NMath Reference Guide

## PLS |

Class PLS2CrossValidationWithJackknife performs an evaluation of a PLS (Partial Least
Squares) model with model coefficient variance estimates and confidence intervals.

Inheritance Hierarchy

Syntax

The PLS2CrossValidationWithJackknife type exposes the following members.

Constructors

Name | Description | |
---|---|---|

PLS2CrossValidationWithJackknife | Default constructor. Constructs a PLS2CrossValidationWithJackknife instance that uses the "leave one out" cross validation and the Nipals algorithm. No scaling will be done and full model coefficients will be used in the jackknife coefficient variance estimate computation. LeaveOneOutSubsets | |

PLS2CrossValidationWithJackknife(Boolean) | Constructs a PLS2CrossValidationWithJackknife instance that uses the "leave one out" cross validation and the Nipals algorithm. full model coefficients will be used in the jackknife coefficient variance estimate computation. If true, the learning X data for each subset is scaled by dividing each variable by its sample standard deviation. The prediction data is scaled by the same amount. Note that this will impact performance.LeaveOneOutSubsets | |

PLS2CrossValidationWithJackknife(ICrossValidationSubsets) | Constructs a PLS2CrossValidationWithJackknife instance which uses the given subset generator and the Nipals algorithm. | |

PLS2CrossValidationWithJackknife(ICrossValidationSubsets, Boolean) | Constructs a PLS2CrossValidationWithJackknife instance which uses the given subset generator and the Nipals algorithm. No scaling and full model coefficients will be used in the jackknife coefficient variance estimate computation. No scaling will be done and full model coefficients will be used in the jackknife coefficient variance estimate computation. | |

PLS2CrossValidationWithJackknife(IPLS2Calc, ICrossValidationSubsets) | Constructs a PLS2CrossValidationWithJackknife instance which uses the given PLS calculator and subset generator. No scaling will be done and full model coefficients will be used in the jackknife coefficient variance estimate computation. | |

PLS2CrossValidationWithJackknife(ICrossValidationSubsets, Boolean, Boolean) | Constructs a PLS2CrossValidationWithJackknife instance which uses the given subset generator and the Nipals algorithm. No scaling and full model coefficients will be used in the jackknife coefficient variance estimate computation. No scaling will be done and full model coefficients will be used in the jackknife coefficient variance estimate computation. | |

PLS2CrossValidationWithJackknife(IPLS2Calc, ICrossValidationSubsets, Boolean) | Constructs a PLS2CrossValidationWithJackknife instance which uses the given PLS calculator and subset generator. | |

PLS2CrossValidationWithJackknife(IPLS2Calc, ICrossValidationSubsets, Boolean, Boolean) | Constructs a PLS2CrossValidationWithJackknife instance which uses the given PLS calculator and subset generator. |

Properties

Name | Description | |
---|---|---|

AverageMeanSqrError | Gets the average of the mean square errors for each training/testing subsets pair. | |

Calculator | Gets and sets the PLS2 calculator to use for PLS2 calculations. | |

Coefficients | Gets the coefficients for the full model. | |

CoefficientVariance | Gets the jackknife variance estimates for the model coefficients. | |

IsGood | Whether all the PLS2 calculations were successful. | |

Message | Gets any message that may have been generated by the computation. For example, if the calculation is unsuccessful, the message indicates the reason. | |

Results | Gets the results of the cross validation for each training/testing subsets pair. | |

Scale | Gets and sets the scale property. If true, the learning X data for each subset is scaled by dividing each variable by its sample standard deviation. The prediction data is scaled by the same amount. Note that this will impact performance. | |

SubsetGenerator | Gets and sets the subset generator to use to generate testing and training subsets. | |

UseMeans | Gets and sets the use means property. If true the mean of the coefficients computed in the jackknife replicates will be used to compute variance estimates. If false the full model coefficients will be used. |

Methods

Name | Description | |
---|---|---|

Clone | Creates a deep copy of this PLS2CrossValidationWithJackknife. | |

CoefficientConfidenceIntervals | Calculates the (1 - alpha)x100% confidence intervals for the model coeffficients. The i,j entry corresponds to the i,j entry of the matrix of coefficients accessed by the Coefficients property. | |

DoCrossValidation(DoubleMatrix, DoubleMatrix, Int32) | Perform cross validation and jackknife variance estimation on the given data using the existing calculator and subset generator. | |

DoCrossValidation(DoubleMatrix, DoubleMatrix, IPLS2Calc, Int32) | Performs cross validation and jackknife variance estimation on the given data using the given calculator and number of components. |

Remarks

The original (Tukey) jackknife variance estimator is deﬁned as
((g - 1)/g)*sum(Bi - Bbar)
where g is the number of subsets used in cross validation, Bi is
the estimated coefficients when subset i is left out (called the
jackknife replicates), and Bbar is the mean of the Bi.
However, Martens and Martens (2000) deﬁned the estimator as
((g - 1)/g)*sum(Bi - Bhat)
where Bhat is the coefﬁcient estimate using the entire data set. I.e.,
they use the original ﬁtted coefﬁcients instead of the mean of the jackknife
replicates and is the default for class PLS2CrossValidationWithJackknife.
However it can be made to use the orginal Tukey deﬁnition by setting the
UseMean property to true.

See Also