Choose a model by AIC in a Stepwise Algorithm

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. This is used as the initial model in the stepwise search.
scope defines the range of models examined in the stepwise search.
scale used in the definition of the AIC statistic for selecting the models, currently only for lm, aov and glm models.
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".
trace if positive, information is printed during the running of step.
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.

Description

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' Cp, this is done and the tables are labelled appropriately.

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 function extractAIC.glm 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.)

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).

Note

This function differs considerably from the function in S, which uses a number of approximations and does not compute the correct AIC.

Author(s)

B.D. Ripley

See Also

add1, drop1

Examples

example(lm)
step(lm.D9)  

data(swiss)
summary(lm1 <- lm(Fertility ~ ., data = swiss))
slm1 <- step(lm1)
summary(slm1)
slm1 $ anova

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