Priors for non-media variables

[priyadarshinirc]

Hi, I wanted to ask how do I set negative priors for a variable that has a negative impact on my KPI (for example price on sales)? I have been setting negative values for gamma_n and xi_n but the results are far from ideal.

[sonriks6]

Hello,

You can play around the meridian.model.prior_distribution.PriorDistribution container and adjust the default distributions for gamma_n (non-media treatments) and (controls) but this will impact all the variables, as my undestanding by default controls are modeled as Normal(0,5) so should account for negative impacts as well.

    gamma_n=tfp.distributions.HalfNormal(scale=2.0, name=constants.GAMMA_N),
    gamma_c=tfp.distributions.Normal(loc=-2.0, scale=5.0, name=constants.GAMMA_C)

[dattatreyam23]

Hi @priyadarshinirc,

Thank you for reaching out to the Google Meridian support team.

First, I want to clarify that Meridian does not estimate a causal effect for control variables. No matter what sign is on the coefficient, it would not be correct to infer that a control variable has a positive or negative impact. The documentation on control variables provides more details.

Second, for non-treatment variables the impact cannot simply be classified as positive or negative. The impact is defined as the difference between 1) expected outcome where non-media treatment is set to historical values and 2) expected outcome under the counterfactual where non-media treatment is set to a baseline value. The baseline value can be specified via the non_media_baseline_values argument of Analyzer.incremental_outcome(). (It is not currently possible to specify the baseline value for the summary output or any method besides Analyzer.incremental_outcome(). The baseline is always set to the minimum historical value for these other methods.)

Now for each geo and time period, if the historical value exceeds the baseline value then a positive coefficient implies a positive impact for that geo and time period. A positive coefficient implies a negative impact if the baseline value is greater than the historical value. The non-media treatment variable's incremental outcome is aggregated over all geos and time periods.

You correctly asserted that gamma_n and xi_n are the parameters that affect the non-media treatment contribution. gamma_n is the coefficient mean parameter and xi_n is the coefficient standard deviation (each geo can have a different coefficient).

• You said that you are setting a prior distribution on xi_n that allows negative values, but you should not do this. The xi_n prior should take only positive values. You could also set the xi_n prior to tfp.distributions.Deterministic(0) to force all geos to share a common coefficient value.

• For gamma_n, you could specify a distribution that takes only positive or only negative values. However, keep in mind that a positive coefficient could imply a positive impact for some geos and a negative impact in others (depending on whether the historical value exceeds the non_media_baseline_values or not).

• You might need to test out a few prior options to see what works best for your data. Most importantly, be sure to assess MCMC convergence by looking at the R-hat statistics. If you specify a negative prior for xi_n, for example, I don't expect that the sampling would converge.

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

Thank you,

Google Meridian Support Team

[gmoosman]

Super interesting.
I have several price variables set to non_media.
Some come out with a positive contribution and others a negative.
How would you interpret thos?

[cpulavarthi]

Hello @gmoosman,

A positive contribution means that the expected outcome under the historical price values is greater than the expected outcome when price is set to its baseline value.

By default the baseline value for each non-media treatment variable it is the minimum observed historical value across all geos and time periods. If you are using the incremental_outcome method, the non_media_baseline_values argument allows you to set a different baseline value.

The contribution has a posterior distribution which reflects statistical uncertainty in the estimates. The contribution may be positive for some posterior draws and negative for others.

For a given posterior draw, the price coefficient may be positive for certain geos and negative for others. Even if the coefficient has the same sign for all geos, the contribution may still be positive for some geos and/or time periods and negative for others, since the contribution depends on the historical price relative to the baseline price.

Information about non-media treatment variables can be found here.

Feel free to reach out for any further queries.

Thank you

Google Meridian Support Team