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Negative Binomial GAM and GAMM to Analyse Amphibian Roadkills

  • A.F. Zuur
  • A. Mira
  • F. Carvalho
  • E.N. Ieno
  • A.A. Saveliev
  • G.M. Smith
  • N.J. Walker
Chapter
Part of the Statistics for Biology and Health book series (SBH)

Abstract

This chapter analyses amphibian fatalities along a road in Portugal. The data are counts of kills making a Gaussian distribution unlikely; restricting our choice of techniques. We began with generalised linear models (GLM) and generalised additive models (GAM) with a Poisson distribution, but these models were overdispersed. To solve this, you can either apply a quasi-Poisson GLM or GAM, or use the negative binomial distribution (Chapter 9). In this particular example, either approaches can be applied as the overdispersion was fairly small (around 5), but with many ecological data sets it can be considerably larger, in which case the negative binomial GLM (or GAM) is the natural choice. As many textbooks give examples using quasi-Poisson GAMs and GLMs and only a few using the negative binomial, we decided to use the negative binomial distribution.

Keywords

Explanatory Variable Variance Inflation Factor Generalise Additive Model Negative Binomial Distribution Land Cover Class 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • A.F. Zuur
    • 1
  • A. Mira
    • 2
  • F. Carvalho
    • 2
  • E.N. Ieno
    • 3
  • A.A. Saveliev
    • 4
  • G.M. Smith
    • 5
  • N.J. Walker
    • 6
  1. 1.Highland Statistics Ltd.NewburghUK
  2. 2.Unidade de Biologia da Conservação, Departamento de BiologiaUniversidade de ÉvoraÉvoraPortugal
  3. 3.Highland Statistics LTD.NewburghUK
  4. 4.Faculty of EcologyKazan State UniversityKazanRussia
  5. 5.School of Science and EnvironmentBath Spa UniversityBathUK
  6. 6.Woodchester Park CSLGloucesterUK

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