A functional dependent variable $y_i(t)$ is approximated by a
single functional covariate $x_i(s)$ plus an intercept function
$\alpha(t)$, and the covariate can affect the dependent variable
for all values of its argument. The equation for the model is
$$y_i(t) = \beta_0(t) + \int \beta_1(s,t) x_i(s) ds + e_i(t)$$
for $i = 1,...,N$. The regression function $\beta_1(s,t)$ is a
bivariate function. The final term $e_i(t)$ is a residual, lack of
fit or error term. There is no need for values $s$ and $t$
to be on the same continuum.
Usage
linmod(xfdobj, yfdobj, betaList, wtvec=NULL)
Arguments
xfdobj
a functional data object for the covariate
yfdobj
a functional data object for the dependent variable
betaList
a list object of length 3. The first element is a functional
parameter object specifying a basis and a roughness penalty for the
intercept term, the second element is a functional parameter object
for the regression function as a function
wtvec
a vector of weights for each observation. Its default value is
NULL, in which case the weights are assumed to be 1.
Value
a named list of length 3 with the following entries:
beta0estfdthe intercept functional data object.
beta1estbifda bivariate functional data object for the regression function.
yhatfdobja functional data object for the approximation to the dependent
variable defined by the linear model, if the dependent variable is
functional. Otherwise the matrix of approximate values.