add1 {base} | R Documentation

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

### Description

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.

### Usage

    add1(object, scope, ...)
    add1.default(object, scope, scale = 0, test = c("none", "Chisq"),
                 k = 2, trace = FALSE, ...)
    add1.lm(object, scope, scale = 0, test = c("none", "Chisq", "F"),
            x = NULL, k = 2, ...)
    add1.glm(object, scope, dispersion = 0, x = NULL,
             test = c("none", "Chisq", "F"), k = 2, ...)

    drop1(object, scope, ...)
    drop1.default(object, scope, scale = 0, test = c("none", "Chisq"),
                  k = 2, trace = FALSE, ...)
    drop1.lm(object, scope, scale = 0, all.cols = TRUE,
             test=c("none", "Chisq", "F"),k = 2, ...)
    drop1.glm(object, scope, dispersion = 0, test = c("none", "Chisq", "F"),
              k = 2, ...)

### Arguments

`object` | a fitted model object.
`scope` | a formula giving the terms to be considered for adding or dropping.
`scale, dispersion` | an estimate of the residual mean square to be used in computing Cp. 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 Chisq 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.
`k` | the penalty constant in AIC / Cp.
`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.
`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.

### 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.

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' Cp, RSS/scale + 2p - n. Where Cp is used, the column is labelled as `Cp` rather than `AIC`.

### Value

An object of class `"anova"` summarizing the differences in fit between the models.

### 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, although it is not for the methods for `"lm"` and `"glm"`.

### 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' Cp and Akaike's AIC are used, not those of the authors of the models chapter of S.

### Author(s)

B. D. Ripley

### See Also

`step`, `aov`, `lm`, `extractAIC`.

### Examples

    example(step)#-> swiss
    add1(lm1, ~ I(Education^2) + .^2)
    drop1(lm1, test="F")

    example(glm)
    drop1(glm.D93, test="Chisq")
    drop1(glm.D93, test="F")

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