High Collinearity in Binary Classification: VIF, SHAP, and Interpretation Strategy

You are modeling a binary outcome Y. Two numeric features A and B are highly correlated: corr(A, B) = 0.98. Other features exist but are only weakly correlated with A and B. You fit:

• (i) a logistic regression (GLM), and
• (ii) a gradient-boosted tree model (GBDT).

Answer the following:

1. Variance Inflation Factor (VIF)
   • Compute/estimate the VIF for A and B given corr(A, B) = 0.98 (assume other features add little to R²).
   • Interpret typical VIF/tolerance thresholds that indicate problematic multicollinearity and what that means for logistic regression coefficients.
2. SHAP with near-duplicate features
   • Explain how SHAP values behave when A and B are near-duplicates under interventional vs conditional SHAP formulations.
   • Why can attributions be unstable or split unpredictably across A and B (for both GLM and GBDT)?
3. Defensible interpretation workflow
   • Propose a workflow to interpret such models: e.g., feature clustering and grouped SHAP, permutation importance conditional on the other feature, and re-fitting after removing one of the pair.
   • Describe the diagnostics you expect to see if A and B are redundant.
4. Modeling recommendations and validation
   • Recommend modeling changes (e.g., elastic net for GLM; feature grouping or regularization choices for trees) to handle collinearity.
   • Describe how you would validate that both interpretability and predictive performance remain acceptable.