# outlierTest

##### Bonferroni Outlier Test

Reports the Bonferroni p-values for testing each observation in turn to be a mean-shift outlier, based Studentized residuals in linear (t-tests), generalized linear models (normal tests), and linear mixed models.

- Keywords
- regression, htest

##### Usage

`outlierTest(model, ...)`# S3 method for lm
outlierTest(model, cutoff=0.05, n.max=10, order=TRUE,
labels=names(rstudent), ...)
# S3 method for lmerMod
outlierTest(model, ...)

# S3 method for outlierTest
print(x, digits=5, ...)

##### Arguments

- model
an

`lm`

,`glm`

, or`lmerMod`

model object; the`"lmerMod"`

method calls the`"lm"`

method and can take the same arguments.- cutoff
observations with Bonferroni p-values exceeding

`cutoff`

are not reported, unless no observations are nominated, in which case the one with the largest Studentized residual is reported.- n.max
maximum number of observations to report (default,

`10`

).- order
report Studenized residuals in descending order of magnitude? (default,

`TRUE`

).- labels
an optional vector of observation names.

- ...
arguments passed down to methods functions.

- x
`outlierTest`

object.- digits
number of digits for reported p-values.

##### Details

For a linear model, p-values reported use the t distribution with degrees of
freedom one less than the residual df for the model. For a generalized
linear model, p-values are based on the standard-normal distribution. The Bonferroni
adjustment multiplies the usual two-sided p-value by the number of
observations. The `lm`

method works for `glm`

objects. To show all
of the observations set `cutoff=Inf`

and `n.max=Inf`

.

##### Value

an object of class `outlierTest`

, which is normally just
printed.

##### References

Cook, R. D. and Weisberg, S. (1982)
*Residuals and Influence in Regression.* Chapman and Hall, https://conservancy.umn.edu/handle/11299/37076.

Fox, J. (2016)
*Applied Regression Analysis and Generalized Linear Models*,
Third Edition. Sage.

Fox, J. and Weisberg, S. (2019)
*An R Companion to Applied Regression*, Third Edition, Sage.

Weisberg, S. (2014) *Applied Linear Regression*, Fourth Edition, Wiley.

Williams, D. A. (1987)
Generalized linear model diagnostics using the deviance and single
case deletions. *Applied Statistics* **36**, 181--191.

##### Examples

```
# NOT RUN {
outlierTest(lm(prestige ~ income + education, data=Duncan))
# }
```

*Documentation reproduced from package car, version 3.0-4, License: GPL (>= 2)*