Bayesian generalized additive models for location, scale and shape for zero-inflated and overdispersed count data
AbstractFrequent problems in applied research that prevent the application of the classical Poisson log-linear model for analyzing count data include overdispersion, an excess of zeros compared to the Poisson distribution, correlated responses, as well as complex predictor structures comprising nonlinear effects of continuous covariates, interactions or spatial effects. We propose a general class of Bayesian generalized additive models for zero-inflated and overdispersed count data within the framework of generalized additive models for location, scale and shape where semiparametric predictors can be specified for several parameters of a count data distribution. As special instances, we consider the zero-inflated Poisson, the negative binomial and the zero-inflated negative binomial distribution as standard options for applied work. The additive predictor specifications rely on basis function approximations for the different types of effects in combination with Gaussian smoothness priors. We develop Bayesian inference based on Markov chain Monte Carlo simulation techniques where suitable proposal densities are constructed based on iteratively weighted least squares approximations to the full conditionals. To ensure practicability of the inference we consider theoretical properties like the involved question whether the joint posterior is proper. The proposed approach is evaluated in simulation studies and applied to count data arising from patent citations and claim frequencies in car insurances. For the comparison of models with respect to the distribution, we consider quantile residuals as an effective graphical device and scoring rules that allow to quantify the predictive ability of the models. The deviance information criterion is used for further model specification.
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Bibliographic InfoPaper provided by Faculty of Economics and Statistics, University of Innsbruck in its series Working Papers with number 2013-12.
Date of creation: Jun 2013
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iteratively weighted least squares; Markov chain Monte Carlo; penalized splines; zero-inflated negative binomial; zero-inflated Poisson;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-06-09 (All new papers)
- NEP-ECM-2013-06-09 (Econometrics)
- NEP-FOR-2013-06-09 (Forecasting)
- NEP-ORE-2013-06-09 (Operations Research)
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- Klein, Nadja & Denuit, Michel & Lang, Stefan & Kneib, Thomas, 2014. "Nonlife ratemaking and risk management with Bayesian generalized additive models for location, scale, and shape," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 225-249.
- 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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