andreas & Lang, Stefan, 2006. "Generalized structured additive regression based on Bayesian P-splines," Computational Statistics & Data Analysis, Elsevier, vol. 50(4), pages 967-991, February.
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    Cited by:

    1. Tomas, Julien & Planchet, Frédéric, 2013. "Multidimensional smoothing by adaptive local kernel-weighted log-likelihood: Application to long-term care insurance," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 573-589.

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    More about this item

    Keywords

    Bayesian hierarchical models; multilevel models; P-splines; spatial heterogeneity;
    All these keywords.

    JEL classification:

    • C - Mathematical and Quantitative Methods

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