# qda

From MASS v7.3-0
by Brian Ripley

##### Quadratic Discriminant Analysis

Quadratic discriminant analysis.

- Keywords
- multivariate

##### Usage

`qda(x, ...)`## S3 method for class 'formula':
qda(formula, data, \dots, subset, na.action)

## S3 method for class 'default':
qda(x, grouping, prior = proportions,
method, CV = FALSE, nu, \dots)

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

## S3 method for class 'matrix':
qda(x, grouping, \dots, 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
`NA`

s 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 - 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

##### Examples

```
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
```

*Documentation reproduced from package MASS, version 7.3-0, License: GPL-2 | GPL-3*

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