

   FFiinndd AAlliiaasseess ((DDeeppeennddeenncciieess)) iinn aa MMooddeell

        alias(object, ...)
        alias.formula(object, data, ...)
        alias.lm(object, complete = TRUE, partial = FALSE, partial.pattern = FALSE)

   AArrgguummeennttss::

     object: A fitted model object, for example from `lm' or
             `aov', or a formula for `alias.formula'.

       data: Optionally, a data frame to search for the objects
             in the formula.

   complete: Should information on complete aliasing be
             included?

    partial: Should information on partial aliasing be
             included?

   partial.pattern: Should partial aliasing be presented in a
             schematic way? If this is done, the results are
             presented in a more compact way, usually giving
             the deciles of the coefficients.

   DDeessccrriippttiioonn::

        Although the main method is for class `"lm"', `alias'
        is most useful for experimental designs and so is used
        with fits from `aov'.  Complete aliasing refers to
        effects in linear models that cannot be estimated inde-
        pendently of the terms which occur earlier in the model
        and so have their coefficients omitted from the fit.
        Partial aliasing refers to effects that can be esti-
        mated less precisely because of correlations induced by
        the design.

   VVaalluuee::

        A list (of `class "listof"') containing components

      Model: Description of the model; usually the formula.

   Complete: A matrix with columns corresponding to effects
             that are linearly dependent on the rows; may be of
             class `"mtable"' which has its own `print' method.

    Partial: The correlations of the estimable effects, with a
             zero diagonal.

   NNoottee::

        The aliasing pattern may depend on the contrasts in
        use: Helmert contrasts are probably most useful.

        The defaults are different from those in S.

   AAuutthhoorr((ss))::

        B.D. Ripley

   EExxaammpplleess::

        ## From Venables and Ripley (1997) p.210.
        N <- c(0,1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,1,0,1,1,0,0)
        P <- c(1,1,0,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0)
        K <- c(1,0,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0,1,1,1,0,1,0)
        yield <- c(49.5,62.8,46.8,57.0,59.8,58.5,55.5,56.0,62.8,55.8,69.5,55.0,
                   62.0,48.8,45.5,44.2,52.0,51.5,49.8,48.8,57.2,59.0,53.2,56.0)
        npk <- data.frame(block=gl(6,4), N=factor(N), P=factor(P),
                          K=factor(K), yield=yield)

        ## The next line is optional (for fractions package which gives neater
        ## results.)
        has.VR <- require(MASS, quietly = TRUE)

        op <- options(contrasts=c("contr.helmert", "contr.poly"))
        npk.aov <- aov(yield ~ block + N*P*K, npk)
        alias(npk.aov)
        if(has.VR) detach(package:MASS)
        options(op)# reset

