Choose a model by AIC in a Stepwise Algorithm

DESCRIPTION:

Performs stepwise model selection by exact AIC.

USAGE:

stepAIC(object, scope, scale = 0,
        direction = c("both", "backward", "forward"),
        trace = 1, keep = NULL, steps = 1000, use.start = F, k = 2, ...)
extractAIC(fit, scale, k = 2, ...)

REQUIRED ARGUMENTS:

object fit
an object representing a model of an appropriate class. This is used as the initial model in the stepwise search.

OPTIONAL ARGUMENTS:

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.
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.)

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). If the original fit is a formal (`S4' class) the result is a list with components fit, anova and perhaps keep .

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 Hasties. (The additive constant is chosen so that in that case AIC is identical to Mallows' Cp if the scale is known.)

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 specifes the upper component, and the lower model is empty. If scope is missing, the initial model is used as the upper model.

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.

NOTE:

The model fitting must apply the models to the same dataset. This may be a problem if there are missing values and an na.action other than na.fail is used (as may be the default if options(na.action=) has been set, including in R). We suggest you remove the missing values first.

SEE ALSO:

, , ,

EXAMPLES:

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 = F)
quine.stp$anova

cpus1 <- cpus
attach(cpus)
for(v in names(cpus)[2:7])
  cpus1[[v]] <- cut(cpus[[v]], unique(quantile(cpus[[v]])),
                    include.lowest = T)
detach()
set.seed(123)
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=F)
cpus.lm2$anova

birthwt.glm <- glm(low ~ ., family=binomial, data=bwt)
birthwt.step <- stepAIC(birthwt.glm, trace=F)
birthwt.step$anova
birthwt.step2 <- stepAIC(birthwt.glm, ~ .^2 + I(scale(age)^2)
    + I(scale(lwt)^2), trace=F)
birthwt.step2$anova
quine.nb <- glm.nb(Days ~ .^4, data=quine)
quine.nb2 <- stepAIC(quine.nb)
quine.nb2$anova