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Bayesian Structured Additive Distributional Regression for Multivariate Responses


  • Nadja Klein


  • Thomas Kneib


  • Stephan Klasen


  • Stefan Lang



In this paper, we propose a unified Bayesian approach for multivariate structured additive distributional regression analysis where inference is applicable to a huge class of multivariate response distributions, comprising continuous, discrete and latent models, and where each parameter of these potentially complex distributions is modelled by a structured additive predictor. The latter is an additive composition of different types of covariate effects e.g. nonlinear effects of continuous variables, random effects, spatial variations, or interaction effects. Inference is realised by a generic, efficient Markov chain Monte Carlo algorithm based on iteratively weighted least squares approximations and with multivariate Gaussian priors to enforce specific properties of functional effects. Examples will be given by illustrations on analysing the joint model of risk factors for chronic and acute childhood malnutrition in India and on ecological regression for German election results.

Suggested Citation

  • Nadja Klein & Thomas Kneib & Stephan Klasen & Stefan Lang, 2013. "Bayesian Structured Additive Distributional Regression for Multivariate Responses," Working Papers 2013-35, Faculty of Economics and Statistics, University of Innsbruck.
  • Handle: RePEc:inn:wpaper:2013-35

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    References listed on IDEAS

    1. Koop, Gary & Osiewalski, Jacek & Steel, Mark F. J., 1995. "Bayesian long-run prediction in time series models," Journal of Econometrics, Elsevier, vol. 69(1), pages 61-80, September.
    2. Lown, Cara & Morgan, Donald P., 2006. "The Credit Cycle and the Business Cycle: New Findings Using the Loan Officer Opinion Survey," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 38(6), pages 1575-1597, September.
    3. Chikuse, Yasuko, 1990. "The matrix angular central Gaussian distribution," Journal of Multivariate Analysis, Elsevier, vol. 33(2), pages 265-274, May.
    4. Angela Maddalonia & Jose-Luis Peydro, 2013. "Monetary Policy, macroprudential Policy, and Banking Stability: Evidence from the Euro Area," International Journal of Central Banking, International Journal of Central Banking, vol. 9(1), pages 121-169, March.
    5. Strachan, Rodney W. & Inder, Brett, 2004. "Bayesian analysis of the error correction model," Journal of Econometrics, Elsevier, vol. 123(2), pages 307-325, December.
    6. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
    7. Phillips, P C B, 1991. "To Criticize the Critics: An Objective Bayesian Analysis of Stochastic Trends," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(4), pages 333-364, Oct.-Dec..
    8. repec:rim:rimwps:02-07 is not listed on IDEAS
    9. Jesper Berg & Annalisa Ferrando & Gabe de Bondt & Silvia Scopel, 2005. "The bank lending survey for the euro area," Occasional Paper Series 23, European Central Bank.
    10. Gary Koop & Roberto León-González & Rodney W. Strachan, 2010. "Efficient Posterior Simulation for Cointegrated Models with Priors on the Cointegration Space," Econometric Reviews, Taylor & Francis Journals, vol. 29(2), pages 224-242, April.
    11. Villani, Mattias, 2006. "Bayesian point estimation of the cointegration space," Journal of Econometrics, Elsevier, vol. 134(2), pages 645-664, October.
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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. repec:eee:csdana:v:112:y:2017:i:c:p:99-113 is not listed on IDEAS
    3. repec:spr:jagbes:v:22:y:2017:i:4:d:10.1007_s13253-017-0284-7 is not listed on IDEAS
    4. Thomas Kneib & Nikolaus Umlauf, 2017. "A Primer on Bayesian Distributional Regression," Working Papers 2017-13, Faculty of Economics and Statistics, University of Innsbruck.


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