

   CCoonnttrraasstt MMaattrriicceess

        contr.helmert(n, contrasts=TRUE)
        contr.poly(n, contrasts=TRUE)
        contr.sum(n, contrasts=TRUE)
        contr.treatment(n, base=1, contrasts=TRUE)

   VVaalluuee::

        A matrix with `n' rows and `k' columns, with `k=n-1' if
        `contrasts' is `TRUE' and `k=n' if `contrasts' is
        `FALSE'.

        The base argument to `contr.treatment()' allows you to
        specify which group is considered the baseline group.

        These functions are used for creating contrast matrices
        for use in fitting analysis of variance and regression
        models.  The columns of the resulting matrices contain
        contrasts which can be used for coding a factor with
        `n' levels.  The returned value contains the computed
        contrasts.  If the argument `contrasts' is `FALSE' then
        an additional column of ones is prepended to the
        matrix.

        Note that as from R version 0.62.2, `contr.poly'
        returns contrasts based on orthogonal (rather than raw)
        polynomials.

   SSeeee AAllssoo::

        `contrasts', `C', and `aov', `glm', `lm'.

   EExxaammpplleess::

        (cH <- contr.helmert(4))
        apply(cH, 2,sum)# column sums are 0!
        crossprod(cH)# diagonal -- columns are orthogonal

        (cT <- contr.treatment(5))
        all(crossprod(cT) == diag(4))# TRUE: even orthonormal

        (cP <- contr.poly(3))# Linear and Quadratic
        zapsmall(crossprod(cP), dig=15) # orthonormal up to fuzz

