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Visualizing Count Data Regressions Using Rootograms

Author

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  • Kleiber, Christian

    () (University of Basel)

  • Zeileis, Achim

Abstract

The rootogram is a graphical tool associated with the work of J. W. Tukey that was originally used for assessing goodness of fit of univariate distributions. Here we show that rootograms are also useful for diagnosing and treating issues such as overdispersion and/or excess zeros in regression models for count data. We also introduce a weighted version of the rootogram that can be applied out of sample or to (weighted) subsets of the data, e.g., in finite mixture models. Two empirical illustrations are included, one from ethology, the other from public health. The former employs a negative binomial hurdle regression, the latter a two-component finite mixture of negative binomial models. The rootogram is a graphical tool associated with the work of J. W. Tukey that was originally used for assessing goodness of fit of univariate distributions. Here we show that rootograms are also useful for diagnosing and treating issues such as overdispersion and/or excess zeros in regression models for count data. We also introduce a weighted version of the rootogram that can be applied out of sample or to (weighted) subsets of the data, e.g., in finite mixture models. Two empirical illustrations are included, one from ethology, the other from public health. The former employs a negative binomial hurdle regression, the latter a two-component finite mixture of negative binomial models. A further illustration involving underdispersion and an R implementation of our tools are available in the R package 'countreg'.

Suggested Citation

  • Kleiber, Christian & Zeileis, Achim, 2014. "Visualizing Count Data Regressions Using Rootograms," Working papers 2014/13, Faculty of Business and Economics - University of Basel.
  • Handle: RePEc:bsl:wpaper:2014/13
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    References listed on IDEAS

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    1. Cameron,A. Colin & Trivedi,Pravin K., 2013. "Regression Analysis of Count Data," Cambridge Books, Cambridge University Press, number 9781107667273.
    2. Mullahy, John, 1997. "Heterogeneity, Excess Zeros, and the Structure of Count Data Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(3), pages 337-350, May-June.
    3. 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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    7. Fox, John, 2003. "Effect Displays in R for Generalised Linear Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 8(i15).
    8. Cameron, A. Colin & Trivedi, Pravin K., 1990. "Regression-based tests for overdispersion in the Poisson model," Journal of Econometrics, Elsevier, vol. 46(3), pages 347-364, December.
    9. Nikolay Nenovsky & S. Statev, 2006. "Introduction," Post-Print halshs-00260898, HAL.
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    Cited by:

    1. Bilal Barakat, 2017. "Generalised count distributions for modelling parity," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 36(26), pages 745-758, March.

    More about this item

    Keywords

    rootogram ; visualization ; goodness of fit ; count data ; Poisson regression ; negative binomial regression ; hurdle model ; finite mixture;

    JEL classification:

    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C87 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Econometric Software

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