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.

Usage

outlierTest(model, ...)

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

# S3 method for class '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.

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.

Author

John Fox jfox@mcmaster.ca and Sanford Weisberg

Examples

outlierTest(lm(prestige ~ income + education, data=Duncan))
#> No Studentized residuals with Bonferroni p < 0.05
#> Largest |rstudent|:
#>          rstudent unadjusted p-value Bonferroni p
#> minister 3.134519          0.0031772      0.14297