This function is an extension of the linear regression models:
fregre.lm where the \(E[Y|X,Z]\) is related to the linear
prediction \(\eta\) via a link function \(g(.)\).
$$E[Y|X,Z]=\eta=g^{-1}(\alpha+\sum_{j=1}^{p}\beta_{j}Z^{j}+\sum_{k=1}^{q}\frac{1}{\sqrt{T_k}}\int_{T_k}{X^{k}(t)\beta_{k}(t)dt})$$
where \(Z=\left[ Z^1,\cdots,Z^p \right]\) are the
non functional covariates and \(X(t)=\left[ X^{1}(t_1),\cdots,X^{q}(t_q)
\right]\) are the functional ones.
The first item in the data list is called "df" and is a data
frame with the response and non functional explanatory variables, as
glm.
Functional covariates of class fdata or fd are introduced in
the following items in the data list.
basis.x is a list of
basis for represent each functional covariate. The basis object can be
created by the function: create.pc.basis, pca.fd
create.pc.basis, create.fdata.basis o
create.basis.
basis.b is a list of basis for
represent each \(\beta(t)\) parameter. If basis.x is a list of
functional principal components basis (see create.pc.basis or
pca.fd) the argument basis.b is ignored.
represent beta lower than the number of basis used to represent the
functional data.