# add1

##### Add or Drop All Possible Single Terms to a Model

Compute all the single terms in the `scope`

argument that can be
added to or dropped from the model, fit those models and compute a
table of the changes in fit.

- Keywords
- models

##### Usage

`add1(object, scope, …)`# S3 method for default
add1(object, scope, scale = 0, test = c("none", "Chisq"),
k = 2, trace = FALSE, …)

# S3 method for lm
add1(object, scope, scale = 0, test = c("none", "Chisq", "F"),
x = NULL, k = 2, …)

# S3 method for glm
add1(object, scope, scale = 0,
test = c("none", "Rao", "LRT", "Chisq", "F"),
x = NULL, k = 2, …)

drop1(object, scope, …)

# S3 method for default
drop1(object, scope, scale = 0, test = c("none", "Chisq"),
k = 2, trace = FALSE, …)

# S3 method for lm
drop1(object, scope, scale = 0, all.cols = TRUE,
test = c("none", "Chisq", "F"), k = 2, …)

# S3 method for glm
drop1(object, scope, scale = 0,
test = c("none", "Rao", "LRT", "Chisq", "F"),
k = 2, …)

##### Arguments

- object
- a fitted model object.
- scope
- a formula giving the terms to be considered for adding or dropping.
- scale
- an estimate of the residual mean square to be
used in computing \(C_p\). Ignored if
`0`

or`NULL`

. - test
- should the results include a test statistic relative to the
original model? The F test is only appropriate for
`lm`

and`aov`

models or perhaps for`glm`

fits with estimated dispersion. The \(\chi^2\) test can be an exact test (`lm`

models with known scale) or a likelihood-ratio test or a test of the reduction in scaled deviance depending on the method. For`glm`

fits, you can also choose`"LRT"`

and`"Rao"`

for likelihood ratio tests and Rao's efficient score test. The former is synonymous with`"Chisq"`

(although both have an asymptotic chi-square distribution). Values can be abbreviated. - k
- the penalty constant in AIC / \(C_p\).
- trace
- if
`TRUE`

, print out progress reports. - x
- a model matrix containing columns for the fitted model and all
terms in the upper scope. Useful if
`add1`

is to be called repeatedly.**Warning:**no checks are done on its validity. - all.cols
- (Provided for compatibility with S.) Logical to specify
whether all columns of the design matrix should be used. If
`FALSE`

then non-estimable columns are dropped, but the result is not usually statistically meaningful. - …
- further arguments passed to or from other methods.

##### Details

For `drop1`

methods, a missing `scope`

is taken to be all
terms in the model. The hierarchy is respected when considering terms
to be added or dropped: all main effects contained in a second-order
interaction must remain, and so on. In a `scope`

formula `.`

means ‘what is already there’. The methods for `lm`

and `glm`

are more
efficient in that they do not recompute the model matrix and call the
`fit`

methods directly. The default output table gives AIC, defined as minus twice log
likelihood plus \(2p\) where \(p\) is the rank of the model (the
number of effective parameters). This is only defined up to an
additive constant (like log-likelihoods). For linear Gaussian models
with fixed scale, the constant is chosen to give Mallows' \(C_p\),
\(RSS/scale + 2p - n\). Where \(C_p\) is used,
the column is labelled as `Cp`

rather than `AIC`

. The F tests for the `"glm"`

methods are based on analysis of
deviance tests, so if the dispersion is estimated it is based on the
residual deviance, unlike the F tests of `anova.glm`

.

##### Value

An object of class `"anova"`

summarizing the differences in fit
between the models.

##### Note

These are not fully equivalent to the functions in S. There is no
`keep`

argument, and the methods used are not quite so
computationally efficient. Their authors' definitions of Mallows' \(C_p\) and Akaike's AIC
are used, not those of the authors of the models chapter of S.

##### Warning

The model fitting must apply the models to the same dataset. Most
methods will attempt to use a subset of the data with no missing
values for any of the variables if `na.action = na.omit`

, but
this may give biased results. Only use these functions with data
containing missing values with great care. The default methods make calls to the function `nobs`

to
check that the number of observations involved in the fitting process
remained unchanged.

##### References

Chambers, J. M. (1992)
*Linear models.*
Chapter 4 of *Statistical Models in S*
eds J. M. Chambers and T. J. Hastie, Wadsworth & Brooks/Cole.

##### See Also

`step`

, `aov`

, `lm`

,
`extractAIC`

, `anova`

##### Examples

`library(stats)`

```
require(graphics); require(utils)
## following example(swiss)
lm1 <- lm(Fertility ~ ., data = swiss)
add1(lm1, ~ I(Education^2) + .^2)
drop1(lm1, test = "F") # So called 'type II' anova
## following example(glm)
drop1(glm.D93, test = "Chisq")
drop1(glm.D93, test = "F")
add1(glm.D93, scope = ~outcome*treatment, test = "Rao") ## Pearson Chi-square
```

*Documentation reproduced from package stats, version 3.3.3, License: Part of R 3.3.3*