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) = β_{0} (t) + \int β_{1} (s, t) x_{i} (s) d s + 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

Examples

Run this code

#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.

Run the code above in your browser using DataLab

Data engineering and BI courses are free!