fRegress {fda}R Documentation

A Functional Regression Analysis of the Concurrent Type

Description

This function carries out a functional regression analysis, where either the dependent variable or one or more independent variables are functional. Non-functional variables may be included on either side of the equation. In a concurrent functional linear model all function variables are all evaluated at a common time or argument value $t$. That is, the fit is defined in terms of the behavior of all variables at a fixed time, or in terms of "now" behavior.

Usage

fRegress(yfdPar, xfdlist, betalist)

Arguments

yfdPar the dependent variable object. It may be an object of three possible classes:
  • a vector if the dependent variable is scalar.
  • a functional data object if the dependent variable is functional.
  • a functional parameter object if the dependent variable is functional, and if it is necessary to smooth the prediction of the dependent variable.
xfdlist a list of length equal to the number of independent variables. Members of this list are the independent variables. They be objects of either of these two classes:
  • a vector if the independent dependent variable is scalar.
  • a functional data object if the dependent variable is functional.

In either case, the object must have the same number of replications as the dependent variable object. That is, if it is a scalar, it must be of the same length as the dependent variable, and if it is functional, it must have the same number of replications as the dependent variable.
betalist a list of length equal to the number of independent variables. Members of this list define the regression functions to be estimated. They are functional parameter objects. Note that even if corresponding independent variable is scalar, its regression coefficient will be functional if the dependent variable is functional. Each of these functional parameter objects defines a single functional data object, that is, with only one replication.

Details

In the computation of regression function estimates, all independent variables are treated as if they are functional. If argument xfdlist contains one or more vectors, these are converted to functional data objects having the constant basis with coefficients equal to the elements of the vector.

Needless to say, if all the variables in the model are scalar, use this function, but rather either ls or lsfit.

Value

a named list of length 6 with these members:

yfdPar yhe first argument in the call to fRegress.
xfdlist the second argument in the call to fRegress.
betalist the third argument in the call to fRegress.
betaestlist a list of length equal to the number of independent variables and with members having the same functional parameter structure as the corresponding members of betalist. These are the estimated regression coefficient functions.
yhatfdobj a functional data object if the dependent variable is functional or a vector if the dependent variable is scalar. This is the set of predicted by the functional regression model for the dependent variable.
Cmatinv a matrix containing the inverse of the coefficient matrix for the linear equations that define the solution to the regression problem. This matrix is required for function fRegress.stderr that estimates confidence regions for the regression coefficient function estimates.

See Also

fRegress.stderr, fRegress.CV, linmod

Examples

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[Package fda version 1.1.2 Index]