stepAIC                 package:MASS                 R Documentation

Choose a model by AIC in a Stepwise Algorithm

Description:

     Performs stepwise model selection by AIC.

Usage:

     stepAIC(object, scope, scale = 0,
             direction = c("both", "backward", "forward"),
             trace = 1, keep = NULL, steps = 1000, use.start = FALSE,
             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.
          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' and 'aov' models (see
          'extractAIC' for details). 

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. *Not used* in R. 

       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:

     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.

     Models specified by 'scope' can be templates to update 'object' as
     used by 'update.formula'.

     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 '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'.)

     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).

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 is the default in R). We suggest
     you remove the missing values first.

References:

     Venables, W. N. and Ripley, B. D. (2002) _Modern Applied
     Statistics with S._ Fourth edition.  Springer.

See Also:

     'addterm', 'dropterm', 'step'

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 = FALSE)
     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 = 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

