

   MMooddeell FFoorrmmuullaaee

        y ~ model
        formula(object)
        formula.default(anything)
        formula.formula(formula.obj)
        formula.terms(terms.obj)
        formula.data.frame(df)
        as.formula(object)

   DDeessccrriippttiioonn::

        The generic function `formula' and its specific methods
        provide a way of extracting formulae which have been
        included in other objects.

        `as.formula' is almost identical, additionally preserv-
        ing attributes when `object' already inherits from
        `"formula"'.

   DDeettaaiillss::

        The models fit by, e.g., the `lm' and `glm' functions
        are specified in a compact symbolic form.  The `~'
        operator is basic in the formation of such models.  An
        expression of the form `y~model' is interpreted as a
        specification that the response `y' is modelled by a
        linear predictor specified symbolically by `model'.
        Such a model consists of a series of terms separated by
        `+' operators.  The terms themselves consist of vari-
        able and factor names separated by `:' operators.  Such
        a term is interpreted as the interaction of all the
        variables and factors appearing in the term.

        In addition to `+' and `:', a number of other operators
        are useful in model formulae.  The `*' operator denotes
        factor crossing: `a*b' interpreted as `a+b+a:b'.  The
        `^' operator indicates crossing to the specified
        degree.  For example `(a+b+c)^2' is identical to
        `(a+b+c)*(a+b+c)' which in turn expands to a formula
        containing the main effects for `a', `b' and `c'
        together with their second-order interactions.  The
        `%in%' operator indicates that the terms on its left
        are nested within those on the right.  For example
        `a+b%in%a' expands to the formula `a+a:b'.

        While formulae usually involve just variable and factor
        names, they can also involve arithmetic expressions.
        The formula `log(y)~a+log(x)' is quite legal.  When
        such arithmetic expressions involve operators which are
        also used symbolically in model formulae, there can be
        confusion between arithmetic and symbolic operator use.
        To avoid this confusion, the function `I()' can be used
        to bracket those portions of a model formula where the
        operators are used in their arithmetic sense.  For
        example, in the formula `y~a+I(b+c)', the term `b+c' is
        to be interpreted as the sum of `b' and `c'.

   VVaalluuee::

        All the functions above produce an object of class
        `formula' which contains a symbolic model formula.

   SSeeee AAllssoo::

        `lm', `glm', `terms'.

   EExxaammpplleess::

        class(fo <- y ~ x1*x2) # "formula"
        fo
        typeof(fo)# R internal : "language"
        terms(fo)

        ## Create a formula for a model with a large number of variables:
        xnam <- paste("x", 1:25, sep="")
        (fmla <- as.formula(paste("y ~ ", paste(xnam, collapse= "+"))))

