Population for scaling the KPI in the Geo Model

[uomodellamansarda]

Based on the documentation, when modelling on Geo-level we need to scale the KPI based on the population.
To do that, we need to define the Population on a weekly basis in our input file.

Scaling function: KPI units

If we use the Google data from Reach and Frequency, we will have weekly data with a certain fluctuation, if I use demographic data from Wikipedia, or from other sources, I can have maximum a yearly change.

My questions are:

1. Why is there a need to scale based on the population? It's not very clear to me why is required. I understand the following explanation:

"KPI units are population scaled to put all geos on roughly the same scale. This way model parameters don't need to scale with
population size.

After population scaling, the KPI is scaled to have mean zero and standard deviation one. Centering to mean zero makes it reasonable to choose a prior centered at zero for the intercept terms (knot_values and tau_g). Scaling to standard deviation one puts parameters on a scale such that reasonable default priors can be assigned."

but Impressions and budget usually are already set based on the population or market size by the media planner. I am quite confused here.

2. Can I use reach and frequency population data for one geo, and for another one where I don't have this information use the wikipedia population dataset? _What should I expect in a model where one geo has weekly fluctuation and another one has a yearly fluctuation?

[cpulavarthi]

Hello @uomodellamansarda,

Thank you for contacting us!

One point of clarification is that Meridian requires a single population value for each geo. The population cannot be time varying. If you load data from a CSV file where the population is time varying, then the mean population value of each geo is used.

Question 1

Note that Meridian scales both the KPI and media units by population (see input data).

Scaling the media units by population allows us to use common $ec_i$ parameters for all geos (see model spec). The $ec_i$ parameter represents the half-saturation point of the Hill function, which should scale with the population.

Scaling the KPI by population puts the from the geo-level coefficients ($\beta_{g,i}$) on roughly the same scale so the random effect distribution does not need to scale with the population. Note that the output of the Hill function is a value between 0 and 1, so if we did not sale the KPI by population then the coefficients would need to scale with the population.

Question 2

Reach and frequency data is probably not relevant for selecting the population size.

The population is a geo-level value. It does not vary by media channel or by time period. You can mix and match data sources, but be sure that the scale of each geo's population makes sense relative to the other geos. The overall scale of the population values does not matter. For example, setting the populations to GeoA=10, GeoB=15, GeoC=20 would result in the same model as GeoA=1000, GeoB=1500, GeoC=2000.

A suggestion would be to use a variable that reflects your target market size in each geo, but ultimately you can choose any population values that you think make the model spec fit your data.

Feel free to reach out if you have any further questions regarding this.

Google Meridian Support Team

[uomodellamansarda]

One point of clarification is that Meridian requires a single population value for each geo. The population cannot be time varying. If you load data from a CSV file where the population is time varying, then the mean population value of each geo is used.

We got weekly fluctuation in the population from Reach and Frequency dataset from Google.
We can use an average for the full time period, but if it's true that we need one costant population for the full time window for each geos (p1,p2,...pn, with n the number of geos), how this is possible?
This can be misleading for anyone working with R&F dataset.

[cpulavarthi]

Hello @uomodellamansarda,

Population data can be obtained from any source, but it is recommended to choose a variable that represents the target market size of your particular business. Please be aware that if you use the CsvDataLoader and the population value varies by time period, then the average value for each geo is used.

Hope this answers your queries. Do reach out if you have any further questions.

Google Meridian Support Team

[uomodellamansarda]

Yes it's clear and we are already using the average for the full year.

Indeed it was weird to get a weekly fluctuating dataset from Google MMM Data Platform where Reach and Frequency is extracted.