R: Discriminant analysis by Fisher Rule.

daFisher {robCompositions} | R Documentation

## Discriminant analysis by Fisher Rule.

### Description

Discriminant analysis by Fishers rule using the logratio approach to compositional data.

### Usage

    daFisher(x, grp, coda = TRUE, method = "classical",
      plotScore = FALSE, ...)

    ## S3 method for class 'daFisher'
    print(x, ...)

    ## S3 method for class 'daFisher'
    predict(object, ..., newdata)

    ## S3 method for class 'daFisher'
    summary(object, ...)

### Arguments

`x` | a matrix or data frame containing the explanatory variables (training set)
`grp` | grouping variable: a factor specifying the class for each observation.
`coda` | TRUE, when the underlying data are compositions.
`method` | “classical” or “robust” estimation.
`plotScore` | TRUE, if the scores should be plotted automatically.
`...` | additional arguments for the print method passed through
`object` | object of class “daFisher”
`newdata` | new data in the appropriate form (CoDa, etc)

### Details

The Fisher rule leads only to linear boundaries. However, this method allows for dimension reduction and thus for a better visualization of the separation boundaries. For the Fisher discriminant rule (Fisher, 1938; Rao, 1948) the assumption of normal distribution of the groups is not explicitly required, although the method looses its optimality in case of deviations from normality.

The classical Fisher discriminant rule is invariant to ilr coordinates and clr coefficients. The robust rule is invariant to ilr transformations if affine equivariant robust estimators of location and covariance are taken.

Robustification is done (method “robust”) by estimating the columnwise means and the covariance by the Minimum Covariance Estimator.

### Value

an object of class “daFisher” including the following elements

`B` | Between variance of the groups
`W` | Within variance of the groups
`loadings` | loadings
`scores` | fisher scores
`mc` | table indicating misclassifications
`mcrate` | misclassification rate
`coda` | coda
`grp` | grouping
`grppred` | predicted groups
`xc` | xc
`meanj` | meanj
`cv` | cv
`pj` | pj
`meanov` | meanov
`fdiscr` | fdiscr

### Author(s)

Peter Filzmoser, Matthias Templ.

### References

Filzmoser, P. and Hron, K. and Templ, M. (2012) Discriminant analysis for compositional data and robust parameter estimation. Computational Statistics, 27(4), 585-604.

Fisher, R. A. (1938) The statistical utiliziation of multiple measurements. Annals of Eugenics, 8, 376-386.

Rao, C.R. (1948) The utilization of multiple measurements in problems of biological classification. Journal of the Royal Statistical Society, Series B, 10, 159-203.

### See Also

`Linda`

### Examples

    ## toy data (non-compositional)
    require(MASS)
    x1 <- mvrnorm(20,c(0,0,0),diag(3))
    x2 <- mvrnorm(30,c(3,0,0),diag(3))
    x3 <- mvrnorm(40,c(0,3,0),diag(3))
    X <- rbind(x1,x2,x3)
    grp=c(rep(1,20),rep(2,30),rep(3,40))

    #par(mfrow=c(1,2))
    d1 <- daFisher(X,grp=grp,method="classical",coda=FALSE)
    d2 <- daFisher(X,grp=grp,method="robust",coda=FALSE)
    d2
    summary(d2)
    predict(d2, newdata = X)

    ## example with olive data:
    ## Not run:
    data(olive, package = "RnavGraph")
    # exclude zeros (alternatively impute them if
    # the detection limit is known using impRZilr())
    ind <- which(olive == 0, arr.ind = TRUE)[,1]
    olives <- olive[-ind, ]
    x <- olives[, 4:10]
    grp <- olives$Region # 3 groups
    res <- daFisher(x,grp)
    res
    summary(res)
    res <- daFisher(x, grp, plotScore = TRUE)
    res <- daFisher(x, grp, method = "robust")
    res
    summary(res)
    predict(res, newdata = x)
    res <- daFisher(x,grp, plotScore = TRUE, method = "robust")

    # 9 regions
    grp <- olives$Area
    res <- daFisher(x, grp, plotScore = TRUE)
    res
    summary(res)
    predict(res, newdata = x)

    ## End(Not run)

[Package robCompositions version 2.1.0 Index]