# step: Choose a model by AIC in a Stepwise Algorithm

Description Usage Arguments Details Value Warning Note Author(s) References See Also Examples

### Description

Select a formula-based model by AIC.

### Usage

 ```1 2 3``` ```step(object, scope, scale = 0, direction = c("both", "backward", "forward"), trace = 1, keep = NULL, steps = 1000, k = 2, ...) ```

### Arguments

 `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`.

### Details

`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' Cp, 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`.)

### 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).

### Warning

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.

### Note

This function differs considerably from the function in S, which uses a number of approximations and does not in general compute the correct AIC.

This is a minimal implementation. Use `stepAIC` in package MASS for a wider range of object classes.

### Author(s)

B. D. Ripley: `step` is a slightly simplified version of `stepAIC` in package MASS (Venables & Ripley, 2002 and earlier editions).

The idea of a `step` function follows that described in Hastie & Pregibon (1992); but the implementation in R is more general.

### References

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).

`stepAIC` in MASS, `add1`, `drop1`
 ```1 2 3 4 5 6 7 8``` ```## following on from example(lm) step(lm.D9) summary(lm1 <- lm(Fertility ~ ., data = swiss)) slm1 <- step(lm1) summary(slm1) slm1\$anova ```