slda {ipred} | R Documentation |

Linear discriminant analysis based on left-spherically distributed linear scores.

## S3 method for class 'formula': slda(formula, data, subset, na.action=na.rpart, ...) ## S3 method for class 'factor': slda(y, X, q=NULL, ...)

`y` |
the response variable: a factor vector of class labels. |

`X` |
a data frame of predictor variables. |

`q` |
the number of positive eigenvalues the scores are derived from, see below. |

`formula` |
a formula of the form `lhs ~ rhs` where `lhs`
is the response variable and `rhs` a set of
predictors. |

`data` |
optional data frame containing the variables in the model formula. |

`subset` |
optional vector specifying a subset of observations to be used. |

`na.action` |
function which indicates what should happen when
the data contain `NA` s. Defaults to
`na.rpart` . |

`...` |
additional parameters passed to `lda` . |

This function implements the LDA for *q*-dimensional linear scores of
the original *p* predictors derived from the *PC_q* rule by Laeuter
et al. (1998). Based on the product sum matrix

*W = (X - bar{X})^top(X - bar{X})*

the eigenvalue problem *WD = diag(W)DL* is solved. The first *q*
columns *D_q* of *D* are used as a weight matrix for the
original *p* predictors: *XD_q*. By default, *q* is the number
of eigenvalues greater one. The *q*-dimensional linear scores are
left-spherically distributed and are used as predictors for a classical
LDA.

This form of reduction of the dimensionality was developed for discriminant analysis problems by Laeuter (1992) and was used for multivariate tests by Laeuter et al. (1998), Kropf (2000) gives an overview. For details on left-spherically distributions see Fang and Zhang (1990).

An object of class `slda`

, a list with components

`scores` |
the weight matrix. |

`mylda` |
an object of class `lda` . |

Torsten.Hothorn <Torsten.Hothorn@rzmail.uni-erlangen.de>

Fang Kai-Tai and Zhang Yao-Ting (1990), *Generalized Multivariate
Analysis*, Springer, Berlin.

Siegfried Kropf (2000), *Hochdimensionale multivariate Verfahren in der
medizinischen Statistik*, Shaker Verlag, Aachen (in german).

Juergen Laeuter (1992), *Stabile multivariate Verfahren*,
Akademie Verlag, Berlin (in german).

Juergen Laeuter, Ekkehard Glimm and Siegfried Kropf (1998), Multivariate
Tests Based on Left-Spherically Distributed Linear Scores. *The Annals
of Statistics*, **26**(5) 1972–1988.

learn <- as.data.frame(mlbench.twonorm(100)) test <- as.data.frame(mlbench.twonorm(1000)) mlda <- lda(classes ~ ., data=learn) mslda <- slda(classes ~ ., data=learn) print(mean(predict(mlda, newdata=test)$class != test$classes)) print(mean(predict(mslda, newdata=test)$class != test$classes))

[Package *ipred* version 0.8-1 Index]