Specify a Smoothing Spline Fit in a GAM Formula
A symbolic wrapper to indicate a smooth term in a formala argument to gam
the univariate predictor, or expression, that evaluates to a numeric vector.
the target equivalent degrees of freedom, used as a smoothing
parameter. The real smoothing parameter (
can be used as smoothing parameter, with values typically in
a response variable passed to
If this argument is present, then
s returns the vector
x, endowed with a number of
attributes. The vector itself is used in the construction of the model
matrix, while the attributes are needed for the backfitting algorithms
general.wam (weighted additive model) or
s.wam (currently not
implemented). Since smoothing splines reproduces linear fits, the linear
part will be efficiently computed with the other parametric linear parts
of the model.
s itself does no smoothing; it simply sets things up
One important attribute is named
call. For example,
has a call component
gam.s(data[["s(x)"]], z, w, spar = 1, df = 4).
This is an expression that gets evaluated repeatedly in
(the backfitting algorithm).
gam.s returns an object with components
The residuals from the smooth fit. Note that the
smoother removes the parametric part of the fit (using a linear fit
the nonlinear degrees of freedom
the pointwise variance for the nonlinear fit
gam.s is evaluated with an
xeval argument, it returns a
vector of predictions.
Written by Trevor Hastie, following closely the design in the "Generalized Additive Models" chapter (Hastie, 1992) in Chambers and Hastie (1992).
Hastie, T. J. (1992) Generalized additive models. Chapter 7 of Statistical Models in S eds J. M. Chambers and T. J. Hastie, Wadsworth \& Brooks/Cole.
Hastie, T. and Tibshirani, R. (1990) Generalized Additive Models. London: Chapman and Hall.
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