

   QQuuaaddrraattiicc DDiissccrriimmiinnaanntt AAnnaallyyssiiss

        qda(formula, data, prior = proportions, subset,
                           na.action = na.fail, method, CV=F, nu)
        qda(x,   grouping, prior = proportions, subset,
                           na.action = na.fail, method, CV=F, nu)

   AArrgguummeennttss::

    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 `for-
             mula' are preferentially to be taken.

          x: (required if no formula is given as the principal
             argument.)  a matrix or data frame or Matrix con-
             taining 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 train-
             ing 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 argu-
             ment 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 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 propor-
             tions in the whole dataset are used.

         nu: degrees of freedom for `method = t'.

   DDeessccrriippttiioonn::

        Quadratic discriminant analysis.

   DDeettaaiillss::

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

   VVaalluuee::

        an object of class qda containing the following compo-
        nents:

      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 disper-
             sion matrix.

        lev: the levels of the grouping factor.

      terms: (if formula is a formula) an object of mode
             expression and class term summarizing the  for-
             mula.

       call: the (matched) function call.

             unless `CV=T', when the return value is a list
             with components:

      class: The MAP classification (a factor)

   posterior: posterior probabilities for the classes

   SSeeee AAllssoo::

        `predict.qda', `lda'

   EExxaammpplleess::

        data(iris3)
        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

