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Bayesian structured additive distributional regression for multivariate responses

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  • Nadja Klein
  • Thomas Kneib
  • Stephan Klasen
  • Stefan Lang

Abstract

type="main" xml:id="rssc12090-abs-0001"> We propose a unified Bayesian approach for multivariate structured additive distributional regression analysis comprising a huge class of continuous, discrete and latent multivariate response distributions, 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. non-linear effects of continuous covariates, random effects, spatial effects or interaction effects. Inference is realized by a generic, computationally 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. Applications to illustrate our approach include a joint model of risk factors for chronic and acute childhood undernutrition in India and ecological regressions studying the drivers of election results in Germany.

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  • Nadja Klein & Thomas Kneib & Stephan Klasen & Stefan Lang, 2015. "Bayesian structured additive distributional regression for multivariate responses," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 64(4), pages 569-591, August.
    • Handle: RePEc:bla:jorssc:v:64:y:2015:i:4:p:569-591
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    File URL: http://hdl.handle.net/10.1111/rssc.2015.64.issue-4
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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, Oxford University Press and the European Agricultural and Applied Economics Publications Foundation, vol. 43(4), pages 663-698.
    2. Seiler, Johannes & Harttgen, Kenneth & Kneib, Thomas & Lang, Stefan, 2021. "Modelling children's anthropometric status using Bayesian distributional regression merging socio-economic and remote sensed data from South Asia and sub-Saharan Africa," Economics & Human Biology, Elsevier, vol. 40(C).
    3. Maike Hohberg & Francesco Donat & Giampiero Marra & Thomas Kneib, 2021. "Beyond unidimensional poverty analysis using distributional copula models for mixed ordered‐continuous outcomes," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(5), pages 1365-1390, November.
    4. Klein, Nadja & Denuit, Michel & Lang, Stefan & Kneib, Thomas, 2013. "Nonlife Ratemaking and Risk Management with Bayesian Additive Models for Location, Scale and Shape," LIDAM Discussion Papers ISBA 2013045, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Nadja Klein & Torsten Hothorn & Luisa Barbanti & Thomas Kneib, 2022. "Multivariate conditional transformation models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(1), pages 116-142, March.
    6. Angelo Moretti, 2023. "Estimation of small area proportions under a bivariate logistic mixed model," Quality & Quantity: International Journal of Methodology, Springer, vol. 57(4), pages 3663-3684, August.
    7. Marra, Giampiero & Radice, Rosalba, 2017. "Bivariate copula additive models for location, scale and shape," Computational Statistics & Data Analysis, Elsevier, vol. 112(C), pages 99-113.
    8. Thaden, Hauke & Klein, Nadja & Kneib, Thomas, 2019. "Multivariate effect priors in bivariate semiparametric recursive Gaussian models," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 51-66.
    9. Kneib, Thomas & Silbersdorff, Alexander & Säfken, Benjamin, 2023. "Rage Against the Mean – A Review of Distributional Regression Approaches," Econometrics and Statistics, Elsevier, vol. 26(C), pages 99-123.
    10. W. H. Bonat & J. Olivero & M. Grande-Vega & M. A. Farfán & J. E. Fa, 2017. "Modelling the Covariance Structure in Marginal Multivariate Count Models: Hunting in Bioko Island," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 22(4), pages 446-464, December.
    11. Xu Chen & Surya T. Tokdar, 2021. "Joint quantile regression for spatial data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(4), pages 826-852, September.
    12. Thomas Kneib & Nikolaus Umlauf, 2017. "A Primer on Bayesian Distributional Regression," Working Papers 2017-13, Faculty of Economics and Statistics, Universität Innsbruck.
    13. Alexander Silbersdorff & Kai Sebastian Schneider, 2019. "Distributional Regression Techniques in Socioeconomic Research on the Inequality of Health with an Application on the Relationship between Mental Health and Income," IJERPH, MDPI, vol. 16(20), pages 1-28, October.
    14. Ezra Gayawan & Funmilayo Adenike Fadiji, 2021. "Joint Spatial Modelling of Childhood Morbidity in West Africa Using a Distributional Bivariate Probit Model," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 13(1), pages 56-76, April.
    15. Muschinski, Thomas & Mayr, Georg J. & Simon, Thorsten & Umlauf, Nikolaus & Zeileis, Achim, 2024. "Cholesky-based multivariate Gaussian regression," Econometrics and Statistics, Elsevier, vol. 29(C), pages 261-281.

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