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Negative Binomial GAM and GAMM to Analyse Amphibian Roadkills

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.

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Notes

  1. 1.

    We used R version 2.6 and mgcv version 1.3–27. More recent versions of R and mgcv require a small modification to the code; see the book website (www.highstat.com) for updated code.

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Zuur, A. et al. (2009). Negative Binomial GAM and GAMM to Analyse Amphibian Roadkills. In: Mixed effects models and extensions in ecology with R. Statistics for Biology and Health. Springer, New York, NY. https://doi.org/10.1007/978-0-387-87458-6_16

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