[R] Multivariate spline regression and predicted values

[Simon Wood]

One possibility is....

library(mgcv)

## isotropic thin plate spline smoother
b <- gam(Y~s(X[,1],X[,2]))
predict(b,newdata=list(X=W))

## tensor product smoother
b <- gam(Y~te(X[,1],X[,2]))
predict(b,newdata=list(X=W))

## variant tensor product smoother
b <- gam(Y~t2(X[,1],X[,2]))
predict(b,newdata=list(X=W))

... these would all result in penalized regression spline fits with 
smoothing parameters estimated (by GCV, by default). If you don't want 
penalization then use, e.g. s(X[,1],X[,2],fx=TRUE) to get pure 
regression spline (`k' argument to s, te and t2 controls spline basis 
dimension --- see docs).

best,
simon

On 09/20/2011 03:11 PM, Max Farrell wrote:
> Hello,
>
> I am trying to estimate a multivariate regression of Y on X with
> regression splines. Y is (nx1), and X is (nxd), with d>1. I assume the
> data is generated by some unknown regression function f(X), as in Y =
> f(X) + u, where u is some well-behaved regression error. I want to
> estimate f(X) via regression splines (tensor product splines). Then, I
> want to get the predicted values for some new points W.
>
> To be concrete, here is an example of what I want:
>
> #dimensions of the model
> d=2
> n=1000
> #some random data
> X<- matrix(runif(d*n,-2,2),n,d)
> U<- rnorm(n)
> Y<- X[,1] + X[,2] + U
> # a new point for prediction
> W<- matrix(rep(0),1,d)
>
> Now if I wanted to use local polynomials instead of splines, I could
> load the 'locfit' package and run (something like):
>
> lp.results<- smooth.lf(X,Y,kern="epan",kt="prod",deg=1,alpha=c(0,0.25,0),xev=W,direct=TRUE)$y
>
> Or, if X was univariate (ie d=1), I could use (something like):
>
> spl.results<- predict(smooth.spline(X,Y, nknots=6),W)
>
> But smooth.spline only works for univariate data. I looked at the
> "crs" package, and it at least will fit the multivariate spline, but I
> don't see how to predict the new data from this. That is, I run a
> command like:
>
> spl.fit<- crs(Y~X[,1] + X[,2],basis="tensor",
> degree=c(3,3),segments=c(4,4),degree.min=3,degree.max=3, kernel=FALSE,
> cv="none",knots="uniform",prune=FALSE)
>
> Then what?
>
> What I really want is the spline version of the smooth.lf command
> above, or the multivariate version of smooth.spline. Any ideas/help?
>
> Thanks,
> Max
>
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