The extreme case is selected with regard to the cases’ values on an independent variable or the outcome. It is defined by the absolute difference between the case value on the chosen variable and the variable’s mean. For example, for the outcome the extremeness of a case is defined as \(|Y_i-\hat{Y}|\), with \(i\) being the case index. The extreme case is the case with the maximum absolute difference. (see Seawright (2016)) Depending on the research question or substantive interest, one might be interested in the extreme case in the lower or upper range of a variable. Extremeness is then calculated with \(Y_i-\hat{Y}\).
The extreme_on_x() and extreme_on_y() functions take an lm object as input and calculate the extremeness of all cases. For extremeness on an independent variable, one additionally needs to specify the variable of interest as a character. The output is a dataframe and cases are ordered by absolute extremeness in decreasing order. The dataframe also presents the extremeness values that show whether the case is extreme in the lower range of the variable (negative values) or the positive range (positive values).
df <- lm(mpg ~ disp + wt, data = mtcars)
extreme_on_x(df, "wt")
#> mpg disp wt abs. extremeness extremeness
#> Lincoln Continental 10.4 460.0 5.424 2.20675 2.20675
#> Chrysler Imperial 14.7 440.0 5.345 2.12775 2.12775
#> Cadillac Fleetwood 10.4 472.0 5.250 2.03275 2.03275
#> Lotus Europa 30.4 95.1 1.513 1.70425 -1.70425
#> Honda Civic 30.4 75.7 1.615 1.60225 -1.60225
#> Toyota Corolla 33.9 71.1 1.835 1.38225 -1.38225
#> Fiat X1-9 27.3 79.0 1.935 1.28225 -1.28225
#> Porsche 914-2 26.0 120.3 2.140 1.07725 -1.07725
#> Fiat 128 32.4 78.7 2.200 1.01725 -1.01725
#> Datsun 710 22.8 108.0 2.320 0.89725 -0.89725
#> Merc 450SE 16.4 275.8 4.070 0.85275 0.85275
#> Toyota Corona 21.5 120.1 2.465 0.75225 -0.75225
#> Pontiac Firebird 19.2 400.0 3.845 0.62775 0.62775
#> Camaro Z28 13.3 350.0 3.840 0.62275 0.62275
#> Mazda RX4 21.0 160.0 2.620 0.59725 -0.59725
#> Merc 450SLC 15.2 275.8 3.780 0.56275 0.56275
#> Merc 450SL 17.3 275.8 3.730 0.51275 0.51275
#> Ferrari Dino 19.7 145.0 2.770 0.44725 -0.44725
#> Volvo 142E 21.4 121.0 2.780 0.43725 -0.43725
#> Duster 360 14.3 360.0 3.570 0.35275 0.35275
#> Maserati Bora 15.0 301.0 3.570 0.35275 0.35275
#> Mazda RX4 Wag 21.0 160.0 2.875 0.34225 -0.34225
#> Dodge Challenger 15.5 318.0 3.520 0.30275 0.30275
#> Valiant 18.1 225.0 3.460 0.24275 0.24275
#> Hornet Sportabout 18.7 360.0 3.440 0.22275 0.22275
#> Merc 280 19.2 167.6 3.440 0.22275 0.22275
#> Merc 280C 17.8 167.6 3.440 0.22275 0.22275
#> AMC Javelin 15.2 304.0 3.435 0.21775 0.21775
#> Merc 230 22.8 140.8 3.150 0.06725 -0.06725
#> Ford Pantera L 15.8 351.0 3.170 0.04725 -0.04725
#> Merc 240D 24.4 146.7 3.190 0.02725 -0.02725
#> Hornet 4 Drive 21.4 258.0 3.215 0.00225 -0.00225The calculation of extremeness on the outcome only requires an lm object as input.
df <- lm(mpg ~ disp + wt, data = mtcars)
Y_extreme <- extreme_on_y(df)
head(Y_extreme)
#> mpg disp wt abs. extremeness extremeness
#> Toyota Corolla 33.9 71.1 1.835 13.809375 13.809375
#> Fiat 128 32.4 78.7 2.200 12.309375 12.309375
#> Honda Civic 30.4 75.7 1.615 10.309375 10.309375
#> Lotus Europa 30.4 95.1 1.513 10.309375 10.309375
#> Cadillac Fleetwood 10.4 472.0 5.250 9.690625 -9.690625
#> Lincoln Continental 10.4 460.0 5.424 9.690625 -9.690625