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Regression Models for Count Data in R


Author Info

  • Simon Jackman
  • Christian Kleiber


  • Achim Zeileis

    (University of Basel)


The classical Poisson, geometric and negative binomial regression models for count data belong to the family of generalized linear models and are available at the core of the statistics toolbox in the R system for statistical computing. After reviewing the conceptual and computational features of these methods, a new implementation of zero-inflated and hurdle regression models in the functions zeroinfl() and hurdle() from the package pscl is introduced. It re-uses design and functionality of the basic R functions just as the underlying conceptual tools extend the classical models. Both model classes are able to incorporate over-dispersion and excess zeros - two problems that typically occur in count data sets in economics and the social and political sciences - better than their classical counterparts. Using cross-section data on the demand for medical care, it is illustrated how the classical as well as the zero-augmented models can be fitted, inspected and tested in practice.

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Bibliographic Info

Paper provided by Faculty of Business and Economics - University of Basel in its series Working papers with number 2007/24.

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Date of creation: 2007
Date of revision:
Handle: RePEc:bsl:wpaper:2007/24

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Keywords: GLM / Poisson model / negative binomial model / zero-inflated model / hurdle model;

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  1. Deb, Partha & Trivedi, Pravin K, 1997. "Demand for Medical Care by the Elderly: A Finite Mixture Approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(3), pages 313-36, May-June.
  2. Achim Zeileis, . "Econometric Computing with HC and HAC Covariance Matrix Estimators," Journal of Statistical Software, American Statistical Association, vol. 11(i10).
  3. Achim Zeileis, . "Object-oriented Computation of Sandwich Estimators," Journal of Statistical Software, American Statistical Association, vol. 16(i09).
  4. D. Mikis Stasinopoulos & Robert A. Rigby, . "Generalized Additive Models for Location Scale and Shape (GAMLSS) in R," Journal of Statistical Software, American Statistical Association, vol. 23(i07).
  5. Friedrich Leisch, . "FlexMix: A General Framework for Finite Mixture Models and Latent Class Regression in R," Journal of Statistical Software, American Statistical Association, vol. 11(i08).
  6. Mullahy, John, 1986. "Specification and testing of some modified count data models," Journal of Econometrics, Elsevier, vol. 33(3), pages 341-365, December.
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Cited by:
  1. Achim Zeileis & Roger Koenker, . "Econometrics in R: Past, Present, and Future," Journal of Statistical Software, American Statistical Association, vol. 27(i01).
  2. Simon Frey & Roland Linder & Georg Juckel & Tom Stargardt, 2014. "Cost-effectiveness of long-acting injectable risperidone versus flupentixol decanoate in the treatment of schizophrenia: a Markov model parameterized using administrative data," The European Journal of Health Economics, Springer, vol. 15(2), pages 133-142, March.
  3. Binder, Stefan & Macfarlane, Gregory S. & Garrow, Laurie A. & Bierlaire, Michel, 2014. "Associations among household characteristics, vehicle characteristics and emissions failures: An application of targeted marketing data," Transportation Research Part A: Policy and Practice, Elsevier, vol. 59(C), pages 122-133.
  4. Sarah Harris & Wendy Anderson & Musa Kilinc & Liam Fogarty, 2012. "The relationship between fire behaviour measures and community loss: an exploratory analysis for developing a bushfire severity scale," Natural Hazards, International Society for the Prevention and Mitigation of Natural Hazards, vol. 63(2), pages 391-415, September.
  5. Christian Kleiber & Achim Zeileis, 2014. "Visualizing Count Data Regressions Using Rootograms," Working Papers 2014-20, Faculty of Economics and Statistics, University of Innsbruck.
  6. Yee, Thomas W., 2014. "Reduced-rank vector generalized linear models with two linear predictors," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 889-902.
  7. Hai Liu & Kung-Sik Chan, . "Introducing COZIGAM: An R Package for Unconstrained and Constrained Zero-Inflated Generalized Additive Model Analysis," Journal of Statistical Software, American Statistical Association, vol. 35(i11).
  8. Alberto Baccini & Lucio Barabesi & Martina Cioni & Caterina Pisani, 2013. "Crossing the hurdle: the determinants of individual scientific performance," Department of Economics University of Siena 691, Department of Economics, University of Siena.
  9. Sewando, Ponsian T. & Mdoe, N. Y. S. & Mutabazi, K. D. S, 2011. "Farmers’ preferential choice decisions to alternative cassava value chain strands in Morogoro rural district, Tanzania," MPRA Paper 29797, University Library of Munich, Germany.
  10. Christian Pierdzioch & Eike Emrich, 2013. "A Note on Corruption and National Olympic Success," Atlantic Economic Journal, International Atlantic Economic Society, vol. 41(4), pages 405-411, December.
  11. Nils B. Weidmann, 2009. "Violence and the Changing Ethnic Map: The Endogeneity of Territory and Conflict in Bosnia," HiCN Working Papers 64, Households in Conflict Network.
  12. Francisco Cribari-Neto & Achim Zeileis, . "Beta Regression in R," Journal of Statistical Software, American Statistical Association, vol. 34(i02).
  13. Matthias Bannert & Andreas Dibiasi, 2014. "Unveiling Participant Level Determinants of Unit Non-Response in Business Tendency Surveys," KOF Working papers 14-363, KOF Swiss Economic Institute, ETH Zurich.
  14. Achim Zeileis & Yves Croissant, . "Extended Model Formulas in R: Multiple Parts and Multiple Responses," Journal of Statistical Software, American Statistical Association, vol. 34(i01).
  15. Yoshitsugu Kitazawa, 2014. "Consistent estimation for the full-fledged fixed effects zero-inflated Poisson model," Discussion Papers 66, Kyushu Sangyo University, Faculty of Economics.


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