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I have been seeing a lot of multiple regression models that have an adstock term. This term is a decay function of media. The idea is that when media is turned off, there is a decay in its effect that may last up to 2 weeks!

I am skeptical of adstock. I think that when marketing mix models are solely multiple regression models they ignore autocorrelation and the effect that they perceive as adstock is mostly autocorrelation.

Further, from Rob Hyndman's Forecasting Book he states that

Behavioural theory tells us that intentions predict behaviour if the intentions are measured just before the behaviour.

Therefore the idea that purchase-intent is still lingering 2 weeks after seeing a 15 sec commercial is suspect.

Are there any papers addressing adstock in the presence of autocorrelation?

Further Adstock Reading:

  1. Related Thread

  2. Example Of Calculating Adstock In R

  3. Advertising Adstock Paper

  4. Marketing Mix Models In R

Alex
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    Is this a statistics question or is this about economics? – Sextus Empiricus Mar 28 '18 at 20:09
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    Since the main point of argument is that `adstock` is being used in place of autocorrelation I felt like Cross Validated was the best place to ask this question. – Alex Mar 28 '18 at 20:11
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    What causes autocorrelation in the data? I guess this is still more about a physical/economic model, and much less about statistics. The statistics is more about translating a physical model, where all parameters are known, into a statistical model where we wish to use data, with random aspects, to estimate parameters of the physical model. – Sextus Empiricus Mar 28 '18 at 20:15
  • Autocorrelation is a phenomenon of time-series data. This is true even of [random walks](https://en.wikipedia.org/wiki/Random_walk) Also see this [thread](https://stats.stackexchange.com/questions/181167/what-is-the-autocorrelation-for-a-random-walk). When data is in a time-series it is useful to assume that the observations are no longer identically distributed. – Alex Mar 28 '18 at 20:18
  • I *know* the phenomenon, but you would have to state *what causes* this phenomenon for this particular time-series data. – Sextus Empiricus Mar 28 '18 at 20:19
  • Oh, I see what you are saying. I am not an expert in forecasting. I do not know what causes autocorrelation, but I think that stating `adstock` is the cause would be filling the gap with something that does not necessarily have to be true. – Alex Mar 28 '18 at 20:25
  • I am confused about your question now. Apparently there is a phenomenon: when advertising stops then the intent to buy/or actual buying behavior declines. 1) Are you arguing against the observation of the *phenomenon* that this does not have a half life of two weeks? Or that it does not exist at all. 2) Or are you arguing against the *used principles in the underlying mechanistic model*, that this is not some process in which some parameter has an exponential decay, instead it is a process due to some different principle that causes autocorrelation (which actually could still be see as decay)? – Sextus Empiricus Mar 29 '18 at 09:05
  • @MartijnWeterings Great clarifying question. I am asking about **2**. This is why I wonder if `adstock` is a myth. We observe some exponential decay, but to attribute it to a lag effect of media, maybe giving media too much credit, but maybe I am wrong and the decay that we observed is 100% due to the effect of media tailing off. I really don't know. Hence my ask for papers debunking `adstock` --- if they exist --- and my hypothesis that maybe what we observe is a process due to some different principle that causes autocorrelation. – Alex Mar 29 '18 at 12:18
  • Could it be *both*? Both adstock (Is this the observed phenomenon or the mechanistic explanation of decay? I am not familiar with this) and something else (e.g. people that bought something might buy it again some other time, although this decays over time without new stimulation) might be present. Your ideas about something else being present as well, might not necessarily debunk adstock, and only make it less relevant. Also the point of your argument is not clear. As @Aksakal wrote, industry doesn't care much (where it comes from), as long as it works. **Now, I return to my 1st comment** – Sextus Empiricus Mar 29 '18 at 12:29

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I don't understand your argument. Would you say that the moment the ad is off its effect is completely erased instantaneously? That probably is not a reasonable assumption. So, some kind of an temporal decay of ad's effect sounds very reasonable to me.

In physics of radioactivity there's a very similar half-life concept: it's time when the half of nuclei are gone. For instance, uranium 238 has 4.5 mln years when half of them are gone. The same for Cesium 137 is 30 years and Polonium 214 is less than a millisecond.

My point is that having adstock or similar decay variable doesn't contradict your intuition. Suppose you think the ad's effect is gone in a day, then set its half life to one day or one hour, whatever fits your data. It doesn't have to be two weeks for every ad, each ad may/should have its own half life.

I agree with your observation that marketing mix models tend to be cross sectional regression models. I'm not sure why. You can't do time series on them, so more advanced analysis must have to be longitudinal models, such as mixed effects. I believe that ideally they should account for autocorrelation, but it's very difficult.

Aksakal
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  • Thanks! I would argue that radio active half-life is very much a causal process. In media mix models the outcome is sales and the input is media. I think that the phenomena of customer behavior and radio active decay are on different realms of causality. – Alex Mar 28 '18 at 19:50
  • Ok, then set the half life to one or two days. Better yet try to measure the half life, maybe some kind of intervention study or a direct experiment (A/B?) could be set up – Aksakal Mar 28 '18 at 19:52
  • Yes, I agree with you, a sound experimental design would help us discover/quantify the effect of half-life. I have no issue with that. My issue is that adstock is not attributed in this manner in practice. – Alex Mar 28 '18 at 20:01
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    @Alex, the reason is because nobody really validates ad mix models. Nobody opens their models and checks the assumptions, otherwise they'd be asked why they set adstock to 2 weeks half-life and they'd have to defend the assumption. This is not the case in the industry, ad people are left alone. The clients only look at very aggregated results, and try to judge whether the campaign is working based on that. There's no detailed analysis and validation of models – Aksakal Mar 28 '18 at 20:20
  • What do you mean when you say, "You can't do time series on them..."? I have had some limited success with [Dynamic Regression] (https://otexts.org/fpp2/dynamic.html). – Alex Mar 28 '18 at 20:38
  • You can't run vector autoregression (VAR) like models on millions of customers. I mean in practical sense you have to resort to mixed effect type of longitudinal models, or end up aggregating to large groups etc. In any case straight ARIMA type of analysis on account level is not feasible – Aksakal Mar 28 '18 at 20:41
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This is just for posterity. I found this where advertising was used to change road safety behavior. In it they considered adstock, but since their estimated equations already implied half life effect they did not see much benefit by including adstock measure.

our estimated equations implicitly incorporate a half life type of effect so there is nothing to be gained by adopting an Adstock measure

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Alex
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