Interpretation of VIF/Tolerance in glm vs lm

[mattansb]

(Not really a bug
My understanding of VIF/Tolerance was that they reflect the overlap of information between predictors, regardless of their conditional/marginal association with the outcome.

However, this would mean that two models with the same model matrix would have the same VIFs/Tolerances, but this seems not to be the case (below). What am I missunderstanding?

library(performance)
#> Warning: package 'performance' was built under R version 4.2.2

f <- am ~ factor(cyl) + hp + disp

m1 <- lm(f, data = mtcars)
m2 <- glm(f, data = mtcars, family = binomial("logit"))

Shouldn’t these be the same?

check_collinearity(m1)
#> # Check for Multicollinearity
#> 
#> Low Correlation
#> 
#>         Term  VIF    VIF 95% CI Increased SE Tolerance Tolerance 95% CI
#>  factor(cyl) 8.12 [5.00, 13.66]         2.85      0.12     [0.07, 0.20]
#> 
#> Moderate Correlation
#> 
#>  Term  VIF    VIF 95% CI Increased SE Tolerance Tolerance 95% CI
#>    hp 3.52  [2.32, 5.80]         1.88      0.28     [0.17, 0.43]
#>  disp 6.20 [3.88, 10.39]         2.49      0.16     [0.10, 0.26]
check_collinearity(m2)
#> # Check for Multicollinearity
#> 
#> High Correlation
#> 
#>         Term    VIF      VIF 95% CI Increased SE Tolerance Tolerance 95% CI
#>  factor(cyl)  26.61 [15.79,  45.35]         5.16      0.04     [0.02, 0.06]
#>           hp  82.00 [48.11, 140.27]         9.06      0.01     [0.01, 0.02]
#>         disp 167.13 [97.79, 286.15]        12.93  5.98e-03     [0.00, 0.01]

^{Created on 2023-01-16 with reprex v2.0.2}