How are smoothing splines used in the GAM?
In order to run the gam () correctly I need the effective degrees of freedom (obtained from optimal λ using CV), with added smoothing splines, s (), in its function. A smoothing spline is basically a natural cubic spline at every unique level of x (i).
Are there any smooths in the mgcv package?
The smooths built into the mgcv package are all based one way or another on low rank versions of splines. For the full rank versions see Wahba (1990). Note that smooths can be used rather flexibly in gam models.
Which is the tuning parameter for smoothing splines?
A smoothing spline is basically a natural cubic spline at every unique level of x (i). The tuning parameter λ controls the roughness of the smoothing spline, and hence the effective degrees of freedom which I have to add in the gam (), if I recall correctly.
How to estimate the smoothness of a GAM?
IWhich can be estimated using… library(mgcv) ct1 <- gam(Volume ~ s(Height) + s(Girth), family=Gamma(link=log),data=trees) Igamproduces a representation for the smooth functions, and estimates them along with their degree of smoothness.
When to use a smoothing spline in R?
In order to fit more general sorts of GAMs, using smoothing splines or other components that cannot be expressed in terms of basis functions and then fit using least squares regression, we will need to use the gam library in R. The s () function, which is part of the gam library, is used to indicate that we would like to use a smoothing spline.
Where can I find splines and GAMS in R?
This lab on Splines and GAMs in R comes from p. 293-297 of “Introduction to Statistical Learning with Applications in R” by Gareth James, Daniela Witten, Trevor Hastie and Robert Tibshirani. It was re-implemented in Fall 2016 in tidyverse format by Amelia McNamara and R. Jordan Crouser at Smith College.