# 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).

##### Usage

```
rstudent(model, ...)
rstudent.lm(model, infl=influence(model))
rstudent.glm(model, infl=influence(model))
hatvalues(model, ...)
hatvalues.lm(model, infl=influence(model))
cookd(model, ...)
cookd.lm(model, infl=influence(model), sumry=summary(model))
cookd.glm(model, infl=influence(model), sumry=summary(model))
dfbeta(model, ...)
dfbeta.lm(model, infl=influence(model))
dfbetas(model, ...)
dfbetas.lm(model, infl=influence(model), sumry=summary(model))
influence(model, ...)
influence.lm(model)
influence.glm(model)
```

##### 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`

. - ...
- 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],{studentized residuals.},[object Object],{observation leverages.},[object Object],{Cook's distance influence measure for observations.},[object Object],{change in each coefficient upon deleting observations.},[object Object],{standardized change in each coefficient for deleting observations.}

##### 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: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.*
[object Object]

`influence.measures`

*Documentation reproduced from package car, version 0.8-1, License: GPL version 2 or newer*