fda (version 6.1.4)

linmod: Fit Fully Functional Linear Model

Description

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)

Value

a named list of length 3 with the following entries:

beta0estfd

the intercept functional data object.

beta1estbifd

a bivariate functional data object for the regression function.

yhatfdobj

a 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.

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.

See Also

bifdPar, fRegress

Examples

#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.