ssanova0 {gss}

Fitting Smoothing Spline ANOVA Models

Description

Fit smoothing spline ANOVA models in Gaussian regression. The symbolic model specification via formula follows the same rules as in lm.

Usage

ssanova0(formula, type=NULL, data=list(), weights, subset,
         offset, na.action=na.omit, partial=NULL, method="v",
         varht=1, prec=1e-7, maxiter=30)

Arguments

formula

Symbolic description of the model to be fit.

type

List specifying the type of spline for each variable. See mkterm for details.

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 method="v" for GCV, method="m" for GML (REML), and method="u" for Mallow's CL.

varht

External variance estimate needed for method="u". Ignored when method="v" or method="m" are specified.

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.

Details

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}).

Value

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.

Note

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.

References

Wahba, G. (1990), Spline Models for Observational Data. Philadelphia: SIAM.

Gu, C. (2013), Smoothing Spline ANOVA Models (2nd Ed). New York: Springer-Verlag.

Gu, C. (2014), Smoothing Spline ANOVA Models: R Package gss. Journal of Statistical Software, 58(5), 1-25. URL http://www.jstatsoft.org/v58/i05/.

Examples

## 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)