A symbolic wrapper to indicate a smooth term in a formala argument to gam
gam.s(x, y, w = rep(1, length(x)), df = 4, spar = 1, xeval)s(x, df = 4, spar = 1)
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.
the univariate predictor, or expression, that evaluates to a numeric vector.
a response variable passed to gam.s during backfitting
weights
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.
If this argument is present, then gam.s produces a
prediction at xeval.
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.
Cantoni, E. and hastie, T. (2002) Degrees-of-freedom tests for smoothing splines, Biometrika 89(2), 251-263
lo, smooth.spline, bs,
ns, poly
# 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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