[R-sig-ME] mgcv: 3D tensor product smoothers and ti()

[Mark Payne]

Hi,
(PS This was originally posted to r-help, but didn't get a reply, so
am trying again here)

I am trying to fit a smoothing model where there are three dimensions
over which I can smooth (x,y,z). I expect interactions between some,
or all, of these terms, and so I have set up my model as

mdl <- gam(PA ~ s(x) + s(y) + s(z) + te(x,y) + te(x,z) + te(y,z) +
te(x,y,z),...)

I have recently read about the ti(), "tensor product interaction
smoother", which takes care of these interaction terms elegantly and
does the nesting properly. The help file says "This is much better
than attempting the same thing with ‘s’or ‘te’ terms representing the
interactions (although mgcv does not forbid it)." There is a 2D
example there also. But I don't understand how I should set this up
for my 3D example.

Does anyone have experience with this, and can explain how I should do
it properly?

Mark