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Generalized Linear Models and Extensions, 3rd Edition

Author

Listed:
  • James W. Hardin
  • Joseph W. Hilbe

Abstract

Generalized linear models (GLMs) extend linear regression to models with a non-Gaussian, or even discrete, response. GLM theory is predicated on the exponential family of distributions—a class so rich that it includes the commonly used logit, probit, and Poisson distributions. Although one can fit these models in Stata by using specialized commands (for example, logit for logit models), fitting them as GLMs with Stata’s glm command offers some advantages. For example, model diagnostics may be calculated and interpreted similarly regardless of the assumed distribution. This text thoroughly covers GLMs, both theoretically and computationally. The theory consists of showing how the various GLMs are special cases of the exponential family, general properties of this family of distributions, and the derivation of maximum likelihood (ML) estimators and standard errors. The book shows how iteratively reweighted least squares, another method of parameter estimation, is a consequence of ML estimation via Fisher scoring. The authors also discuss different methods of estimating standard errors, including robust methods, robust methods with clustering, Newey–West, outer product of the gradient, bootstrap, and jackknife.

Suggested Citation

  • James W. Hardin & Joseph W. Hilbe, 2012. "Generalized Linear Models and Extensions, 3rd Edition," Stata Press books, StataCorp LP, edition 3, number glmext, April.
  • Handle: RePEc:tsj:spbook:glmext
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    9. Bornmann, Lutz & Williams, Richard, 2013. "How to calculate the practical significance of citation impact differences? An empirical example from evaluative institutional bibliometrics using adjusted predictions and marginal effects," Journal of Informetrics, Elsevier, vol. 7(2), pages 562-574.
    10. Herrera, Liliana & Nieto, Mariano, 2016. "PhD careers in Spanish industry: Job determinants in manufacturing versus non-manufacturing firms," Technological Forecasting and Social Change, Elsevier, vol. 113(PB), pages 341-351.
    11. Bellmann Lutz & Gerner Hans-Dieter, 2012. "Further Training and Company-Level Pacts for Employment in Germany," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 232(2), pages 98-115, April.
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    14. Stanislav Kolenikov, 2001. "Review of Stata 7," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(5), pages 637-646.
    15. Lutz Bornmann, 2015. "Interrater reliability and convergent validity of F1000Prime peer review," Journal of the Association for Information Science & Technology, Association for Information Science & Technology, vol. 66(12), pages 2415-2426, December.
    16. Fikriye Kurtoğlu & M. Revan Özkale, 2016. "Liu estimation in generalized linear models: application on gamma distributed response variable," Statistical Papers, Springer, vol. 57(4), pages 911-928, December.
    17. Jones, Mark & Dobson, Annette & Onslow, Mark & Carey, Brenda, 2009. "Negative binomial mixed models for analysis of stuttering rates," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4590-4600, October.
    18. Andries, Petra & Hünermund, Paul, 2014. "Staging innovation projects: (when) does it pay off?," ZEW Discussion Papers 14-091, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
    19. García Arancibia, Rodrigo & Rossini, Gustavo & Depetris Guiguet, Edith, 2015. "Wine Label Descriptors and Shelf Price Paid by Argentine Consumers," Agricultural Economics Review, Greek Association of Agricultural Economists, vol. 16(2), June.

    More about this item

    Keywords

    generalized linear models; logit; probit; Poisson;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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