Linear discriminant analysis based on left-spherically
distributed linear scores.
Usage
## S3 method for class 'formula'
slda(formula, data, subset, na.action=na.rpart, ...)
## S3 method for class 'factor'
slda(y, X, q=NULL, ...)
Arguments
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 NAs. Defaults to
na.rpart.
...
additional parameters passed to lda.
Details
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 - ar{X})^\top(X - ar{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).
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.