two questions - understanding auto knots feature or knots in general and hill curve transformations

[jmp1989]

Hill Curve Transformations:

Question #1.  

help = analyzer.Analyzer(mmm)
help_df = help.hill_curves().query("channel_type=='media' and distribution =='posterior' ")
px.line(help_df, x='media_units', y='mean', color='channel')

How can I take this which is the hill curves and have it translated into a more communicable output? Or am I misunderstanding this entirely. On the x axis here I have media_units from 0-10 and the 'mean' from 0-0.8. It appears that the data is scaled or transformed in some way, I'm guessing by population. How can I just get the 'real' values here? For example in the dummy dataset the spends per day are upwards of 1-15k per day and the conversions target is maybe 1mil++
How can I see on that scale.

enable_aks & knots:

How can I properly or systematically iterate on knots? It appears that this is extremely important when it comes to the model. I don't know how to properly think about if a knot is every 4 weeks in the data or 6 or 26. It seems the way I go about it is just testing over and over... but again I don't know if this makes sense or if there is a smarter way to go about doing this.

For example, do I place knots before or after or in the middle of some sort of spike or dip?

[cpulavarthi]

Hello @jmp1989,

Thank you for contacting us!

Question 1:

• Media units are scaled according to the definition on this documentation page. For example, for paid media, media units are first population scaled and then scaled by its population-scaled median.
• The Hill saturation curve measures the diminishing marginal returns of media spending, as explained on this documentation page. Note, from the formula of Hill function, that the Hill function always returns a value between 0 and 1.
• On a side note, Meridian provides a plotting function for Hill curve; see plot_hill_curves().
• Note also that, you could decide on whether to use media impressions or media spending as your media units. Based on your choice, the x-axis for the Hill curve will show the range of the scaled values of these media units.
• If you are interested in how media spending changes with incremental outcome (for example, you mentioned conversion as the outcome), you want to look at response curve instead. Meridian also offers a plotting function for response curve; see plot_response_curves.

Question 2:

• Meridian offers automatic knot selection (AKS) which can be enabled by setting enable_aks = True in ModelSpec, which could be a good starting point. I would recommend reading the documentation page on how to fully utilize the AKS feature.
• In particular, once AKS is enabled in ModelSpec, you can retrieve the list of knot locations that Meridian selected for inspection and to make further adjustments.
• The linked documentation page also has many helpful pointers on considering the bias-variance trade-off regarding placement of knots. For example, you might prefer to add knots during periods -- before, at and after a dip or spike -- where you prefer low bias in the estimates (e.g., a holiday season), if those time points weren't already selected by the AKS algorithm.

Do reach out if you have any further questions regarding this.

Google Meridian Support Team