Interpreting Adstock Decay Curves based on different Time Granularity

[pli-pcln]

Hello, my question is in the title.

I've run models with both weekly and daily aggregations. However, I noticed that regardless of this or the type of decay I'm using (geometric or binomial), the recommended value for the max_lag is still the same (2-10 time periods for geometric, for example).

But when switching between these time granularities (daily vs weekly), the time periods will mean very different things. In a weekly, I'm observing high adstock decays for upper-funnel channels when the max lag is 8 or 12, meaning 8 or 12 weeks. However, when switching to a daily model, the decay seems much smaller for the same channel; even when max lag is set to 14 (days), the same upper funnel channels are now decaying much sooner, between 2 and 7 time periods (days).

How do I know which one of these is "true"? Why should a change in the time granularity affect the interpretation of the decays so dramatically? Or am I misinterpreting this?

[dattatreyam23]

Hi @pli-pcln ,

Thank you for contacting us!

max_lag is based on the time granularity of your dataset. If you have daily data, max_lag = 8 means 8 days. If you have weekly data, max_lag = 8 means 8 weeks.

The value of max_lag dictates how many time periods the media effects are allowed to last, so you should set max_lag based on your knowledge/understanding of the duration of media effects in your context. Hence, if you kept max_lag somewhat similar (e.g., 10-14) while switching from weekly to daily data, you effectively reduced the maximum possible memory of the model from ~3 months (12 weeks) to ~2 weeks (14 days), which might be a probable cause for the same.

You may try adjusting the max_lag argument to change the maximum number of future time periods affected. You could also try using custom alpha_m priors to encourage longer-term effects; an alpha_m prior with more mass closer to 1 will encourage this.Correspodingly, you may inspect the learned decay rates, using plot_adstock_decay() to visually compare the "weekly" curve against the "daily" curve to see if they cover the same absolute amount of time. See here for a detailed discussion on the same.

Hence, to sum up, if you expect long term effects that are not materializing in a model, some combination of the binomial decay curve, modifying the prior on alpha, and changing the max_lag can help. Please see our documentation on Considerations for long term effects for more info.

However, I would like to inform you of an important caveat about setting the max_lag parameter. The typical recommendation for max_lag is between 2 and 10 weeks to balance performance and efficiency. Modeling effects that last much longer than that are generally outside the scope of the standard carryover effect captured by the Adstock function within typical max_lag settings. Meridian's structure, while measuring long-term average effectiveness within the modeling window, is not specifically designed to isolate and quantify distinct "long-term" (e.g., brand-building) effects lasting, say over a year and a half, separate from the standard carryover effect.

Feel free to reach out if you have any questions or suggestions regarding the same.

Thank you,

Google Meridian Support Team

[pli-pcln]

Thanks @dattatreyam23 for your response.

I have set large priors on my awareness campaigns as you suggested and kept these the same between my daily and weekly models but I get very different results so I don't think this is it.

In the weekly case, we typically expect long term effects in the months which is why setting a max_lag value of 8 or 12 was appropriate, and the plots from plot_adstock_decay() showed as much. However, to preserve this in the daily case we would effectively need to multiply max_lag by 7 to keep the same decay. If Meridian is not able to effectively model beyond ~10 time periods for geometric decays, then basically we're saying that a daily granularity will reduce the model's ability to detect longer adstocks beyond a few days. This may be a problem for our awareness campaigns.

Against recommendation, I tried setting a max_lag of this length in my daily model but it did nothing to extend the decay; it merely extended the x-axis, which visually "smushed" the curves to the left side of the charts. So it appears extending the max_lag even beyond what's recommended won't significantly alter the results for my daily model. I may need to switch to a weekly model to get around this but I wasn't expecting the time granularity of the data to have such a big impact on the adstock measurement. If it can change so much depending on the granularity, how can I trust which decay curve is the more accurate for the channel?

I can consider a binomial decay but the significantly heavier weight on later periods runs counter to our understanding for how the decay should look, unless the posterior alphas can remain below 0.5.

[cpulavarthi]

Hi @pli-pcln,

Thanks for the follow up. As you are seeing, Meridian was developed in the context of the most common aggregation level for MMMs, which is weekly data. Because most default settings were selected to support weekly data, switching to an aggregation level that is much finer or coarser than weekly does require some adjustment to the model settings and may produce results different from what you find using the weekly default settings.

As mentioned earlier, some of the changes needed include adjusting max_lag, the alpha_m prior, and possibly some of the other priors as needed. For example, for alpha_m with a daily granularity and geometric decay, to achieve equivalent decay to alpha=0.8 in weekly data after 10 weeks requires an alpha of 0.969 in daily data. To train a daily model to such a high alpha_m value, it may require using a somewhat informative custom prior with a limited support for some [c, 1) - perhaps [0.7, 1) or [0.8, 1). The restricted support should encourage the model to keep alpha_m in that high range.

If you have been using the same alpha_m priors for both weekly and daily data, your results will continue to differ between the two models. Could you share what priors for alpha_m you are using for the two types of models?

Google Meridian Support Team

[pli-pcln]

@cpulavarthi I see, I realize I'm not setting the adstock priors appropriately. I was only adjusting the b value of the Uniform distribution and didn't realize I could set both a and b to bound the priors more tightly. Making a tighter interval seems to help a lot.

It's good to know Meridian was primarily designed around a weekly time aggregation. I wasn't aware of this.

Thanks for the help, we can mark this as resolved.