lda
Linear discriminant analysis.
 Keywords
 multivariate
Usage
lda(x, …)# S3 method for formula
lda(formula, data, …, subset, na.action)
# S3 method for default
lda(x, grouping, prior = proportions, tol = 1.0e4,
method, CV = FALSE, nu, …)
# S3 method for data.frame
lda(x, …)
# S3 method for matrix
lda(x, grouping, …, subset, na.action)
Arguments
 formula

A formula of the form
groups ~ x1 + x2 + …
That is, the response is the grouping factor and the right hand side specifies the (nonfactor) discriminators.  data

Data frame from which variables specified in
formula
are preferentially to be taken.  x
 (required if no formula is given as the principal argument.) a matrix or data frame or Matrix containing the explanatory variables.
 grouping
 (required if no formula principal argument is given.) a factor specifying the class for each observation.
 prior
 the prior probabilities of class membership. If unspecified, the class proportions for the training set are used. If present, the probabilities should be specified in the order of the factor levels.
 tol

A tolerance to decide if a matrix is singular; it will reject variables
and linear combinations of unitvariance variables whose variance is
less than
tol^2
.  subset
 An index vector specifying the cases to be used in the training sample. (NOTE: If given, this argument must be named.)
 na.action

A function to specify the action to be taken if
NA
s are found. The default action is for the procedure to fail. An alternative isna.omit
, which leads to rejection of cases with missing values on any required variable. (NOTE: If given, this argument must be named.)  method

"moment"
for standard estimators of the mean and variance,"mle"
for MLEs,"mve"
to usecov.mve
, or"t"
for robust estimates based on a \(t\) distribution.  CV
 If true, returns results (classes and posterior probabilities) for leaveoneout crossvalidation. Note that if the prior is estimated, the proportions in the whole dataset are used.
 nu

degrees of freedom for
method = "t"
.  …
 arguments passed to or from other methods.
Details
The function
tries hard to detect if the withinclass covariance matrix is
singular. If any variable has withingroup variance less than
tol^2
it will stop and report the variable as constant. This
could result from poor scaling of the problem, but is more
likely to result from constant variables. Specifying the prior
will affect the classification unless
overridden in predict.lda
. Unlike in most statistical packages, it
will also affect the rotation of the linear discriminants within their
space, as a weighted betweengroups covariance matrix is used. Thus
the first few linear discriminants emphasize the differences between
groups with the weights given by the prior, which may differ from
their prevalence in the dataset. If one or more groups is missing in the supplied data, they are dropped
with a warning, but the classifications produced are with respect to the
original set of levels.
Value
If CV = TRUE
the return value is a list with components
class
, the MAP classification (a factor), and posterior
,
posterior probabilities for the classes. Otherwise it is an object of class "lda"
containing the
following components:
Note
This function may be called giving either a formula and
optional data frame, or a matrix and grouping factor as the first
two arguments. All other arguments are optional, but subset=
and
na.action=
, if required, must be fully named. If a formula is given as the principal argument the object may be
modified using update()
in the usual way.
References
Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer. Ripley, B. D. (1996) Pattern Recognition and Neural Networks. Cambridge University Press.
See Also
Examples
library(MASS)
Iris < data.frame(rbind(iris3[,,1], iris3[,,2], iris3[,,3]),
Sp = rep(c("s","c","v"), rep(50,3)))
train < sample(1:150, 75)
table(Iris$Sp[train])
## your answer may differ
## c s v
## 22 23 30
z < lda(Sp ~ ., Iris, prior = c(1,1,1)/3, subset = train)
predict(z, Iris[train, ])$class
## [1] s s s s s s s s s s s s s s s s s s s s s s s s s s s c c c
## [31] c c c c c c c v c c c c v c c c c c c c c c c c c v v v v v
## [61] v v v v v v v v v v v v v v v
(z1 < update(z, . ~ .  Petal.W.))