stepAIC {MASS}R Documentation

Choose a model by AIC in a Stepwise Algorithm

Description

Performs stepwise model selection by exact AIC.

Usage

stepAIC(object, scope, scale, direction=c("both", "backward", "forward"), 
        trace=1, keep=NULL, steps=1000, use.start=FALSE, k=2, ...)
extractAIC(fit, scale, k=2, ...)

Arguments

object fit 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 stepAIC(). Larger values may give more information on the fitting process.
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.
use.start if true the updated fits are done starting at the linear predictor for the currently selected model. This may speed up the iterative calculations for glm (and other fits), but it can also slow them down.
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. (None are currently used.)

Details

stepAIC differs from step and especially step.glm in using the exact AIC rather than potentially misleading one-step approximations. It is also much more widely applicable: all that is required is a method for extractAIC, which should return a vector c(modeldf, AIC). The default method handles linear models (lm, aov and glm of family "Gaussian" with identity link) using addterm.lm and dropterm.lm: for these the results are similar to step.glm except that the AIC quoted is Akaike's not Hastie's. (The additive constant is chosen so that in that case AIC is identical to Mallows' Cp if the scale is known.)

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.)

Where a conventional deviance exists (e.g. for lm, aov and glm fits) this is quoted in the analysis of variance table: it is the unscaled deviance.

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).

See Also

addterm, dropterm, step

Examples

data(quine)
quine.hi <- aov(log(Days + 2.5) ~ .^4, quine)
quine.nxt <- update(quine.hi, . ~ . - Eth:Sex:Age:Lrn)
quine.stp <- stepAIC(quine.nxt, 
    scope = list(upper = ~Eth*Sex*Age*Lrn, lower = ~1), 
    trace = FALSE)
quine.stp$anova

data(cpus)
cpus1 <- cpus
attach(cpus)
for(v in names(cpus)[2:6]) 
  cpus1[[v]] <- cut(cpus[[v]], unique(quantile(cpus[[v]])), 
                    include.lowest = TRUE)
detach()
cpus0 <- cpus1[, 2:8]  # excludes names, authors' predictions
cpus.samp <- sample(1:209, 100)
cpus.lm <- lm(log10(perf) ~ ., data=cpus1[cpus.samp,2:8])
cpus.lm2 <- stepAIC(cpus.lm, trace=FALSE)
cpus.lm2$anova

example(birthwt)
birthwt.glm <- glm(low ~ ., family=binomial, data=bwt)
birthwt.step <- stepAIC(birthwt.glm, trace=FALSE)
birthwt.step$anova
birthwt.step2 <- stepAIC(birthwt.glm, ~ .^2 + I(scale(age)^2)
    + I(scale(lwt)^2), trace=FALSE)
birthwt.step2$anova

quine.nb <- glm.nb(Days ~ .^4, data=quine)
quine.nb2 <- stepAIC(quine.nb)
quine.nb2$anova