## Model Formulae

## Usage

    y ~ model
    formula(object)
    formula.default(anything)
    formula.formula(formula.obj)
    formula.terms(terms.obj)

## Description

The models fit by 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 variable 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`.

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

## Value

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

## See Also

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

## Examples

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

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