linmod function

Fit Fully Functional Linear Model

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

[REMOVE_ME]$y_i(t) = \beta_0(t) + \int \beta_1(s,t) x_i(s) ds + e_i(t) [REMOVE_ME_2]$

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.

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

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.

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.

Returns

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.

References

Ramsay, James O., Hooker, Giles, and Graves, Spencer (2009), Functional data analysis with 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 Also

bifdPar, fRegress

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

#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.