I would like to apply a gam model on a dataset with specifying the types of functions to use.
It would be something like :
y ~ cst1 * (s(var1)-s(var2)) * (1 - exp(var3*cst2))
This model could be fit with
nls, the non-linear least squares package. This will allow you to model the formula you want directly. The splines will need to be done manually, though. This question gets at what you would be trying to do.
As far as getting the splines to be the same for
var2, you can do this by subtracting the basis matrices. Basically you want to compute the coefficient vector
A where the term is
A * s(var1) + A * s(var2) = A * (s(var1) - s(var2)). You wouldn't want to just do
s(var1 - var2); in general,
f(x) - f(y) != f(x - y). To do this in R, you would
Compute the spline basis matrices with
var2, giving them the same knots. You need to specify both the
knots and the
Boundary.knots parameters so that the two splines will share the same basis.
Subtract the two spline basis matrices (the output from the
Adapt the resulting subtracted spline basis matrix for the
nls formula, as they do in the question I linked earlier.