Select a formula-based model by AIC.

```
step(object, scope, scale = 0,
direction = c("both", "backward", "forward"),
trace = 1, keep = NULL, steps = 1000, k = 2, …)
```

object

an object representing a model of an appropriate class (mainly
`"lm"`

and `"glm"`

).
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`

, `aov`

and
`glm`

models. The default value, `0`

, indicates
the scale should be estimated: see `extractAIC`

.

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"`

. Values can be abbreviated.

trace

if positive, information is printed during the running of `step`

.
Larger values may give more detailed information.

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.

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`

.

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).

The model fitting must apply the models to the same dataset. This
may be a problem if there are missing values and R's default of
`na.action = na.omit`

is used. We suggest you remove the
missing values first.

Calls to the function `nobs`

are used to check that the
number of observations involved in the fitting process remains unchanged.

`step`

uses `add1`

and `drop1`

repeatedly; it will work for any method for which they work, and that
is determined by having a valid method for `extractAIC`

.
When the additive constant can be chosen so that AIC is equal to
Mallows' \(C_p\), this is done and the tables are labelled
appropriately.

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`

. So using
`.`

in a `scope`

formula means ‘what is
already there’, with `.^2`

indicating all interactions of
existing terms.

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
function `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`

.)

Hastie, T. J. and Pregibon, D. (1992)
*Generalized linear models.*
Chapter 6 of *Statistical Models in S*
eds J. M. Chambers and T. J. Hastie, Wadsworth & Brooks/Cole.

Venables, W. N. and Ripley, B. D. (2002)
*Modern Applied Statistics with S.*
New York: Springer (4th ed).

```
# NOT RUN {
## following on from example(lm)
utils::example("lm", echo = FALSE)
step(lm.D9)
summary(lm1 <- lm(Fertility ~ ., data = swiss))
slm1 <- step(lm1)
summary(slm1)
slm1$anova
# }
```

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