Confusion with infinite VIF confidence intervals

[jmgirard]

While teaching with easystats, I am finding many students are getting confused and misled by the visualization of infinite confidence intervals around VIF. Quite a few every semester write up something like, "given the arrows extending above 10, multicollinearity is indicated." Could the infinite ones just be hidden?

library(easystats)
#> # Attaching packages: easystats 0.7.4
#> ✔ bayestestR  0.16.0   ✔ correlation 0.8.7 
#> ✔ datawizard  1.1.0    ✔ effectsize  1.0.0 
#> ✔ insight     1.3.0    ✔ modelbased  0.11.0
#> ✔ performance 0.14.0   ✔ parameters  0.26.0
#> ✔ report      0.6.1    ✔ see         0.11.0

Working Well

fit <- lm(body_mass ~ 1 + sex + bill_len + bill_dep, data = penguins)
(cc <- check_collinearity(fit))
#> # Check for Multicollinearity
#> 
#> Low Correlation
#> 
#>      Term  VIF   VIF 95% CI adj. VIF Tolerance Tolerance 95% CI
#>       sex 1.50 [1.33, 1.76]     1.22      0.67     [0.57, 0.75]
#>  bill_len 1.36 [1.22, 1.60]     1.17      0.73     [0.63, 0.82]
#>  bill_dep 1.40 [1.25, 1.64]     1.18      0.72     [0.61, 0.80]
plot(cc)

Confusing to Students

fit2 <- lm(body_mass ~ 1 + sex + year, data = penguins)
(cc2 <- check_collinearity(fit2))
#> # Check for Multicollinearity
#> 
#> Low Correlation
#> 
#>  Term  VIF  VIF 95% CI adj. VIF Tolerance Tolerance 95% CI
#>   sex 1.00 [1.00, Inf]     1.00      1.00     [0.00, 1.00]
#>  year 1.00 [1.00, Inf]     1.00      1.00     [0.00, 1.00]
plot(cc2)

^{Created on 2025-05-23 with reprex v2.1.1}

[bwiernik]

Is omitting improper CIs really better though? I'd fear that would lead to misinterpreting the 1 VIF point estimate as indicating no collinearity, when really the interpretation should be "the CI says we don't have enough data here to interpret this". That seems like it's an important lesson to learn, even if it's tricky.

[jmgirard]

I think part of the problem is that the bottom of the circles are cut off, so they are looking for dots and seeing half-dots and arrows. Even if we keep the improper CIs, I think we need to work on how this gets presented (graphically and in the subtitle and in the documentation).

[bwiernik]

One option would be to add an annotation to the graph saying "Infinite values in confidence interval. Data may not be informative regarding multicollinearity. Interpret VIF results cautiously."

[jmgirard]

Sure. Or even a warning message with interpretation guidance that appears before/after the figure in console.