gam.s  R Documentation 
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)
x 
the univariate predictor, or expression, that evaluates to a numeric vector. 
y 
a response variable passed to 
w 
weights 
df 
the target equivalent degrees of freedom, used as a smoothing
parameter. The real smoothing parameter ( 
spar 
can be used as smoothing parameter, with values typically in

xeval 
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
. 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
residuals 
The
residuals from the smooth fit. Note that the smoother removes the parametric
part of the fit (using a linear fit in 
nl.df 
the nonlinear degrees of freedom 
var 
the pointwise variance for the nonlinear fit 
When 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.
Cantoni, E. and hastie, T. (2002) Degreesoffreedom tests for smoothing splines, Biometrika 89(2), 251263
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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