Feature: Controlled Direct Effect (CDE) helper

Summary

When a model has a mediator (X → M → Y with X → Y), users often want to decompose the total effect into direct and indirect components. For linear Gaussian models, `indirect := a*b` is exact. For non-linear models (Bernoulli, Poisson), the product of coefficients is only approximate — the correct approach is the controlled direct effect: fix the mediator at a value (e.g., its mean) while varying the treatment, then compare to the total effect.

Currently, computing the CDE requires two manual `do()` calls — one setting both the treatment and the mediator, another setting only the treatment — and taking the difference. A convenience method would make this a single call.

Proposed API

# CDE: fix mediator at its mean, vary treatment
model.cde("Y", treatment="X", mediator="M")

# CDE: fix mediator at a specific value
model.cde("Y", treatment="X", mediator="M", mediator_value=0.5)

# Proportion mediated (requires CDE)
model.proportion_mediated("Y", treatment="X", mediator="M")
# → posterior distribution of (total - CDE) / total

Motivation

This pattern appears naturally in applied work:

• SaaS funnels: engagement → activation → conversion (all Bernoulli). What fraction of the engagement effect on conversion is mediated through activation?
• Marketing: spend → brand awareness → sales. How much of the spend effect goes through the brand channel vs. directly?
• Vaccine surrogates: treatment → biomarker → outcome. Is the biomarker a valid surrogate endpoint?

The `saas_funnel.qmd` and `vaccine_surrogates.qmd` examples already demonstrate this workflow manually. A built-in helper would make it ergonomic.

This is identified in the PRD (`prd_v1.md`, §12) as a planned post-v1 convenience feature. It would also be useful in the PyMC Labs causal inference workshop (currently in planning), where Session 7 covers heterogeneous treatment effects and mediation decomposition.

Start with prd_v1.md §12 to understand the planned post-v1 scope, then read saas_funnel.qmd and vaccine_surrogates.qmd for the existing manual do() workflow. Define completion around replacing those repeated calls with the proposed cde() helper and adding proportion_mediated() with the stated posterior calculation.