# Choose a model by AIC in a Stepwise Algorithm Performs stepwise model selection by AIC. ```r 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 . - `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.) ## Returns 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). ## 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 specifies 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. ## 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 ). 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 ```r 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$anova cpus1 <- cpus for(v in names(cpus)[2:7]) cpus1[[v]] <- cut(cpus[[v]], unique(quantile(cpus[[v]])), include.lowest = TRUE) cpus0 <- cpus1[, 2:8] # excludes names, authors' predictions cpus.samp <- sample(1:209, 100) cpus.lm <- lm(log10(perf) ~ ., data = cpus1[cpus.samp,2:8]) cpus.lm2 <- stepAIC(cpus.lm, trace = FALSE) cpus.lm2$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 ```

stepAIC function