VIF (Variation Inflation Factor) vs. GVIF (Generalized VIF):

 VIF (Variation Inflation Factor) vs. GVIF (Generalized VIF):

Handling Multicollinearity with Factor Variables
When building regression models, checking multicollinearity is crucial.

For continuous predictors, VIF helps identify multicollinearity. But categorical variables with multiple levels (factors) need special treatment

A factor with k levels is represented by d=k−1 dummy variables. These dummies are inherently correlated because they encode the same categorical feature.
In this case we use the Generalized Variance Inflation Factor (GVIF) — which measures multicollinearity jointly for all dummy variables representing a factor.

When calculating GVIF for a factor variable, we regress all its dummy variables simultaneously on the other predictors in the model
GVIFj​=(1/ (1−Rj^2​​)^d)

Adjusted GVIF=GVIF^(1/(2⋅d))

d = number of dummy variables (degrees of freedom for the factor).
This adjustment scales GVIF to be comparable to standard VIF values.


Key reasons to consider GVIF:
Treating the factor’s dummies jointly prevents misleading interpretations of multicollinearity.
It reflects the true inflation of variance caused by correlation between the factor and other predictors.
Helps in making informed decisions about feature selection and model stability.