Feature engineering and preprocessing · insight-1115

Replace two near-duplicate prices with one level and one gap before interpreting a linear model

Situation
Own fare and competitor fare move together, both sit in a linear or logistic model, and their coefficients flip sign between retrains.
Action
Reparameterize as a level (own fare or the pair's mean) and a gap (own minus competitor, or log ratio); confirm predictions are unchanged and check coefficient stability across bootstrap refits.
Reason
A linear reparameterization spans the same space, so ordinary least squares predicts the same, but the coefficients now answer separate questions with much less shared variance.
Boundary
Coefficient-reading work on prices, budgets and capacities that co-move.

Symptom or risk

Opposite-signed, high-variance coefficients make the price effect unreadable even though predictions are fine.

Penalized models, whose penalty is not invariant to reparameterization, and tree models, which ignore the algebra.

Level and gap need clear definitions in the report, and a gap in absolute units can be confusing across markets.

Interpreting the gap as causal when the competitor reacts to the same demand signal.