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Bayesian generalized additive models for location, scale and shape for zero-inflated and overdispersed count data

Author

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  • Nadja Klein

    ()

  • Thomas Kneib

    ()

  • Stefan Lang

    ()

Abstract

Frequent 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.

Suggested Citation

  • Nadja Klein & Thomas Kneib & Stefan Lang, 2013. "Bayesian generalized additive models for location, scale and shape for zero-inflated and overdispersed count data," Working Papers 2013-12, Faculty of Economics and Statistics, University of Innsbruck.
  • Handle: RePEc:inn:wpaper:2013-12
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    References listed on IDEAS

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    1. Plott, Charles R & Sunder, Shyam, 1982. "Efficiency of Experimental Security Markets with Insider Information: An Application of Rational-Expectations Models," Journal of Political Economy, University of Chicago Press, vol. 90(4), pages 663-698, August.
    2. Camerer, Colin & Weigelt, Keith, 1991. "Information Mirages in Experimental Asset Markets," The Journal of Business, University of Chicago Press, vol. 64(4), pages 463-493, October.
    3. Easley, David & O'Hara, Maureen, 1987. "Price, trade size, and information in securities markets," Journal of Financial Economics, Elsevier, vol. 19(1), pages 69-90, September.
    4. Ron Kaniel & Hong Liu, 2006. "So What Orders Do Informed Traders Use?," The Journal of Business, University of Chicago Press, vol. 79(4), pages 1867-1914, July.
    5. Martin Barner & Francesco Feri & Charles R. Plott, 2005. "On the microstructure of price determination and information aggregation with sequential and asymmetric information arrival in an experimental asset market," Annals of Finance, Springer, pages 73-107.
    6. Jürgen Huber & Martin Angerer & Michael Kirchler, 2011. "Experimental asset markets with endogenous choice of costly asymmetric information," Experimental Economics, Springer;Economic Science Association, vol. 14(2), pages 223-240, May.
    7. Chakravarty Sugato & Holden Craig W., 1995. "An Integrated Model of Market and Limit Orders," Journal of Financial Intermediation, Elsevier, vol. 4(3), pages 213-241, July.
    8. repec:pit:wpaper:489 is not listed on IDEAS
    9. Bloomfield, Robert & O'Hara, Maureen & Saar, Gideon, 2005. "The "make or take" decision in an electronic market: Evidence on the evolution of liquidity," Journal of Financial Economics, Elsevier, vol. 75(1), pages 165-199, January.
    10. Meulbroek, Lisa K, 1992. " An Empirical Analysis of Illegal Insider Trading," Journal of Finance, American Finance Association, vol. 47(5), pages 1661-1699, December.
    11. Antoine J. Bruguier & Steven R. Quartz & Peter Bossaerts, 2010. "Exploring the Nature of "Trader Intuition"," Journal of Finance, American Finance Association, vol. 65(5), pages 1703-1723, October.
    12. Holden, Craig W & Subrahmanyam, Avanidhar, 1992. " Long-Lived Private Information and Imperfect Competition," Journal of Finance, American Finance Association, vol. 47(1), pages 247-270, March.
    13. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    14. Goettler, Ronald L. & Parlour, Christine A. & Rajan, Uday, 2009. "Informed traders and limit order markets," Journal of Financial Economics, Elsevier, vol. 93(1), pages 67-87, July.
    15. Martin Barner & Francesco Feri & Charles R. Plott, 2005. "On the microstructure of price determination and information aggregation with sequential and asymmetric information arrival in an experimental asset market," Annals of Finance, Springer, pages 73-107.
    16. Smith, Vernon L, 1982. "Markets as Economizers of Information: Experimental Examination of the "Hayek Hypothesis"," Economic Inquiry, Western Economic Association International, vol. 20(2), pages 165-179, April.
    17. Charles R. Schnitzlein, 2002. "Price Formation and Market Quality When the Number and Presence of Insiders Is Unknown," Review of Financial Studies, Society for Financial Studies, vol. 15(4), pages 1077-1109.
    18. Michael Kirchler & Jurgen Huber & Thomas Stockl, 2012. "Thar She Bursts: Reducing Confusion Reduces Bubbles," American Economic Review, American Economic Association, pages 865-883.
    19. Michael Kirchler & Jurgen Huber & Thomas Stockl, 2012. "Thar She Bursts: Reducing Confusion Reduces Bubbles," American Economic Review, American Economic Association, pages 865-883.
    20. Urs Fischbacher, 2007. "z-Tree: Zurich toolbox for ready-made economic experiments," Experimental Economics, Springer;Economic Science Association, vol. 10(2), pages 171-178, June.
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    Cited by:

    1. 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.
    2. 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.

    More about this item

    Keywords

    iteratively weighted least squares; Markov chain Monte Carlo; penalized splines; zero-inflated negative binomial; zero-inflated Poisson;

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