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EllenJCoombs / cetacean-strandings-project

Repository for strandings project
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GAM paragraph #7

Closed nhcooper123 closed 6 years ago

nhcooper123 commented 6 years ago

Please provide a paragraph of what you would write about this GAM for a paper (can be rough obviously)

dill commented 6 years ago

Something along the lines of...

We modelled the total number of stranded individuals as a sum of smooth functions of covariates in the generalized additive model (GAM) framework (e.g., Wood 2017). To account for changes in population (and therefore potential for detection of stranded cetaceans) we used yearly (human, UK and Irish) population as a fixed offset in the model. We included smooths of the variables listed in Table XX. Smooths were modelled using a thin plate spline basis with shrinkage (Marra and Wood, 2011) which allowed terms to be effectively removed from the model (effect size shrunk to zero) during fitting, thus terms were selected during fitting the model. As we wanted to model species-specific effects, we included a factor-smooth interaction between year and species; this term fitted a smooth of time for each species but allowed common smooths to be fitted for the other covariates. An advantage of this approach is that the per-species smooths are estimated as deviations from a base-level smooth and species have a common smoothing parameter (hence have the same amount of wigglyness, though their shapes are different), so some information is shared between species. We fitted our model with several appropriate candidate response distributions: Poisson, quasi-Poisson, negative binomial and Tweedie. We used standard residual checks for GAMs to decide between response distributions. REstricted Maximum Likelihood was used to fit the models in the R package mgcv (Wood, 2011).

References

Marra, G, and SN Wood. “Practical Variable Selection for Generalized Additive Models.” Computational Statistics and Data Analysis 55, no. 7 (2011): 2372–2387.

Wood, SN “Fast Stable Restricted Maximum Likelihood and Marginal Likelihood Estimation of Semiparametric Generalized Linear Models.” Journal of the Royal Statistical Society: Series B (Statistical Methodology) 73, no. 1 (2011): 3–36.

Wood, SN Generalized Additive Models: An Introduction with R, Second Edition. CRC Press, 2017.