Most typical and most deviant"
In MMRcaseselection: Case Classification and Selection Based on Regression Results

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

library(MMRcaseselection)

One can use four functions to choose four types of cases without classifying all cases as either typical or deviant. The most typical and most deviant cases are proposed by Seawright and Gerring (2008). The most typical case has the smallest residual of all cases. The most deviant case has the largest residual of all cases. The two functions most_typical() and most_deviant() work in the same way and show you the case with its residual. The input into the function is an lm object.

df <- lm(mpg ~ disp + wt, data = mtcars)
most_typical(df)
most_deviant(df)

The most deviant case does not distinguish between cases that have a large negative and a large positive residual. Cases with a negative residual are overpredicted because the predicted outcome is higher than the observed outcome. Cases with a positive residual are underpredicted because the predicted outcome is lower than the observed outcome. It might not matter whether a case is overpredicted or underpredicted because both subtypes of outliers can have the same type of deviance. However, one might be interested in knowing whether a case has a positive or negative residual and what the most overpredicted and underpredicted cases are. This is what the functions most_overpredicted() and most_underpredicted() achieve, each taking an lm object as input.

# largest positive residual
most_underpredicted(df)
# largest negative residual
most_overpredicted(df)

The package does not include functions for plotting the cases. There are multiple, very useful packages such as the olsrr package that can be used for the easy visualization of residuals.