[R] Multivariate spline regression and predicted values

[Max Farrell]

Thank you for the reply, it looks like the second option (te) will
work perfectly!

Max

On Tue, Sep 20, 2011 at 2:39 PM, Max Farrell <maxhf at umich.edu> wrote:
> 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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>>
>