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)[2:7])
      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