| lo {gam} | R Documentation |
A symbolic wrapper to indicate a smooth term in a formala argument to gam
lo(..., span=0.5, degree=1) gam.lo(x, y, w, span, degree, ncols, xeval)
... |
the unspecified ... can be a comma-separated list of numeric vectors, numeric matrix, or expressions that evaluate to either of these. If it is a list of vectors, they must all have the same length. |
span |
the number of observations in a neighborhood. This is the smoothing parameter for a loess fit. |
degree |
the degree of local polynomial to be fit; currently restricted to be 1 or 2. |
x |
for gam.lo, the appropriate basis of polynomials
generated from the arguments to lo. These are also the
variables that receive linear coefficients in the GAM fit. |
y |
a response variable passed to gam.lo during backfitting |
w |
weights |
ncols |
for gam.lo the number of columns in x used as
the smoothing inputs to local regression. For example, if
degree=2, then x has two columns defining a degree-2
polynomial basis. Both are needed for the parameteric part of the fit,
but ncol=1 telling the local regression routine that the first
column is the actually smoothing variable. |
xeval |
If this argument is present, then gam.lo produces a
prediction at xeval. |
A smoother in gam separates out the parametric part of the fit
from the non-parametric part. For local regression, the parametric
part of the fit is specified by the particular polynomial being fit
locally. The workhorse function gam.lo fits the local
polynomial, then strips off this parametric part. All the parametric
pieces from all the terms in the additive model are fit
simultaneously in one operation for each loop of the backfitting
algorithm.
lo returns a numeric matrix. The simplest case is when there is a
single argument to lo and degree=1; a one-column matrix is
returned, consisting of a normalized version of the vector. If
degree=2 in this case, a two-column matrix is returned, consisting
of a degree-2 polynomial basis. Similarly, if there are
two arguments, or the single argument is a two-column matrix, either a
two-column matrix is returned if degree=1, or a five-column matrix
consisting of powers and products up to degree 2. Any dimensional
argument is allowed, but typically one or two vectors are used in
practice.
The matrix is endowed with a number of attributes; the matrix itself is
used in the construction of the model matrix, while the attributes are
needed for the backfitting algorithms all.wam (weighted additive
model) or lo.wam (currently not implemented). Local-linear curve
or surface fits reproduce linear responses, while local-quadratic fits
reproduce quadratic curves or surfaces. These parts of the loess
fit are computed exactly together with the other parametric linear parts
Note that lo itself does no smoothing; it simply sets things up
for gam; gam.lo does the actual smoothing.
of the model.
One important attribute is named call. For example, lo(x)
has a call component
gam.lo(data[["lo(x)"]], z, w, span = 0.5, degree = 1, ncols = 1).
This is an expression that gets evaluated repeatedly in all.wam
(the backfitting algorithm).
gam.lo 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
with the columns in x), so these residual represent the
nonlinear part of the fit. |
nl.df |
the nonlinear degrees of freedom |
var |
the pointwise variance for the nonlinear fit |
When gam.lo is evaluated with an xeval argument, it returns a
matrix 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.
y ~ Age + lo(Start, span=.5)
# fit Start using a loess smooth with a span of 0.5.
y ~ lo(Age) + lo(Start, Number)
y ~ lo(Age, 0.5) # the argument name for span is not needed.