step {stats}  R Documentation 
Choose a model by AIC in a Stepwise Algorithm
Description
Select a formulabased model by AIC.
Usage
step(object, scope, scale = 0,
direction = c("both", "backward", "forward"),
trace = 1, keep = NULL, steps = 1000, k = 2, ...)
Arguments
object 
an object representing a model of an appropriate class (mainly

scope 
defines the range of models examined in the stepwise search.
This should be either a single formula, or a list containing
components 
scale 
used in the definition of the AIC statistic for selecting the models,
currently only for 
direction 
the mode of stepwise search, can be one of 
trace 
if positive, information is printed during the running of 
keep 
a filter function whose input is a fitted model object and the
associated 
steps 
the maximum number of steps to be considered. The default is 1000 (essentially as many as required). It is typically used to stop the process early. 
k 
the multiple of the number of degrees of freedom used for the penalty.
Only 
... 
any additional arguments to 
Details
step
uses add1
and drop1
repeatedly; it will work for any method for which they work, and that
is determined by having a valid method for extractAIC
.
When the additive constant can be chosen so that AIC is equal to
Mallows' C_p
, this is done and the tables are labelled
appropriately.
The set of models searched is determined by the scope
argument.
The righthandside of its lower
component is always included
in the model, and righthandside of the model is included in the
upper
component. If scope
is a single formula, it
specifies the upper
component, and the lower
model is
empty. If scope
is missing, the initial model is used as the
upper
model.
Models specified by scope
can be templates to update
object
as used by update.formula
. So using
.
in a scope
formula means ‘what is
already there’, with .^2
indicating all interactions of
existing terms.
There is a potential problem in using glm
fits with a
variable scale
, as in that case the deviance is not simply
related to the maximized loglikelihood. The "glm"
method for
function extractAIC
makes the
appropriate adjustment for a gaussian
family, but may need to be
amended for other cases. (The binomial
and poisson
families have fixed scale
by default and do not correspond
to a particular maximumlikelihood problem for variable scale
.)
Value
the stepwiseselected model is returned, with up to two additional
components. There is an "anova"
component corresponding to the
steps taken in the search, as well as a "keep"
component if the
keep=
argument was supplied in the call. The
"Resid. Dev"
column of the analysis of deviance table refers
to a constant minus twice the maximized log likelihood: it will be a
deviance only in cases where a saturated model is welldefined
(thus excluding lm
, aov
and survreg
fits,
for example).
Warning
The model fitting must apply the models to the same dataset. This
may be a problem if there are missing values and R's default of
na.action = na.omit
is used. We suggest you remove the
missing values first.
Calls to the function nobs
are used to check that the
number of observations involved in the fitting process remains unchanged.
Note
This function differs considerably from the function in S, which uses a number of approximations and does not in general compute the correct AIC.
This is a minimal implementation. Use stepAIC
in package MASS for a wider range of object classes.
Author(s)
B. D. Ripley: step
is a slightly simplified version of
stepAIC
in package MASS (Venables &
Ripley, 2002 and earlier editions).
The idea of a step
function follows that described in Hastie &
Pregibon (1992); but the implementation in R is more general.
References
Hastie, T. J. and Pregibon, D. (1992) Generalized linear models. Chapter 6 of Statistical Models in S eds J. M. Chambers and T. J. Hastie, Wadsworth & Brooks/Cole.
Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. New York: Springer (4th ed).
See Also
Examples
## following on from example(lm)
step(lm.D9)
summary(lm1 < lm(Fertility ~ ., data = swiss))
slm1 < step(lm1)
summary(slm1)
slm1$anova