| ssanova0 {gss} | R Documentation |
Fit smoothing spline ANOVA models in Gaussian regression. The
symbolic model specification via formula follows the same
rules as in lm.
ssanova0(formula, type=NULL, data=list(), weights, subset,
offset, na.action=na.omit, partial=NULL, method="v",
varht=1, prec=1e-7, maxiter=30)
formula |
Symbolic description of the model to be fit. |
type |
List specifying the type of spline for each variable.
See |
data |
Optional data frame containing the variables in the model. |
weights |
Optional vector of weights to be used in the fitting process. |
subset |
Optional vector specifying a subset of observations to be used in the fitting process. |
offset |
Optional offset term with known parameter 1. |
na.action |
Function which indicates what should happen when the data contain NAs. |
partial |
Optional symbolic description of parametric terms in partial spline models. |
method |
Method for smoothing parameter selection. Supported
are |
varht |
External variance estimate needed for
|
prec |
Precision requirement in the iteration for multiple smoothing parameter selection. Ignored when only one smoothing parameter is involved. |
maxiter |
Maximum number of iterations allowed for multiple smoothing parameter selection. Ignored when only one smoothing parameter is involved. |
The model specification via formula is intuitive. For
example, y~x1*x2 yields a model of the form
y = C + f_{1}(x1) + f_{2}(x2) + f_{12}(x1,x2) + e
with the terms denoted by "1", "x1", "x2", and
"x1:x2".
The model terms are sums of unpenalized and penalized terms. Attached to every penalized term there is a smoothing parameter, and the model complexity is largely determined by the number of smoothing parameters.
ssanova0 and the affiliated methods provide a front end to
RKPACK, a collection of RATFOR routines for nonparametric regression
via the penalized least squares. The algorithms implemented in
RKPACK are of the order O(n^{3}).
ssanova0 returns a list object of class
c("ssanova0","ssanova").
The method summary.ssanova0 can be used to obtain
summaries of the fits. The method predict.ssanova0
can be used to evaluate the fits at arbitrary points along with
standard errors. The methods residuals.ssanova and
fitted.ssanova extract the respective traits from the
fits.
For complex models and large sample sizes, the approximate solution
of ssanova can be faster.
The method project is not implemented for
ssanova0, nor is the mixed-effect model support through
mkran.
In gss versions earlier than 1.0, ssanova0 was under
the name ssanova.
Chong Gu, chong@stat.purdue.edu
Gu, C. (2002), Smoothing Spline ANOVA Models. New York: Springer-Verlag.
Wahba, G. (1990), Spline Models for Observational Data. Philadelphia: SIAM.
## Fit a cubic spline x <- runif(100); y <- 5 + 3*sin(2*pi*x) + rnorm(x) cubic.fit <- ssanova0(y~x,method="m") ## Obtain estimates and standard errors on a grid new <- data.frame(x=seq(min(x),max(x),len=50)) est <- predict(cubic.fit,new,se=TRUE) ## Plot the fit and the Bayesian confidence intervals plot(x,y,col=1); lines(new$x,est$fit,col=2) lines(new$x,est$fit+1.96*est$se,col=3) lines(new$x,est$fit-1.96*est$se,col=3) ## Clean up ## Not run: rm(x,y,cubic.fit,new,est) dev.off() ## End(Not run) ## Fit a tensor product cubic spline data(nox) nox.fit <- ssanova0(log10(nox)~comp*equi,data=nox) ## Fit a spline with cubic and nominal marginals nox$comp<-as.factor(nox$comp) nox.fit.n <- ssanova0(log10(nox)~comp*equi,data=nox) ## Fit a spline with cubic and ordinal marginals nox$comp<-as.ordered(nox$comp) nox.fit.o <- ssanova0(log10(nox)~comp*equi,data=nox) ## Clean up ## Not run: rm(nox,nox.fit,nox.fit.n,nox.fit.o)