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BayesX: Analyzing Bayesian Structural Additive Regression Models

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  • Brezger, Andreas
  • Kneib, Thomas
  • Lang, Stefan

Abstract

There has been much recent interest in Bayesian inference for generalized additive and related models. The increasing popularity of Bayesian methods for these and other model classes is mainly caused by the introduction of Markov chain Monte Carlo (MCMC) simulation techniques which allow realistic modeling of complex problems. This paper describes the capabilities of the free software package BayesX for estimating regression models with structured additive predictor based on MCMC inference. The program extends the capabilities of existing software for semiparametric regression included in S-PLUS, SAS, R or Stata. Many model classes well known from the literature are special cases of the models supported by BayesX. Examples are generalized additive (mixed) models, dynamic models, varying coefficient models, geoadditive models, geographically weighted regression and models for space-time regression. BayesX supports the most common distributions for the response variable. For univariate responses these are Gaussian, Binomial, Poisson, Gamma, negative Binomial, zero inflated Poisson and zero inflated negative binomial. For multicategorical responses, both multinomial logit and probit models for unordered categories of the response as well as cumulative threshold models for ordered categories can be estimated. Moreover, BayesX allows the estimation of complex continuous time survival and hazard rate models.

Suggested Citation

  • Brezger, Andreas & Kneib, Thomas & Lang, Stefan, 2005. "BayesX: Analyzing Bayesian Structural Additive Regression Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 14(i11).
  • Handle: RePEc:jss:jstsof:v:014:i11
    DOI: http://hdl.handle.net/10.18637/jss.v014.i11
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    File URL: https://www.jstatsoft.org/index.php/jss/article/view/v014i11/v14i11.pdf
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    References listed on IDEAS

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    1. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika van der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639.
    2. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167.
    3. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506.
    4. E. E. Kammann & M. P. Wand, 2003. "Geoadditive models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 52(1), pages 1-18.
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    Citations

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    Cited by:

    1. Wolfgang Brunauer & Stefan Lang & Wolfgang Feilmayr, 2013. "Hybrid multilevel STAR models for hedonic house prices," Review of Regional Research: Jahrbuch für Regionalwissenschaft, Springer;Gesellschaft für Regionalforschung (GfR), vol. 33(2), pages 151-172, October.
    2. Seongil Jo & Taeyoung Roh & Taeryon Choi, 2016. "Bayesian spectral analysis models for quantile regression with Dirichlet process mixtures," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(1), pages 177-206, March.
    3. Lawrence Kazembe, 2009. "Modelling individual fertility levels in Malawian women: a spatial semiparametric regression model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 18(2), pages 237-255, July.
    4. Umlauf, Nikolaus & Adler, Daniel & Kneib, Thomas & Lang, Stefan & Zeileis, Achim, 2015. "Structured Additive Regression Models: An R Interface to BayesX," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i21).
    5. Elisabeth Waldmann & Thomas Kneib & Yu Ryan Yu & Stefan Lang, 2012. "Bayesian semiparametric additive quantile regression," Working Papers 2012-06, Faculty of Economics and Statistics, University of Innsbruck.
    6. repec:spr:stmapp:v:27:y:2018:i:2:d:10.1007_s10260-017-0405-z is not listed on IDEAS
    7. 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.
    8. W. Brunauer & S. Lang & P. Wechselberger & S. Bienert, 2010. "Additive Hedonic Regression Models with Spatial Scaling Factors: An Application for Rents in Vienna," The Journal of Real Estate Finance and Economics, Springer, vol. 41(4), pages 390-411, November.
    9. Schmidt, Paul & Mühlau, Mark & Schmid, Volker, 2017. "Fitting large-scale structured additive regression models using Krylov subspace methods," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 59-75.
    10. Luping Zhao & Timothy E. Hanson, 2011. "Spatially Dependent Polya Tree Modeling for Survival Data," Biometrics, The International Biometric Society, vol. 67(2), pages 391-403, June.
    11. Lang, Stefan & Steiner, Winfried J. & Weber, Anett & Wechselberger, Peter, 2015. "Accommodating heterogeneity and nonlinearity in price effects for predicting brand sales and profits," European Journal of Operational Research, Elsevier, vol. 246(1), pages 232-241.
    12. Strasak, Alexander M. & Umlauf, Nikolaus & Pfeiffer, Ruth M. & Lang, Stefan, 2011. "Comparing penalized splines and fractional polynomials for flexible modelling of the effects of continuous predictor variables," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1540-1551, April.
    13. A. Brezger & L. Fahrmeir & A. Hennerfeind, 2007. "Adaptive Gaussian Markov random fields with applications in human brain mapping," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 56(3), pages 327-345.
    14. Pebesma, Edzer & Bivand, Roger & Ribeiro, Paulo Justiniano, 2015. "Software for Spatial Statistics," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i01).
    15. Kenneth Harttgen & Stefan Lang & Judith Santer & Johannes Seiler, 2017. "Modeling under-5 mortality through multilevel structured additive regression with varying coefficients for Asia and Sub-Saharan Africa," Working Papers 2017-15, Faculty of Economics and Statistics, University of Innsbruck.
    16. Andreas Brezger & Stefan Lang, 2007. "Simultaneous probability statements for Bayesian P-splines," Working Papers 2007-08, Faculty of Economics and Statistics, University of Innsbruck.

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