Description
Select a formula-based 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 "lm"
and "glm"
). This is used as the initial model in the stepwise search.
scope
defines the range of models examined in the stepwise search. This should be either a single formula, or a list containing components upper
and lower
, both formulae. See the details for how to specify the formulae and how they are used.
scale
used in the definition of the AIC statistic for selecting the models, currently only for lm
, aov
and glm
models. The default value, 0
, indicates the scale should be estimated: see extractAIC
.
direction
the mode of stepwise search, can be one of "both"
, "backward"
, or "forward"
, with a default of "both"
. If the scope
argument is missing the default for direction
is "backward"
. Values can be abbreviated.
trace
if positive, information is printed during the running of step
. Larger values may give more detailed information.
keep
a filter function whose input is a fitted model object and the associated AIC
statistic, and whose output is arbitrary. Typically keep
will select a subset of the components of the object and return them. The default is not to keep anything.
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 k = 2
gives the genuine AIC: k = log(n)
is sometimes referred to as BIC or SBC.
…
any additional arguments to extractAIC
.
Value
the stepwise-selected 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 well-defined (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 Calls to the function na.action = na.omit
is used. We suggest you remove the missing values first.nobs
are used to check that the number of observations involved in the fitting process remains unchanged.
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 right-hand-side of its lower
component is always included in the model, and right-hand-side 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 log-likelihood. 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 maximum-likelihood problem for variable scale
.)
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
stepAIC
in MASS, add1
, drop1
Examples
# NOT RUN {## following on from example(lm)utils::example("lm", echo = FALSE)step(lm.D9)summary(lm1 <- lm(Fertility ~ ., data = swiss))slm1 <- step(lm1)summary(slm1)slm1$anova# }
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