Reply by Claude
Since you’re building an MMM, the fastest path is pymc-marketing, which has a ready-made MMM class rather than making you wire everything up in raw PyMC. A few docs that answer your questions directly:
MMM Example Notebook — end-to-end walkthrough of the whole workflow. Best starting point.
Custom Models with MMM components — covers the adstock and saturation transforms and how to swap between them.
On your specific questions:
Saturation curve — don’t pick by intuition. Fit a couple of candidates (LogisticSaturation is the usual default; MichaelisMenten / HillSaturation are common alternatives) and compare with posterior predictive checks and LOO/WAIC. Let the data and prior knowledge about diminishing returns decide.
Interaction terms — you don’t need the full combinatorial explosion. Standard MMM practice is to start with the additive model (each channel gets its own adstock + saturation, no interactions) and only add an interaction where you have a real business reason to expect one (e.g. TV lifting search response). Testing every combination will overfit and isn’t how MMMs are usually specified.
Start with the example notebook, get a baseline additive model running on your data, then iterate. Happy to help with something more specific once you’ve got that going.
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