Correct the nonlinear effect-heterogeneity examples

[AliFozooni]

Summary

• align the displayed latent-outcome DGP with the code, including the 0.1 threshold and income scaling
• distinguish latent-scale effect modification from conversion-probability CATE
• derive the exact probit CATE induced by the simulated Normal latent model
• replace the universal 50% targeting claim with a small-shift heuristic and the exact finite-shift result
• distinguish the illustrative logistic curve from the probit simulation
• correct the direction and segment labels in the pricing comparison
• compare price increases on a consistent basis and distinguish absolute sales response from price elasticity

Why this matters

Thresholding a latent linear outcome creates nonlinear effect heterogeneity on the observed probability scale. Income does not interact with treatment in the latent model, but it shifts the untreated latent mean and therefore changes the probability-scale CATE through the Normal CDF. The new equations make that mechanism explicit and explain why a treatment policy should focus on the steep region of the response curve, with appropriate caveats for finite shifts and costs.

The pricing example now compares price increases in the same direction. It shows that an absolute response ranking depends on both customer segment and starting price, without calling that raw response a formal elasticity.

Validation

• numerically checked the probit CATE variation and pricing-effect ordering
• built the full Jupyter Book successfully
• inspected the rendered equations
• validated notebook JSON and confirmed that all code, outputs, and execution counts are unchanged

Closes #383
Closes #389
Closes #460
Closes #461