A symbolic wrapper to indicate a smooth term in a formala argument to gam
s(x, df=4, spar=1)
gam.s(x, y, w, df, spar, xeval)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 (spar below) is found
such that df=tr(S)-1, where S is the implicit smoother
matrix. Values for df should be greater than 1, with
df=1 implying a linear fit. If both df and spar are
supplied, the former takes precedence. Note that df is not
necessarily an integer.
can be used as smoothing parameter, with values typically in
(0,1]. See smooth.spline for more details.
a response variable passed to gam.s during backfitting
weights
If this argument is present, then gam.s produces a
prediction at xeval.
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.
Since smoothing splines reproduces linear fits, the linear
part will be efficiently computed with the other parametric linear parts
of the model.
Note that s itself does no smoothing; it simply sets things up
for gam.
One important attribute is named call. For example, s(x)
has a call component
gam.s(data[["s(x)"]], z, w, spar = 1, df = 4).
This is an expression that gets evaluated repeatedly in general.wam
(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
in x), so these residual represent the
nonlinear part of the fit.
the nonlinear degrees of freedom
the pointwise variance for the nonlinear fit
When gam.s is evaluated with an xeval argument, it returns a vector of predictions.
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.
Cantoni, E. and hastie, T. (2002) Degrees-of-freedom tests for smoothing splines, Biometrika 89(2), 251-263
lo, smooth.spline, bs, ns, poly
# NOT RUN {
# fit Start using a smoothing spline with 4 df.
y ~ Age + s(Start, 4)
# fit log(Start) using a smoothing spline with 5 df.
y ~ Age + s(log(Start), df=5)
# }
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