# Cross-validation for penalized PLS based on Spline Transformations

### Description

Computes the nonlinear-regression model for penalized PLS based on B-Spline transformations.

### Usage

1 2 3 4 | ```
ppls.splines.cv(X, y,lambda,
ncomp, degree, order,
nknot, k, kernel,scale,
reduce.knots,select)
``` |

### Arguments

`X` |
matrix of input data |

`y` |
vector of response data |

`lambda` |
vector of candidate parameters lambda for the penalty term. Default value is 1 |

`ncomp` |
Number of PLS components, default value is
min(nrow(X)-1,ncol(Z)), where Z denotes the transformed data
obtained from the function |

`degree` |
Degree of the splines. Default value is 3 |

`order` |
Order of the differences to be computed for the penalty term. Default value is 2. |

`nknot` |
number of knots. Default value is 20 for all variables. |

`k` |
the number of splits in |

`kernel` |
Logical value. If kernel=TRUE, the kernelized version of penalized PLS is computed. Default value is kernel=FALSE |

`scale` |
logical value. If scale=TRUE, the X variables are standardized to have unit variance. Default value is FALSE |

`reduce.knots` |
Logical variable. If |

`select` |
Logical value. If |

### Details

This function computes the cv-optimal nonlinear regression
model with Penalized Partial Least Squares. In a nutshell, the
algorithm works as follows. Starting with a generalized additive
model for the columns of `X`

, each additive component is expanded in terms of a generous
amount of B-Splines basis functions. The basis functions are determined
via their `degree`

and `nknot`

, the number of knots. In order to prevent
overfitting, the additive model is estimated via penalized PLS, where
the penalty term penalizes the differences of a specified `order`

. Consult Kraemer, Boulesteix, and Tutz (2008) for details.

A graphical tool for penalized PLS on splines-transformed data is provided by `graphic.ppls.splines`

.

### Value

`error.cv` |
matrix of cross-validated errors. The rows correspond to the values of lambda, the columns correspond to the number of components. |

`lambda.opt ` |
Optimal value of lambda |

`ncomp.opt` |
Optimal number of penalized PLS components |

`min.ppls` |
Cross-validated error for the optimal penalized PLS solution |

### Author(s)

Nicole Kraemer

### References

N. Kraemer, A.-L. Boulsteix, and G. Tutz (2008). *Penalized Partial Least Squares with Applications
to B-Spline Transformations and Functional Data*. Chemometrics and Intelligent Laboratory Systems, 94, 60 - 69. http://dx.doi.org/10.1016/j.chemolab.2008.06.009

### See Also

`penalized.pls`

,`penalized.pls.cv`

, `graphic.ppls.splines`

### Examples

1 2 3 4 5 6 7 |

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