Gam models with smooth main effects and smooth pairwise interaction

[Isabella Ghement <isabella@stat.ubc.ca>]

    Hi everyone, 

    Can the Splus function "gam" fit a model with smooth main effects and
smooth interaction of the form:

    Y = alpha + g_1(X_1) + g_2(X_2) + g_12(X_1,X_2) + error ?

The latter model is not identifiable unless one imposes restrictions 
on the main effects: 
 
    E(g_1(X_1)) = 0, E(g_2(X_2)) = 0 

and interaction: 

    E(g_12(X_1,X_2)|X_1) = E(g_12(X_1,X_2)|X_2) = 0.

There is nothing in the gam help that indicates that Splus can fit the 
above model and enforce the proper constraints on the interaction term.
But I did find a rather confusing statement there: "Interactions with
nonparametric smooth terms are not fully supported, but will not produce 
errors; they will simply produce the parametric interaction."

    Can anybody shed some light on this issue for me?

    Thank you,

    Isabella Ghement
    Ph.D. Candidate
    Department of Statistics 
    University of British Columbia