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.

### 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.