Open Access
June 2015 Bayesian structured additive distributional regression with an application to regional income inequality in Germany
Nadja Klein, Thomas Kneib, Stefan Lang, Alexander Sohn
Ann. Appl. Stat. 9(2): 1024-1052 (June 2015). DOI: 10.1214/15-AOAS823


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 procedure makes 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.


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Nadja Klein. Thomas Kneib. Stefan Lang. Alexander Sohn. "Bayesian structured additive distributional regression with an application to regional income inequality in Germany." Ann. Appl. Stat. 9 (2) 1024 - 1052, June 2015.


Received: 1 September 2013; Revised: 1 March 2015; Published: June 2015
First available in Project Euclid: 20 July 2015

zbMATH: 06499941
MathSciNet: MR3371346
Digital Object Identifier: 10.1214/15-AOAS823

Keywords: Generalised additive models for location , income distribution , iteratively weighted least squares proposal , Markov chain Monte Carlo , scale and shape , semiparametric regression , wage inequality

Rights: Copyright © 2015 Institute of Mathematical Statistics

Vol.9 • No. 2 • June 2015
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