# Robust PLS for binary classification

### Description

Robust PLS and discriminant analysis for binary classification problems. This method for dimension reduction and discriminant analysis yields a classification model with a partial least squares alike interpretability that is robust to both vertical outliers and leverage points.

### Usage

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### Arguments

`formula` |
a formula, e.g. group ~ X1 + X2 with group a factor with two levels or a numeric vector coding class membership with 1 and -1 and X1,X2 numeric variables. |

`data` |
a data frame or list which contains the variables given in formula. The response specified in the formula needs to be a numeric vector coding the class membership with 1 and-1 or a vector of factors with two levels. |

`a` |
the number of PRM components to be estimated in the model. |

`fun` |
an internal weighting function for case weights. Choices are |

`probp1` |
a quantile close to 1 at which to set the first outlier cutoff for the weighting function. |

`hampelp2` |
a quantile close to 1 with probp1<hampelp2 for second cutoff. Only applies to |

`hampelp3` |
a quantile close to 1 with probp1<hampelp2<hampelp3 for third cutoff. Only applies to |

`probp4` |
a quantile close to zero for the cutoff for potentially wrong class labels (see Reference). Ignorred if |

`yweights` |
logical; if TRUE weights are calculated for observations with potentially wrong class labels. |

`class` |
type of classification; choices are "regfit" or "lda" (see Detail). If "regfit" an object of class prm is returned. |

`prior` |
vector of length 2 with prior probabilities of the groups; only used if class="lda". |

`center` |
type of centering of the data in form of a string that matches an R function, e.g. "mean" or "median". |

`scale` |
type of scaling for the data in form of a string that matches an R function, e.g. "sd" or "qn" or alternatively "no" for no scaling. |

`numit` |
the number of maximal iterations for the convergence of the case weights. |

`prec` |
a value for the precision of the convergence of the case weights. |

### Details

For `class="lda"`

a robust LDA model is estimated in the PRM score space for `class="regfit"`

the model ist a robust PLS regression model on the binary response.

### Value

prmda returns an object of class prmda.

Functions `summary`

, `predict`

and `biplot`

are available. Also the generic functions `coefficients`

, `fitted.values`

and `residuals`

can be used to extract the corresponding elements from the sprmda object.

`scores` |
the matrix of scores. |

`R` |
Direction vectors (or weighting vectors or rotation matrix) to obtain the scores. |

`loadings` |
the matrix of loadings. |

`w` |
the overall case weights used for robust dimenstion reduction and classification (depending on the weight function). |

`wt` |
the group wise obtained case weights in the score space. |

`wy` |
the case weights for potentially mislabeled observations. |

Results from LDA model:

`ldamod` |
list with robust pooled within-group covariance (cov) and the two robust group centers (m1, m2) in the score space |

`ldafit` |
postirior probabilities from robust LDA in the score space. |

`ldaclass` |
predicted class labels from robust LDA in the score space. |

Results from the regression model with binary response:

`coefficients` |
vector of coefficients of the weighted regression model. |

`intercept` |
intercept of weighted regression model. |

`residuals` |
vector of residuals, true response minus estimated response. |

`fitted.values` |
the vector of estimated response values. |

`coefficients.scaled` |
vector of coefficients of the weighted regression model with scaled data. |

`intercept.scaled` |
intercept of weighted regression model with scaled data. |

Data preprocessing:

`YMeans` |
value used internally to center response. |

`XMean` |
vector used internally to center data. |

`Xscales` |
vector used internally to scale data. |

`Yscales` |
value used internally to scale response. |

`inputs` |
list of inputs: parameters, data and scaled data. |

### Author(s)

Irene Hoffmann and Sven Serneels

### References

Hoffmann, I., Filzmoser, P., Serneels, S., Varmuza, K., Sparse and robust PLS for binary classification.

### See Also

`prmdaCV`

### Examples

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