Hierarchical Model Implementation Proposal

[wd60622]

Following the hierarchical configurations and media transformation interface (example here), I think hierarchical models can be supported by similar to current MMM class but with a few modifications. Namely,

• make assumptions about the parameter shapes from the media data shape
  • (date, channel) -> (channel)
  • (date, channel, geo) -> (channel, geo)
• Give flexibility to the user to specify the hierarchical parameters of correct shape
  • (channel, geo) can be generated in too many ways

For example, the user can just toggle out hierarchical_lam and independent_lam for a hierarchical vs non-hierarchical model.

from pymc_markerting.prior import Prior
from pymc_marketing.mmm import GeometricAdstock

independent_lam = Prior("Beta", alpha=1, beta=3, dims=("channel", "geo"))
hierarchical_lam = Prior(
    "Beta",
    alpha=Prior("HalfNormal", dims="channel"), 
    beta=Prior("HalfNormal", dims="channel"), 
    dims=("channel", "geo"),
)

priors = {
  "lam": hierarchical_lam,
}
adstock = GeometricAdstock(priors=priors, l_max=...)

with pm.Model(coords=...) as geo_model: 
    # (date, channel, geo) data suggests (channel, geo) parameters
    dims = get_paramter_dims_from_data(data)
    # (date, channel, geo)
    adstocked_data = adstock.apply(data, dims=dims)
    # similar with saturation
    # (date, channel, geo)
    contributions = saturation.apply(adstocked_data, dims=dims)

It would be up to us to pull out the parameters shapes from data shape, do some validation, combine all into model, etc.

[wd60622]

Some questions that I still have are:

• Will control data also have additional dimensions? Will control data be assumed to have the same dimensions of the media?
• Is there a case where dims(Y) $\subset$ dims(media) $\cup$ dims(control)

Note: The way I am building out #679 will work with additional dims. The dimension of the output is just based on the dimensions of the priors which the use would specify