fRegress {fda} | R Documentation |
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.
fRegress(yfdPar, xfdlist, betalist)
yfdPar |
the dependent variable object. It may be an object of
three possible classes:
|
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:
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. |
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
.
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.
|
fRegress.stderr, fRegress.CV, linmod
#See the weather data analyses in the file this-is-escaped-code{ for #examples of all the cases covered by this-is-escaped-codenormal-bracket40bracket-normal.