Linda: Robust Linear Discriminant Analysis

Description

Robust linear discriminant analysis based on MCD and returns the results as an object of class Linda (aka constructor).

Usage

Linda(x, ...)
# S3 method for default
Linda(x, grouping, prior = proportions, tol = 1.0e-4,
                 method = c("mcd", "mcdA", "mcdB", "mcdC", "fsa", "mrcd", "ogk"),
                 alpha=0.5, l1med=FALSE, cov.control, trace=FALSE, ...)

Value

Returns an S4 object of class Linda

Arguments

x: a matrix or data frame containing the explanatory variables (training set).
grouping: grouping variable: a factor specifying the class for each observation.
prior: prior probabilities, default to the class proportions for the training set.
tol: tolerance
method: method
alpha: this parameter measures the fraction of outliers the algorithm should resist. In MCD alpha controls the size of the subsets over which the determinant is minimized, i.e. alpha*n observations are used for computing the determinant. Allowed values are between 0.5 and 1 and the default is 0.5.
l1med: whether to use L1 median (space median) instead of MCD to compute the group means locations in order to center the data in methods mcdB and mcdC. useful in case of groups with small size. Default is l1med = FALSE.
cov.control: specifies which covariance estimator to use by providing a CovControl-class object. The default is CovControlMcd-class which will indirectly call CovMcd. If cov.control=NULL is specified, the classical estimates will be used by calling CovClassic

trace: whether to print intermediate results. Default is trace = FALSE.
...: arguments passed to or from other methods

Author

Valentin Todorov valentin.todorov@chello.at

Details

details

References

Hawkins, D.M. and McLachlan, G.J. (1997) High-Breakdown Linear Discriminant Analysis, Journal of the American Statistical Association, 92, 136--143.

Todorov V. (2007) Robust selection of variables in linear discriminant analysis, Statistical Methods and Applications, 15, 395--407, doi:10.1007/s10260-006-0032-6.

Todorov, V. and Pires, A.M. (2007) Comparative Performance of Several Robust Linear Discriminant Analysis Methods. REVSTAT Statistical Journal, 5, p 63--83.

Todorov V & Filzmoser P (2009), An Object Oriented Framework for Robust Multivariate Analysis. Journal of Statistical Software, 32(3), 1--47. tools:::Rd_expr_doi("10.18637/jss.v032.i03").

Examples

Run this code

## Example anorexia
library(MASS)
data(anorexia)

## start with the classical estimates
lda <- LdaClassic(Treat~., data=anorexia)
predict(lda)@classification

## try now the robust LDA with the default method (MCD with pooled whitin cov matrix)
rlda <- Linda(Treat~., data= anorexia)
predict(rlda)@classification

## try the other methods
Linda(Treat~., data= anorexia, method="mcdA")
Linda(Treat~., data= anorexia, method="mcdB")
Linda(Treat~., data= anorexia, method="mcdC")

## try the Hawkins&McLachlan method
## use the default method
grp <- anorexia[,1]
grp <- as.factor(grp)
x <- anorexia[,2:3]
Linda(x, grp, method="fsa")

## Do DA with Linda and method mcdB or mcdC, when some classes
## have very few observations. Use L1 median instead of MCD
##  to compute the group means (l1med=TRUE).

data(fish)

# remove observation #14 containing missing value
fish <- fish[-14,]

# The height and width are calculated as percentages 
#   of the third length variable
fish[,5] <- fish[,5]*fish[,4]/100
fish[,6] <- fish[,6]*fish[,4]/100

table(fish$Species) 
Linda(Species~., data=fish, l1med=TRUE)
Linda(Species~., data=fish, method="mcdC", l1med=TRUE)

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