linmod.fd {fda}R Documentation

Fit One of Three Types of Functional Linear Model.

Description

The linear model function described below fits the three types of linear models described in Chapters 9, 10, and 11. At this point the function can only handle a single functional independent variable. The regularization features described in Chapters 10 and 11 are incorporated. To fit a linear model. Three cases are considered:

functional dependent variable and multivariate independent variable, and the functional dependent variable can be multivariate or vector-valued. multivariate dependent variable and functional independent variable, functional dependent variable and a single functional independent variable.

Usage

linmod.fd(xfd, yfd, wtvec=rep(1, nrep), xLfd=2, yLfd=2, xlambda=0, ylambda=0, zmatrnk=p)

Arguments

xfd If the independent variable is multivariate, a design matrix. If the independent variable is functional, a fd object.
yfd If the dependent variable is multivariate, a design matrix. If the dependent variable is functional, a fd object.
wtvec A vector of weights for the replications. By default these are 1's.
xLfd For the independent variable, the order derivative to be penalized if an integer, or a linear differential operator if a functional data object.
yLfd For the dependent variable, the order derivative to be penalized if an integer, or a linear differential operator if a functional data object.
xlambda A smoothing parameter for the independent variable. This is zero by default.
ylambda A smoothing parameter for the dependent variable. This is zero by default.
zmatrnk The actual rank of independent variable matrix for the function DV/multivariate IV case. This is permitted to be less than the number of columns of this matrix.

Details

Value

Returns a list with the following entries: "alpha" The intercept, either a scalar or a functional data object as the model requires. If the dependent variable is multivariate, there is one for each column of the matrix input as argument yfd. Otherwise this is a single constant. "regfd" A functional data object for the regression function. The structure of this object depends on the three cases: functional DV/multivariate IV: a univariate functional data object with a replication corresponding to each column dimension in the matrix input for argument xfd, and a function (3rd dimension in the coefficient matrix) for each function in the DV, multivariate DV/functional IV: a univariate functional data object having a replication correponding to each column of the matrix input as argument yfd. functional DV/functional IV: a bivariate functional object of the bifd class. "hatfd" 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.

Note

Author(s)

References

See Also

Examples






[Package fda version 1.0 Index]