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BrunaLab / HeliconiaDemography

Effects of drought and habitat fragmentation on Heliconia acuminata.
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Justification for gamma parameter #17

Closed Aariq closed 3 years ago

Aariq commented 3 years ago

In gam(), you can adjust the smoothing with gamma. Values above 1 increase the smoothness. Teller et al. use a value of 1.2, but I don't think they justify that particular value. Simon Wood says in his book:

Another choice is the parameter gamma which can be used to multiply the model effective degrees of freedom in the GCV or UBRE scores in order to (usually) increase the amount of smoothing selected. The default value is 1, but GCV is known to have some tendency to overfitting on occasion, and it has been suggested that using γ ≈ 1 . 5 can somewhat correct this without compromising model fit (e.g., Kim and Gu, 2004).

Wood, Simon N.. Generalized Additive Models : An Introduction with R, Second Edition, CRC Press LLC, 2017. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/ufl/detail.action?docID=4862399. Created from ufl on 2021-01-18 11:14:16.

But I think Teller et. al used REML, not GCV. gamma also works with REML, but I'm not sure if it's the same justification, or why you would choose 1.2 and not 1.5 or 1.1.

Aariq commented 3 years ago

Ah, Teller et al. did use GCV: "We chose k by the GCV criterion with model degrees of freedom inflated by 20% to avoid overfitting". The 20% refers to gamma = 1.2

Aariq commented 3 years ago

REML tends to be more resistant to overfitting (Wood 2017), so I'm going to not use gamma (keep it at default of 1).