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
object already inherits from
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further arguments passed to or from other methods.
the environment to associate with the result, if not already a formula.
logical indicating if the environment should be printed as well.
The models fit by, e.g., the
are specified in a compact symbolic form.
~ 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
Such a model consists of a series of terms separated
The terms themselves consist of variable and factor
names separated by
Such a term is interpreted as the interaction of
all the variables and factors appearing in the term.
In addition to
:, a number of other operators are
useful in model formulae. The
* operator denotes factor
a*b interpreted as
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
c together with their second-order interactions.
%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: when fitting a linear model
y ~ x - 1 specifies
a line through the origin. A model with no intercept can be also
y ~ x + 0 or
y ~ 0 + x.
While formulae usually involve just variable and factor
names, they can also involve arithmetic expressions.
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
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
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.
Most model-fitting functions accept formulae with right-hand-side
including the function
offset to indicate terms with a
fixed coefficient of one. Some functions accept other
‘specials’ such as
cluster (see the
specials argument of
There are two special interpretations of
. in a formula. The
usual one is in the context of a
data argument of model
fitting functions and means ‘all columns not otherwise in the
terms.formula. In the context of
update.formula, only, it means ‘what was
previously in this part of the formula’.
formula is called on a fitted model object, either a
specific method is used (such as that for class
"nls") or the
default method. The default first looks for a
component of the object (and evaluates it), then a
component, then a
formula parameter of the call (and evaluates
its value) and finally a
There is a
formula method for data frames. If there is only
one column this forms the RHS with an empty LHS. For more columns,
the first column is the LHS of the formula and the remaining columns
+ form the RHS.
All the functions above produce an object of class
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
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
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.
For formula manipulation:
for typical use:
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class(fo <- y ~ x1*x2) # "formula" fo typeof(fo) # R internal : "language" terms(fo) environment(fo) 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 <- paste0("x", 1:25) (fmla <- as.formula(paste("y ~ ", paste(xnam, collapse= "+"))))