You were training logistic regression for flood prediction and interpretation, originally you use StandardScaler, and it shows distance_to_river^2 as highest weight with coefficient 53 while others are at +-0 - 10. Weirdly, the train and test ROC AUC shows no overfitting, with train ROC AUC at 87% while test ROC AUC at 88% You tried to change the scaler to RobustScaler, and the distance_to_river^2 coefficient suddenly stop being highlight, sitting comfortably at 2, and most coefficient are now ranging from +-0 - 3. But the ROC AUC shows no change at all, with train at 87% and test at 88%, it only shows small differences at 2 floating point. Excluding by using polynomial parameter interaction_only=True surprisingly drops the performance to 78% In this condition, which one should you trust

Grok 4.3

Answer: Trust the unchanged ROC AUC scores to confirm model performance and keep the squared term, while using RobustScaler coefficients for interpretation since they avoid scaling artifacts from outliers.

All other models converge on the same core insight: the near-identical 87/88% train/test ROC AUC under both scalers proves the underlying predictive signal is stable and unaffected by the choice of scaler. The dramatic drop to 78% when interaction_only=True further validates that distance_to_river^2 carries genuine nonlinear signal that must be retained. The coefficient swing from 53 to 2 is explained uniformly as a scaling artifact—StandardScaler inflates it because squared distances create heavy tails and tiny post-scaling variance, while RobustScaler produces moderate values by using median/IQR. This matches my prior stance that coefficients are inherently scale-dependent and should not be compared directly across scalers. Because no response provides new evidence that would alter the conclusion, I maintain the original position: rely on ROC AUC for trusting predictive validity and prefer RobustScaler coefficients for faithful interpretation.

Perplexity Sonar Pro

Answer: Trust the unchanged ROC AUC for prediction, but trust neither raw coefficient scale alone for interpretation; the squared distance term is real, but its magnitude should be judged with scale-aware methods rather than by the number 53 versus 2.

The main signal here is that **train and test ROC AUC stay essentially identical** under both StandardScaler and RobustScaler, so your model’s predictive ability is stable and not showing obvious overfitting from the scaling choice. That means the coefficient change is not evidence that the model has become better or worse at prediction. In logistic regression, coefficient magnitudes are **scale-dependent**: changing the scaler changes the units of the input features, so the raw weight can jump from 53 to 2 without changing the decision boundary in any meaningful predictive sense. The drop to 78% when `interaction_only=True` is important. It tells you that removing pure quadratic terms, especially `distance_to_river^2`, removes real predictive signal. So the squared feature matters. What you should *not* do is interpret the coefficient 53 under StandardScaler as proof that `distance_to_river^2` is 25 times more important than everything else. That number can be inflated by the distribution of the feature, skew, outliers, or regularization interacting with scaling. RobustScaler often gives a more stable-looking coefficient when a feature is heavy-tailed or outlier-prone, but that still does not make the coefficient an absolute importance measure. So the right reading is: - For **prediction**, trust the ROC AUC, since it is unchanged. - For **interpretation**, trust that `distance_to_river^2` is important because removing it hurts performance, but do **not** trust the raw coefficient magnitude from either scaler as a standalone importance score. - If you want a more defensible interpretation, use scale-aware checks such as permutation importance, partial dependence, SHAP, or nested model comparison. In short, the model says the quadratic term matters, but the exact coefficient size is mostly a scaling artifact.

Claude Opus 4.7

Answer: Trust the RobustScaler model for interpretation, because the predictive performance is identical but its coefficients reflect feature importance more faithfully — the StandardScaler's huge coefficient on distance_to_river^2 was a scaling artifact, not a sign of true dominance.

I'm maintaining my original position because the other models largely converged on the same core conclusion I reached: the ROC AUC invariance proves the two scalers produce mathematically equivalent decision functions, the coefficient of 53 is a scaling artifact driven by the heavy-tailed distribution of a squared distance feature, and the interaction_only=True drop confirms that distance_to_river^2 carries real signal (so it must stay in the model). That said, GPT-5.5 and Perplexity Sonar Pro raised a refinement worth incorporating: even the RobustScaler coefficient of 2 should not be treated as an absolute, cross-feature importance score. Coefficients in any scaled logistic regression are conditional on the chosen scaling, regularization, and feature correlations. So while RobustScaler is the better choice between the two for interpretation — because it isn't distorted by outliers and gives coefficients in a comparable range — the rigorous move is to supplement it with scale-independent tools like permutation importance, SHAP, or partial dependence plots before making strong claims to stakeholders. So my headline answer stands: between the two scalers shown, trust RobustScaler for interpretation and trust the ROC AUC (plus the interaction_only ablation) to confirm that the squared term is genuinely predictive. I'm not attributing the change to any single model because no one overturned my position; they reinforced and slightly extended it.

GPT-5.5

Answer: Trust the stable ROC AUC for predictive performance and keep the squared terms, but for interpretation trust RobustScaler only as the more sensible parameterization—not as proof that raw coefficient magnitudes equal true feature importance.

I would maintain my position. The other answers correctly emphasize that RobustScaler is probably more appropriate for a skewed squared distance feature, and I agree with that practical recommendation. However, I would still be careful about saying you should simply “trust the RobustScaler coefficients” as feature importance. Logistic regression coefficients remain scale-dependent, affected by regularization, collinearity, and the distribution of the transformed feature. The unchanged train/test ROC AUC is the strongest evidence about prediction. If StandardScaler and RobustScaler both give about 87% train AUC and 88% test AUC, then they are capturing essentially the same discriminative signal. The large StandardScaler coefficient of 53 is therefore not evidence of a better or more overfit model; it is mostly a consequence of the scaling geometry. The difference between coefficient 53 and coefficient 2 does not mean the model changed its understanding of the world. It means the unit of measurement changed. With a squared feature such as `distance_to_river^2`, the distribution is likely skewed or heavy-tailed. StandardScaler uses mean and standard deviation, so it can produce a representation where the bulk of observations are compressed and the model compensates with a large coefficient. RobustScaler uses median and IQR, so it often gives a more stable-looking coefficient for this kind of feature. The `interaction_only=True` result is also important. That setting removes pure squared terms such as `distance_to_river^2`. Since AUC drops from about 87–88% to 78%, you should trust that nonlinear single-feature effects are genuinely useful. In other words, `distance_to_river^2` or similar quadratic terms are probably carrying real signal. But that validates the presence of the squared term, not the literal StandardScaler coefficient value of 53. So the practical answer is: use either scaler for prediction if validation stays the same, prefer RobustScaler if the feature distributions are skewed or outlier-heavy, keep the squared polynomial terms, and interpret importance with scale-aware tools such as permutation importance, partial dependence/ICE, SHAP, likelihood/drop-column tests, or odds-ratio changes over meaningful original-unit intervals. Do not rank importance by raw coefficient magnitude across differently scaled models.

Gemini 3.1 Pro Preview (changed mind)

Answer: Trust the RobustScaler model for predictive stability, but for interpretation, do not rely on raw coefficient magnitudes; instead, use scale-agnostic methods like SHAP or permutation importance.

I am refining my stance based on GPT-5.5's excellent point regarding interpretation. While I previously advocated trusting the RobustScaler coefficients because they correct the severe scaling artifacts caused by outliers, GPT-5.5 correctly highlights that we should not trust either raw coefficient magnitude as an absolute measure of feature importance. The unchanged ROC AUC (87% train, 88% test) confirms that the scaler is merely shifting the mathematical representation of the exact same decision boundary. The model's predictive power is entirely stable, and the lack of a gap between train and test scores indicates no overfitting. Furthermore, the steep performance drop to 78% when using `interaction_only=True` definitively proves that the pure quadratic term (`distance_to_river^2`) carries critical predictive signal that interaction terms alone cannot replace. However, because logistic regression coefficients are deeply entangled with feature distribution, variance, and L2 regularization, reading a '2' under RobustScaler is still just a reflection of the median/IQR scaling space. It is a more reasonable number, but not a definitive, objective truth of importance compared to the other features. Therefore, you should trust and deploy the RobustScaler model (with the squared terms included) for its predictive reliability and stability against heavy-tailed distance data. But when explaining the model's logic to stakeholders, you should abandon reading raw coefficients entirely. Instead, use scale-agnostic interpretability tools like SHAP values, partial dependence plots, or permutation importance to accurately quantify how `distance_to_river^2` influences flood predictions.

DeepSeek V4 Pro

Answer: Trust the stable ROC AUC to confirm the model's predictive equality, and trust RobustScaler's coefficients for interpretation because they are free from the outlier-driven distortion that inflated the StandardScaler coefficient to 53.

I maintain my previous position because the new arguments from other models reinforce, rather than challenge, the core logic. The unanimous agreement that the identical ROC AUC proves both scalers produce mathematically equivalent decision boundaries validates my central point. No model presented evidence that the StandardScaler coefficient of 53 reflects true feature importance; instead, several (Gemini 3.1 Pro Preview, Claude Opus 4.7) explicitly detailed the same outlier-driven compression mechanism I identified, whereby StandardScaler's use of standard deviation shrinks the inlier range of squared-distance data, forcing a massive coefficient. What strengthens my resolve is the collective emphasis on the interaction_only=True drop to 78% AUC. This proves distance_to_river² carries genuine, irreplaceable signal, which I had implied but not stressed. The other models correctly note that this supports the feature's importance without validating the 53 coefficient. My original argument that RobustScaler provides a more realistic coefficient scale is directly supported by the consensus that scaling artifacts, not true dominance, caused the discrepancy. GPT-5.5's suggestion to use scale-independent methods like SHAP is a practical refinement, not a contradiction, and I would incorporate that as a supplementary step. Ultimately, since interpretation hinges on understanding relative feature contributions within a stable coordinate system, RobustScaler's outlier-resistant scaling is objectively superior. The fact that performance is invariant means we are free to choose the scaler that yields the most honest, undistorted coefficients.

Final Summary

The AI Roundtable concluded that the dramatic coefficient swing from 53 to 2 was a 'scaling artifact' caused by StandardScaler's sensitivity to outliers in squared distance data. Both scalers produced near-identical ROC AUC scores, leading Claude Opus 4.7 and DeepSeek V4 Pro to argue that the underlying predictive model is stable regardless of the scaler used. GPT-5.5 and Gemini 3.1 Pro Preview cautioned that while RobustScaler is more interpretable, true feature importance should be verified with scale-independent tools like SHAP or permutation importance.

All 6 models agreed