Quadratic Discriminant Analysis

Description

Quadratic discriminant analysis.

Usage

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qda(x, ...)

## S3 method for class 'formula'
qda(formula, data, ..., subset, na.action)

## Default S3 method:
qda(x, grouping, prior = proportions,
    method, CV = FALSE, nu, ...)

## S3 method for class 'data.frame'
qda(x, ...)

## S3 method for class 'matrix'
qda(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 (non-factor) 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 specified, the probabilities should be specified in the order of the factor levels.

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 NAs are found. The default action is for the procedure to fail. An alternative is na.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 use cov.mve, or "t" for robust estimates based on a t distribution.

CV

If true, returns results (classes and posterior probabilities) for leave-out-out cross-validation. 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

Uses a QR decomposition which will give an error message if the within-group variance is singular for any group.

Value

an object of class "qda" containing the following components:

prior

the prior probabilities used.

means

the group means.

scaling

for each group i, scaling[,,i] is an array which transforms observations so that within-groups covariance matrix is spherical.

ldet

a vector of half log determinants of the dispersion matrix.

lev

the levels of the grouping factor.

terms

(if formula is a formula) an object of mode expression and class term summarizing the formula.

call

the (matched) function call.

unless CV=TRUE, when the return value is a list with components:

class

The MAP classification (a factor)

posterior

posterior probabilities for the classes

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

predict.qda, lda

Examples

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tr <- sample(1:50, 25)
train <- rbind(iris3[tr,,1], iris3[tr,,2], iris3[tr,,3])
test <- rbind(iris3[-tr,,1], iris3[-tr,,2], iris3[-tr,,3])
cl <- factor(c(rep("s",25), rep("c",25), rep("v",25)))
z <- qda(train, cl)
predict(z,test)$class

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