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Bayesian Structured Additive Distributional Regression


  • Nadja Klein


  • Thomas Kneib


  • Stefan Lang



In this paper, 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 non-standard) 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 is then based on efficient Markov chain Monte Carlo simulation techniques where a generic procedure makes use of distribution-specific iteratively weighted least squares approximations to the full conditionals. We study properties of the resulting model class and provide detailed guidance on practical aspects of model choice including selecting an apropriate response distribution and predictor specification. The importance and flexibility of Bayesian structured additive distributional regression to estimate all parameters as functions of explanatory variables and therefore to obtain more realistic models, is exemplified in two applications with complex response distributions.

Suggested Citation

  • Nadja Klein & Thomas Kneib & Stefan Lang, 2013. "Bayesian Structured Additive Distributional Regression," Working Papers 2013-23, Faculty of Economics and Statistics, University of Innsbruck.
  • Handle: RePEc:inn:wpaper:2013-23

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    References listed on IDEAS

    1. Leisch, Friedrich, 2004. "FlexMix: A General Framework for Finite Mixture Models and Latent Class Regression in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 11(i08).
    2. Grün, Bettina & Leisch, Friedrich, 2008. "FlexMix Version 2: Finite Mixtures with Concomitant Variables and Varying and Constant Parameters," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 28(i04).
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    Cited by:

    1. Alexander März & Nadja Klein & Thomas Kneib & Oliver Musshoff, 2016. "Analysing farmland rental rates using Bayesian geoadditive quantile regression," European Review of Agricultural Economics, Foundation for the European Review of Agricultural Economics, vol. 43(4), pages 663-698.
    2. Nadja Klein & Michel Denuit & Stefan Lang & Thomas Kneib, 2013. "Nonlife Ratemaking and Risk Management with Bayesian Additive Models for Location, Scale and Shape," Working Papers 2013-24, Faculty of Economics and Statistics, University of Innsbruck.
    3. Alexander Razen & Wolfgang Brunauer & Nadja Klein & Thomas Kneib & Stefan Lang & Nikolaus Umlauf, 2014. "Statistical Risk Analysis for Real Estate Collateral Valuation using Bayesian Distributional and Quantile Regression," Working Papers 2014-12, Faculty of Economics and Statistics, University of Innsbruck.


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