Notebook: How to model upper funnel with causal reasoning and PyMC

[cetagostini]

Description

Upper funnel is becoming more and more a topic, and how to model activities which don't fully impact the target or are mediated by different channels is becoming important. Here, I show how to make it following a simple causal approach, which anyone can follow if the DAG is being identified.

Related Issue

• Closes #
• Related to Feature Request: Add support for Demand Generation vs. Demand Capture channel distinction in MMM #1840

Checklist

• Checked that the pre-commit linting/style checks pass. Feel free to comment pre-commit.ci autofix to auto-fix.
• Included tests that prove the fix is effective or that the new feature works
• Added necessary documentation (docstrings and/or example notebooks) using numpydoc format.
• If you are a pro: each commit corresponds to a relevant logical change

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📚 Documentation preview 📚: https://pymc-marketing--1971.org.readthedocs.build/en/1971/

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[juanitorduz]

This looks very exciting @carlosagostini ! I will provide a deep review once is ready 🚀 !

[daniel-saunders-phil]

I'm feeling very old-man-yells-at-cloud but I left reviews on the notebooknb thingy. They have not appear here yet but I hope they do 🤷

Anyway, I have two big picture suggestions:

1. In linear DAGs, you can just calculate the coefficient of x4 on x1 by hand. I think that would provide a clearer target to recover than the full time-series contribution computed through counterfactuals. I see the appeal in non-linear cases but if you can focus on one number, it's much easier to track success (and understand the causes of failure).

Suppose we had a system like:

x3 = 4*x4 + Norm(0,1)
x2 = 2*x3 + Norm(0,1)
x1 = 0.25*x2 + Norm(0,1)

that implies

x2 = 8*x4 + Norm(0,2) + Norm(0,1)
x1 = 2*x4 + Norm(0,0.5) + Norm(0,1) + Norm(0,1)

and you can simplify all the noise terms too:

x1 = 2*x4 + Norm(0,2.5)

2. Try to put a little bit of the theory of the correct way to do earlier in the notebook. If the reader doesn't understand backdoor criteria thinking, I don't know if they would walk away from this notebook understanding why your model works and another doesn't. If they do understand the backdoor criteria, they don't really need the first estimation example to get your point. They can see from the graph alone that putting all variables in the model will give the wrong result. So that reader would just care more about how to code the correct answer. Either way, explain what approach you intend to take and why would make this more digestible (and maybe shorter!)