Multilevel structured additive regression
AbstractModels with structured additive predictor provide a very broad and rich framework for complex regression modeling. They can deal simultaneously with nonlinear covariate effects and time trends, unit- or cluster-specific heterogeneity, spatial heterogeneity and complex interactions between covariates of different type. In this paper, we propose a hierarchical or multilevel version of regression models with structured additive predictor where the regression coefficients of a particular nonlinear term may obey another regression model with structured additive predictor. In that sense, the model is composed of a hierarchy of complex structured additive regression models. The proposed model may be regarded as an extended version of a multilevel model with nonlinear covariate terms in every level of the hierarchy. The model framework is also the basis for generalized random slope modeling based on multiplicative random effects. Inference is fully Bayesian and based on Markov chain Monte Carlo simulation techniques. We provide an in depth description of several highly efficient sampling schemes that allow to estimate complex models with several hierarchy levels and a large number of observations within a couple of minutes (often even seconds). We demonstrate the practicability of the approach in a complex application on childhood undernutrition with large sample size and three hierarchy levels.
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Bibliographic InfoPaper provided by Faculty of Economics and Statistics, University of Innsbruck in its series Working Papers with number 2012-07.
Date of creation: Apr 2012
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Bayesian hierarchical models; kriging; Markov random fields; MCMC; multiplicative random effects; P-splines;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-05-15 (All new papers)
- NEP-ECM-2012-05-15 (Econometrics)
- NEP-ORE-2012-05-15 (Operations Research)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Smith, Michael & Kohn, Robert, 1996.
"Nonparametric regression using Bayesian variable selection,"
Journal of Econometrics,
Elsevier, vol. 75(2), pages 317-343, December.
- Smith, M. & Kohn, R., . "Nonparametric Regression using Bayesian Variable Selection," Statistics Working Paper _009, Australian Graduate School of Management.
- H�vard Rue & Sara Martino & Nicolas Chopin, 2009. "Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 319-392.
- Cottet, Remy & Kohn, Robert J. & Nott, David J., 2008. "Variable Selection and Model Averaging in Semiparametric Overdispersed Generalized Linear Models," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 661-671, June.
- Malavika A Subramanyam & Ichiro Kawachi & Lisa F Berkman & S V Subramanian, 2011. "Is Economic Growth Associated with Reduction in Child Undernutrition in India?," Working Papers id:3926, eSocialSciences.
- Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, October.
- Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, October.
- R. A. Rigby & D. M. Stasinopoulos, 2005. "Generalized additive models for location, scale and shape," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 507-554.
- Park, Trevor & Casella, George, 2008. "The Bayesian Lasso," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 681-686, June.
- Brezger, Andreas & Lang, Stefan, 2006. "Generalized structured additive regression based on Bayesian P-splines," Computational Statistics & Data Analysis, Elsevier, vol. 50(4), pages 967-991, February.
- Panagiotelis, Anastasios & Smith, Michael, 2008. "Bayesian identification, selection and estimation of semiparametric functions in high-dimensional additive models," Journal of Econometrics, Elsevier, vol. 143(2), pages 291-316, April.
- 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.
- Yu Yue & Paul Speckman & Dongchu Sun, 2012. "Priors for Bayesian adaptive spline smoothing," Annals of the Institute of Statistical Mathematics, Springer, vol. 64(3), pages 577-613, June.
- 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.
- 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.
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