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Based on the following hypothetical gam:

fit <- gam(y~ s(x1), s(x2), te(x1,x2))

How would one go about estimating the effect size of s(x1), s(x2) and the interaction term te(x1,x2) on y?

I understand that effect size can be estimated using general linear models through calculation of partial standardized regression coefficients, but is such information also obtainable using gams?

Many thanks.

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I don't think there is any widely accepted concept of effect size for GAMs. GAMS are more often used for prediction, whereas effect sizes moreover concern (finite dimensional) statistical inference. The complexity of GAMs makes the application of statistical tests less straightforward. The strength of using GLMs is that they can summarize possibly complex, non-linear trends using a single parameter; you can get correct inference with model misspecification when you use robust error estimation. That single parameter is seen as summarizing the first order trend when the true relationship is possibly non-linear. Therefore GAMs and GLMs can be complementary, especially when using visualization tools.

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