formula {stats}R Documentation

Model Formulae


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 preserving attributes when object already inherits from "formula". The default value of the env argument is used only when the formula would otherwise lack an environment.


formula(x, ...)
as.formula(object, env = parent.frame())


x, object R object.
... further arguments passed to or from other methods.
env the environment to associate with the result.


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 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. The - operator removes the specified terms, so that (a+b+c)^2 - a:b is identical to a + b + c + b:c + a:c. It can also used to remove the intercept term: y ~ x - 1 is a line through the origin. A model with no intercept can be also specified as y ~ x + 0 or y ~ 0 + x.

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.

Variable names can be quoted by backticks `like this` in formulae, although there is no guarantee that all code using formulae will accept such non-syntactic names.

When formula is called on a fitted model object, either a specific method is used (such as that for class "nls") of the default method. The default first looks for a "formula" component of the object (and evaluates it), then a "terms" component, then a formula parameter of the call (and evaluates its value) and finally a "formula" attribute.


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


A formula object has an associated environment, and this environment (rather than the parent environment) is used by model.frame to evaluate variables that are not found in the supplied data argument.

Formulas created with the ~ operator use the environment in which they were created. Formulas created with as.formula will use the env argument for their environment. Pre-existing formulas extracted with as.formula will only have their environment changed if env is given explicitly.


Chambers, J. M. and Hastie, T. J. (1992) Statistical models. Chapter 2 of Statistical Models in S eds J. M. Chambers and T. J. Hastie, Wadsworth & Brooks/Cole.

See Also


For formula manipulation: terms, and all.vars; for typical use: lm, glm, and coplot.


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

environment(as.formula("y ~ x"))
environment(as.formula("y ~ x",env=new.env()))

## 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= "+"))))

[Package stats version 2.5.0 Index]