# Partial robust M regression

### Description

Partial robust M regression for models with univariate response. This method for dimension reduction and regression analysis yields estimates with a partial least squares alike interpretability that are robust to both vertical outliers and leverage points.

### Usage

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### Arguments

`formula` |
an object of class formula. |

`data` |
a data frame or list which contains the variables given in formula. |

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

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

`probp1` |
the 1-alpha value at which to set the first outlier cutoff for the weighting function. |

`hampelp2` |
the 1-alpha values for second cutoff. Only applies to |

`hampelp3` |
the 1-alpha values for third cutoff. Only applies to |

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

`scale` |
type of scaling for the data in form of a string that matches an R function, e.g. |

`usesvd` |
logical, default is |

`numit` |
the number of maximal iterations for the convergence of the coefficient estimates. |

`prec` |
a value for the precision of estimation of the coefficients. |

### Details

The NIPLS algorithm combined with weighted regression is used for the model estimation.

`a`

is the number of components in the model. Note that it is not possible to simply reduce the number of weighting vectors to obtain a model with a smaller number of components. Each model has to be estimated separately due to its dependence on robust case weights.

### Value

prms returns an object of class prm.

Functions `summary`

, `predict`

and `plot`

are available. Also the generic functions `coefficients`

, `fitted.values`

and `residuals`

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

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

`intercept` |
intercept of weighted regression model. |

`wy` |
the case weights in the y space. |

`wt` |
the case weights in the score space. |

`w` |
the overall case weights used for weighted regression (depending on the weight function). |

`scores` |
the matrix of scores. |

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

`loadings` |
the matrix of loadings. |

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

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

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

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

`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. |

`Yvar` |
percentage of contribution for each component to the explanation of the variance of the response. |

`Xvar` |
percentage of contribution for each component to the explanation of the variance of the variables. |

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

### Author(s)

Sven Serneels, BASF Corp and Irene Hoffmann

### References

Hoffmann, I., Serneels, S., Filzmoser, P., Croux, C. (2015). Sparse partial robust M regression. Chemometrics and Intelligent Laboratory Systems, 149, 50-59.

Serneels, S., Croux, C., Filzmoser, P., Van Espen, P.J. (2005). Partial Robust M-Regression. Chemometrics and Intelligent Laboratory Systems, 79, 55-64.

### See Also

`prmsCV`

, `plot.prm`

, `biplot.prm`

, `predict.prm`

, `sprms`

### Examples

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