Hierarchical marketing mix modeling: what it is, how partial pooling works, and when you need it
A hierarchical marketing mix model estimates effects for several markets, regions or product lines in one model and links them, so units with little data borrow strength from the group: partial pooling. The alternatives are one combined model, or a separate model for each unit.
It matters most where some markets or product lines have thin data. A combined model hides differences; separate models can struggle with little history.
Three ways to model many markets
- Complete pooling: one model for all markets; stable, but assumes every market responds the same way.
- No pooling: a model per market; small markets can return unstable results.
- Partial pooling: each market has its own estimates, linked through a shared group-level distribution.
- More data: twenty regions give far more variation than about 150 national weekly observations.
Partial pooling, explained
- Shrinkage: each estimate moves toward the group in proportion to how little its data supports it.
- Illustrative example: two of twelve television regions opened last year; pooled, they start near the other ten.
- Hyperpriors describe the average effect and the spread around it, estimated along with each market's effect.
- Pooling strength is estimated: strong when markets are similar, weak when they differ.
The differences, dimension by dimension
- Thin data: separate models struggle, a combined model hides it, a hierarchical model borrows.
- Local differences: separate models keep them, a combined one loses them, a hierarchical one keeps supported ones.
- Cost: a hierarchical model is harder to specify, fit and diagnose.
- Framework: native to Bayesian inference; frequentist equivalents exist as mixed-effects models.
How much history a channel needs
- Our fleet: 138 advertisers, more than 870 models, each market fitted separately.
- Two years of history: readable about 97% of the time whatever the budget share, 98.7% under 2%.
- So check history before budget; pooling or an experiment adds what is missing.
Where partial pooling can go wrong
- Different markets get pulled toward ones they do not resemble: the result looks stable and is wrong.
- Grouping is a choice: agree it with the people who know the markets.
- Check: compare pooled estimates with separate models, and inspect units moved a long way.
- Warning sign: very strong pooling across markets the business knows differ.
What neither approach fixes
- Not causal: both can mistake a channel that moved with demand for one that drove it.
- No new data: pooling is only as good as the similarity between units.
- Upkeep: a hierarchical model needs skilled maintenance, and fitting time grows with the units.
How to choose
- A few markets, long histories, different behaviour: separate models.
- Many markets or product lines, thin data in several, similar behaviour: a hierarchical model.
- Budget between regions needs per-region estimates; a national split may need one combined model.
- One channel or market short of history: run an experiment on it, whichever structure you use.
- Either way: check history before blaming the budget, and agree the grouping with people who know the markets.
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Moving to a hierarchical structure
- Data preparation is most of the work: the same weeks, channel definitions and outcome in every market.
- Decide the grouping, and why, before fitting anything.
- Compare market by market with the separate models, and keep them running until differences are understood.
Questions
What is a hierarchical mixed effect model?
A model in which each group, such as a market, has its own parameters, linked through a shared distribution. It is how partial pooling is implemented.
Can you provide an example of a hierarchical model?
A retailer modeling television across twelve regions in one model, where new regions borrow from the others until their own history builds up.
Why do small channels come back empty in a marketing mix model?
Usually too little history or too little variation in spend. In our fleet, channels with two years of history read about 97% of the time whatever their budget share.
Is a hierarchical model always better?
No. It helps when units are similar and some have thin data. Otherwise separate models are simpler and can be more accurate.
Does a hierarchical model need Bayesian methods?
Partial pooling is most natural in Bayesian inference, where the group-level distribution acts as a prior. Frequentist mixed-effects models offer a similar structure.