

   SSiimmppllee CCoorrrreessppoonnddeennccee AAnnaallyyssiiss

        corresp(tabl, nf=1, ...)

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

       tabl: The function is generic, accepting various forms
             of the principal argument for specifying a two-way
             frequency table.  Currently accepted forms are
             matrices, data frames (coerced to frequency
             tables), objects of class `crosstabs' and formulae
             of the form `~ F1 + F2', where `F1' and `F2' are
             factors.

         nf: The number of factors to be computed. Note that
             although 1 is the most usual, one school of
             thought takes the first two singular vectors for a
             sort of biplot.

        ...: If the principal argument is a formula, a data
             frame may be specified as well from which vari-
             ables in the formula are preferentially satisfied.

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

        Find the principal canonical correlation and corre-
        sponding row- and column-scores from a correspondence
        analysis of a two-way contingency table.

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

        See the reference.  The `plot' method produces a graph-
        ical representation of the table if `nf=1', with the
        areas of circles representing the numbers of points.
        If `nf' is two or more the `biplot' method is called,
        which plots the second and third columns of the matri-
        ces `A = Dr^(-1/2}) U L' and `B = Dc^(-1/2) U V' where
        the singular value decomposition is `U L V'.  Thus the
        x-axis is the canonical correlation times the row and
        column scores. Although this is called a biplot, it
        does not have any useful inner product relationship
        between the row and column scores.  Think of this as an
        equally-scaled plot with two unrelated sets of labels.

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

        An list object of class `correspondence' for which
        `print', `plot' and `biplot' methods are supplied.  The
        main components are the canonical correlation(s) and
        the row and column scores.

   RReeffeerreenncceess::

        Venables  Ripley (1997), chapter 13.

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

        `svd', `princomp'

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

        data(quine)
        ct <- corresp(~ Age + Eth, data=quine)
        ct
        plot(ct)

        data(caith)
        biplot(corresp(caith, nf=2))

