# Fitting Smoothing Spline ANOVA Models Fit smoothing spline ANOVA models in Gaussian regression. The symbolic model specification via `formula` follows the same rules as in `lm`. ```r 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 $O(n^{3})$. ## 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`. ## Returns `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. ## 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 ```r ## 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) ```

ssanova0 function