# Deletion Diagnostics

##### Deletion Diagnostics for Linear and Generalized Linear Models

These functions calculate a variety of leave-one-out deletion diagnostics for linear and generalized linear models, including studentized residuals (for outlier detection), hatvalues (for detecting high-leverage observations), and Cook's distances, dfbeta, and dfbetas (for detecting influential observations).

- Keywords
- models, regression

##### Usage

```
rstudent(model, ...)
rstudent.lm(model, infl=influence(model), names=infl$names, ...)
rstudent.glm(model, infl=influence(model), names=infl$names, ...)
hatvalues(model, ...)
hatvalues.lm(model, infl=influence(model), names=infl$names, ...)
cookd(model, ...)
cookd.lm(model, infl=influence(model), sumry=summary(model), names=infl$names, ...)
cookd.glm(model, infl=influence(model), sumry=summary(model), names=infl$names, ...)
dfbeta(model, ...)
dfbeta.lm(model, infl=influence(model), names=infl$names, ...)
dfbetas(model, ...)
dfbetas.lm(model, infl=influence(model), sumry=summary(model), names=infl$names, ...)
influence(model, ...)
influence.lm(model, do.coef=TRUE, ...)
influence.glm(model, do.coef=TRUE, ...)
```

##### Arguments

- model
`lm`

or`glm`

model object.- infl
- optionally, an influence-object precomputed for the
`model`

by`influence`

. - sumry
- optionally, a summary-object precomputed for the
`model`

by`summary`

. - names
- optionally, a vector of observation names.
- do.coef
- compute and return dfbeta values.
- ...
- arguments to be passed down from generic functions to method functions.

##### Details

Basic quantities are computed by `influence.lm`

or `influence.glm`

, which are slightly
modified versions of `lm.influence`

from the base package. Values for generalized linear
models are approximations, as described in Williams (1987) (except that Cook's distances are
scaled as *F* rather than as chi-square values).
Normally, the generic versions of these functions are the ones to be used directly. For
`hatvalues`

, `dfbeta`

, and `dfbetas`

, the method for linear models
also works for generalized linear models.
The following diagnostics are provided:
[object Object],[object Object],[object Object],[object Object],[object Object]

##### Value

`rstudent`

,`hatvalues`

, and`cookd`

return vectors with one entry for each observation;`dfbeta`

and`dfbetas`

return matrices with rows for observations and columns for coefficients.`influence`

returns a list with entries:names observation names. hat hat-values. sigma leave-one-out estimates of linear-model standard error or generalized-linear-model scale. coefficients dfbeta values. wt.res weighted residuals (for a linear model). dev.res deviance residuals (for a generalized linear model). pear.res Pearson residuals (for a generalized linear model).

##### References

Belsley, D. A. and Kuh, E. and Welsch, R. E. (1980)
*Regression Diagnostics.* Wiley.
Cook, R. D. and Weisberg, S. (1984)
*Residuals and Influence in Regression.* Wiley.
Fox, J. (1997)
*Applied Regression, Linear Models, and Related Methods.* Sage.
Williams, D. A. (1987)
Generalized linear model diagnostics using the deviance and single
case deletions. *Applied Statistics* **36**, 181--191.

##### See Also

##### Examples

```
data(Duncan)
attach(Duncan)
mod <- lm(prestige ~ income + education)
qq.plot(rstudent(mod), distribution="t", df=41)
plot(hatvalues(mod))
plot(cookd(mod))
plot(dfbeta(mod)[,2])
plot(dfbetas(mod)[,2])
```

*Documentation reproduced from package car, version 1.0-2, License: GPL version 2 or newer*