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 2. The first element is a functional parameter
object specifying a basis and a roughness penalty for the intercept term.
The second element is a bivariate functional parameter object for the
bivariate regression 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.
source
Ramsay, James O., Hooker, Giles, and Graves, Spencer (2009)
Functional Data Analysis in R and Matlab, Springer, New York.
Ramsay, James O., and Silverman, Bernard W. (2005), Functional
Data Analysis, 2nd ed., Springer, New York.
Ramsay, James O., and Silverman, Bernard W. (2002), Applied
Functional Data Analysis, Springer, New York
#See the prediction of precipitation using temperature as#the independent variable in the analysis of the daily weather#data, and the analysis of the Swedish mortality data.