| gam {gam} | R Documentation |
gam is used to fit generalized additive models, specified by
giving a symbolic description of the additive predictor and a
description of the error distribution. gam uses the
backfitting algorithm to combine different smoothing or
fitting methods. The methods currently supported are local regression
and smoothing splines.
gam(formula, family = gaussian, data, weights, subset, na.action,
start, etastart, mustart, control = gam.control(...),
model=FALSE, method, x=FALSE, y=TRUE, ...)
gam.fit(x, y, smooth.frame, weights = rep(1,nobs), start = NULL,
etastart = NULL, mustart = NULL, offset = rep(0, nobs), family = gaussian(),
control = gam.control())
formula |
a formula expression as for other regression models, of
the form response ~ predictors. See the documentation of
lm and formula for details. Built-in nonparametric
smoothing terms are indicated by s for smoothing splines or
lo for loess smooth terms. See the documentation for
s and lo for their arguments. Additional smoothers can be
added by creating the appropriate interface functions. Interactions with
nonparametric smooth terms are not fully supported, but will not produce
errors; they will simply produce the usual parametric interaction. |
family |
a description of the error distribution and link
function to be used in the model. This can be a character string
naming a family function, a family function or the result of a call
to a family function. (See family for details of
family functions.) |
data |
an optional data frame containing the variables
in the model. If not found in data, the variables are taken
from environment(formula), typically the environment from
which gam is called. |
weights |
an optional vector of weights to be used in the fitting process. |
subset |
an optional vector specifying a subset of observations to be used in the fitting process. |
na.action |
a function which indicates what should happen
when the data contain NAs. The default is set by
the na.action setting of options, and is
na.fail if that is unset. The “factory-fresh”
default is na.omit. A special method
na.gam.replace allows for mean-imputation of missing
values (assumes missing at random), and works gracefully with gam |
start |
starting values for the parameters in the additive predictor. |
etastart |
starting values for the additive predictor. |
mustart |
starting values for the vector of means. |
offset |
this can be used to specify an a priori known component to be included in the additive predictor during fitting. |
control |
a list of parameters for controlling the fitting
process. See the documentation for gam.control
for details. These can also be set as arguments to gam() itself.
|
model |
a logical value indicating whether model frame should be included as a component of the returned value. |
method |
the method to be used in fitting the parametric part of
the model.
The default method "glm.fit" uses iteratively reweighted
least squares (IWLS). The only current alternative is
"model.frame" which returns the model frame and does no fitting. |
x, y |
For gam:
logical values indicating whether the response
vector and model matrix used in the fitting process
should be returned as components of the returned value.
For gam.fit: x is a model matrix of dimension n
* p, and y is a vector of observations of length n.
|
smooth.frame |
for gam.fit only. This is essentially a
subset of the model frame corresponding to the smooth terms, and has
the ingredients needed for smoothing each variable in the backfitting
algorithm. The elements of this frame are produced by the formula
functions lo and s. |
... |
further arguments passed to or from other methods. |
The gam model is fit using the local scoring algorithm, which
iteratively fits weighted additive models by backfitting. The
backfitting algorithm is a Gauss-Seidel method for fitting additive
models, by iteratively smoothing partial residuals. The algorithm
separates the parametric from the nonparametric part of the fit, and
fits the parametric part using weighted linear least squares within the
backfitting algorithm. This version of gam remains faithful to
the philosophy of GAM models as outlined in the references below.
An object gam.slist (currently set to
c("lo","s","random")) lists the smoothers supported by
gam. Corresponding to each of these is a smoothing function
gam.lo, gam.s etc that take particular arguments and
produce particular output, custom built to serve as building blocks in
the backfitting algorithm. This allows users to add their own smoothing
methods. See the documentation for these methods for further information.
In addition, the object gam.wlist (currently set to
c("s","lo")) lists the smoothers for which efficient backfitters
are provided. These are invoked if all the smoothing methods are of one
kind (either all "lo" or all "s").
gam returns an object of class gam, which inherits from
both glm and lm.
Gam objects can be examined by print, summary,
plot, and anova. Components can be extracted using
extractor functions predict, fitted, residuals,
deviance, formula, and family. Can be modified
using update. It has all the components of a glm object,
with a few more. This also means it can be queried, summarized etc by
methods for glm and lm objects. Other generic functions
that have methods for gam objects are step and
preplot.
The following components must be included in a legitimate `gam' object.
The residuals, fitted values, coefficients and effects should be extracted
by the generic functions of the same name, rather than
by the `$' operator.
The family function returns the entire family object used in the fitting, and deviance can be used to extract the deviance of the fit.
coefficients |
the coefficients of the parametric part of the additive.predictors, which multiply the
columns of the model
matrix.
The names of the coefficients are the names of the
single-degree-of-freedom effects (the columns of the
model matrix).
If the model is overdetermined there will
be missing values in the coefficients corresponding to inestimable
coefficients.
|
additive.predictors |
the additive fit, given by the product of the model matrix and the coefficients, plus the columns of the $smooth component.
|
fitted.values |
the fitted mean values, obtained by transforming the component additive.predictors using the inverse link function.
|
smooth, nl.df, nl.chisq, var |
these four characterize the nonparametric aspect of the fit.
smooth is a matrix of smooth terms, with a column corresponding to each smooth term in the model; if no smooth terms are in the gam model, all these components will be missing.
Each column corresponds to the strictly nonparametric part of the term, while the parametric part is obtained from the model matrix.
nl.df is a vector giving the approximate degrees of freedom for each column of smooth. For smoothing splines specified by s(x), the approximate df will be the trace of the implicit smoother matrix minus 2.
nl.chisq is a vector containing a type of score test for the removal of each of the columns of smooth.
var is a matrix like smooth, containing the approximate pointwise variances for the columns of smooth.
|
smooth.frame |
This is essentially a subset of the model frame
corresponding to the smooth terms, and has the ingredients needed for
making predictions from a gam object |
residuals |
the residuals from the final weighted additive fit; also known as residuals, these are typically not interpretable without rescaling by the weights. |
deviance |
up to a constant, minus twice the maximized log-likelihood. Similar to the residual sum of squares. Where sensible, the constant is chosen so that a saturated model has deviance zero. |
null.deviance |
The deviance for the null model, comparable with
deviance. The null model will include the offset, and an
intercept if there is one in the model |
iter |
the number of local scoring iterations used to compute the estimates. |
family |
a three-element character vector giving the name of the family, the link, and the variance function; mainly for printing purposes. |
weights |
the working weights, that is the weights in the final iteration of the local scoring fit. |
prior.weights |
the case weights initially supplied. |
df.residual |
the residual degrees of freedom. |
df.null |
the residual degrees of freedom for the null model. |
The object will also have the components of a lm object:
coefficients, residuals, fitted.values,
call, terms, and some
others involving the numerical fit. See lm.object.
Written by Trevor Hastie, following closely the design in the
"Generalized Additive Models" chapter (Hastie, 1992) in Chambers and
Hastie (1992), and the philosophy in Hastie and Tibshirani (1991).
This version of gam is adapted from the S
version to match the glm and lm functions in R.
Note that this version of gam is different from the function
with
the same name in the R library mgcv, which uses only smoothing
splines with a focus on automatic smoothing parameter selection via
GCV.
Hastie, T. J. (1991) 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.
Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. New York: Springer.
data(kyphosis) gam(Kyphosis ~ s(Age,4) + Number, family = binomial, data=kyphosis, trace=TRUE) data(airquality) gam(Ozone^(1/3) ~ lo(Solar.R) + lo(Wind, Temp), data=airquality, na=na.gam.replace) gam(Kyphosis ~ poly(Age,2) + s(Start), data=kyphosis, family=binomial, subset=Number>2) data(gam.data) gam.object <- gam(y ~ s(x,6) + z,data=gam.data) summary(gam.object) plot(gam.object,se=TRUE) data(gam.newdata) predict(gam.object,type="terms",newdata=gam.newdata)