# linmod: Fit Fully Functional Linear Model In fda: Functional Data Analysis

 linmod R Documentation

## 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)


### 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:

 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.

### 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

### 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.

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