# Which threshold should I use for GVIF1/(2⋅df)? (Variance Inflation Factor)

I'm using the mtcars dataset in R, I used the car packages to estimate the VIF, but since I have factor variables I got the vif table with GVIF and GVIF1/(2⋅df) values, in another question Which variance inflation factor should I be using: $\text{GVIF}$ or $\text{GVIF}^{1/(2\cdot\text{df})}$?, John Fox, co-author of https://www.tandfonline.com/doi/abs/10.1080/01621459.1992.10475190#.U2jkTFdMzTo, mentioned that they recommend using GVIF^(1/(2*Df)), but I don't know if I should use the rule of thumb of <5 with the standard VIF or I should use another number.

This is my code:

mtcars2 <- within(mtcars, {
vs <- factor(vs, labels = c("V", "S"))
am <- factor(am, labels = c("Automatic", "Manual"))
cyl  <- ordered(cyl)
gear <- ordered(gear)
carb <- ordered(carb)
})

mtcars2$$loghp <- log(mtcars2$$hp)

mtcars2 <- mtcars2 %>%
dplyr::mutate(cylnum = as.numeric(mtcars2\$cyl))%>%
dplyr::mutate(cylcat = cut(cylnum, breaks = c(0, 1, 2, 3),
labels = c("Cyl_4", "Cyl_6", "Cyl_8")))

mtcars2_lm <- mtcars2[, c(1,2,3,5,6,7,8,9,10,11,12)]
model1 <- lm(mpg ~., data = mtcars2_lm)
vif(model1)

GVIF Df GVIF^(1/(2*Df))
cyl 98.027045 2 3.146563
disp 57.217057 1 7.564196
drat 7.105793 1 2.665669
wt 23.490085 1 4.846657
qsec 10.731794 1 3.275942
vs 7.354487 1 2.711916
am 9.936800 1 3.152269
gear 50.681013 2 2.668157
carb 244.371502 5 1.733026
loghp 14.626620 1 3.824476
• Welcome to Cross Validated! Threshold for what?
– Dave
Commented Jan 10, 2022 at 18:01
• For deciding which variables I should delete from my model, I have read that the rule of thumb for continuous variables is 5, so you keep all variables that have a <5 value in its vif score. Commented Jan 10, 2022 at 19:40
• Why do you want to delete variables from your model?
– Dave
Commented Jan 10, 2022 at 19:44
• To prevent the multicollinearity problem Commented Jan 10, 2022 at 19:53
• Also keep in mind that, yes, you might decrease your variance by getting stable coefficient estimates, but that could be at the expense of biasing your model to discount a predictor that does matter, perhaps so much bias that the decrease in variance is not worth the increase in bias.
– Dave
Commented Jan 10, 2022 at 20:06