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I've tried poking around here to get some answers, but some of the information is a bit difficult to determine. This post and the paper that goes with it don't really answer things in the more direct way I'm hoping for (the Wood article isn't really in plain English as it dives fairly heavily into math without a lot of practical explanations behind p values):

How does one intuitively interpret significance of splines/GAM term?

Basically, how should I interpret spline coefficients in a model if they are non-significant? Does this mean that the predictor doesn't explain anything in the model? Or is it just poorly fit to the data distribution? If the latter is the case, how should one adjust?

Edit

This is also an article that seems to indicate that its more conditional upon the data distribution:

GAM interaction- how to interpret

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Yes p values mean something. They are approximate (in the same sense that p values for GLMs are approximate and rely on asymptotic behaviour) but more so because they do not account for the fact that smoothing parameters are estimated but treated as known when computing the p value.

?summary.gam has some details and links to the papers with the supporting math. Basically, so long as you use method = "REML" or method = "ML", they have pretty good properties.

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  • $\begingroup$ Thanks. Its helpful to have that documentation as well as the citations. $\endgroup$ Commented Oct 22, 2022 at 9:02

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