# fdata2pls: Partial least squares components for functional data. In fda.usc: Functional Data Analysis and Utilities for Statistical Computing

 fdata2pls R Documentation

## Partial least squares components for functional data.

### Description

Compute penalized partial least squares (PLS) components for functional data.

### Usage

```fdata2pls(fdataobj, y, ncomp = 2, lambda = 0, P = c(0, 0, 1), norm = TRUE, ...)
```

### Arguments

 `fdataobj` `fdata` class object. `y` Scalar response with length `n`. `ncomp` The number of components to include in the model. `lambda` Amount of penalization. Default value is 0, i.e. no penalization is used. `P` If P is a vector: coefficients to define the penalty matrix object. By default P=c(0,0,1) penalizes the second derivative (curvature) or acceleration. If P is a matrix: the penalty matrix object. `norm` If `TRUE` the `fdataobj` are centered and scaled. `...` Further arguments passed to or from other methods.

### Details

If `norm=TRUE`, computes the PLS by `NIPALS` algorithm and the Degrees of Freedom using the Krylov representation of PLS, see Kraemer and Sugiyama (2011).
If `norm=FALSE`, computes the PLS by Orthogonal Scores Algorithm and the Degrees of Freedom are the number of components `ncomp`, see Martens and Naes (1989).

### Value

`fdata2pls` function return:

• df degree of freedom

• rotation `fdata` class object.

• x Is true the value of the rotated data (the centred data multiplied by the rotation matrix) is returned.

• fdataobj.cen The centered `fdataobj` object.

• mean mean of `fdataobj`.

• lVector of index of principal components.

• C The matched call.

• lambda Amount of penalization.

• P Penalty matrix.

### Author(s)

Manuel Febrero-Bande, Manuel Oviedo de la Fuente manuel.oviedo@usc.es

### References

Kraemer, N., Sugiyama M. (2011). The Degrees of Freedom of Partial Least Squares Regression. Journal of the American Statistical Association. Volume 106, 697-705.

Febrero-Bande, M., Oviedo de la Fuente, M. (2012). Statistical Computing in Functional Data Analysis: The R Package fda.usc. Journal of Statistical Software, 51(4), 1-28. https://www.jstatsoft.org/v51/i04/

Martens, H., Naes, T. (1989) Multivariate calibration. Chichester: Wiley.

Used in: `fregre.pls`, `fregre.pls.cv`. Alternative method: `fdata2pc`.

### Examples

```## Not run:
n= 500;tt= seq(0,1,len=101)
x0<-rproc2fdata(n,tt,sigma="wiener")
x1<-rproc2fdata(n,tt,sigma=0.1)
x<-x0*3+x1
beta = tt*sin(2*pi*tt)^2
fbeta = fdata(beta,tt)
y<-inprod.fdata(x,fbeta)+rnorm(n,sd=0.1)
pls1=fdata2pls(x,y)
pls1\$call
summary(pls1)
pls1\$l
norm.fdata(pls1\$rotation)

## End(Not run)
```

fda.usc documentation built on Oct. 17, 2022, 9:06 a.m.