After we introduced you to the world of **Marketing Mix Modeling **in Part 1 of the series of **VidTao Tracking & Attribution **articles, and after we showed you How to do modeling in Part 2, now it's time to move on to Part 3 with Inceptly's data analyst Dobroslav Slijepcevic.

Let's dive in...

### But… Doesn't the effect of advertisements last longer than a day or a week?

Let us imagine… You are sitting in your favorite armchair and watching some great movie on TV, “Avengers: End Game”, for example, and suddenly, the advertising block begins. Maybe you don’t like watching a bunch of ads instead of your favorite movie, but you don’t have a choice 🙂 And, the fist in your face, a new collection of “Avengers” figures is on sale, exclusively in the official Marvel store in your neighborhood at a special price just for one month! You want to buy the action figures, but, unfortunately, your payment day is three weeks away and you don’t have the money to buy them immediately. You are a patient person who doesn’t want to spend your savings and you are waiting.

In the meantime, you have seen the ad ten more times, and finally, at payday, you buy the new collection of Avengers action figures. Your happiness is unmeasurable, but what the marketing manager would need to do to measure the impact of marketing activities on you?

We are human beings, we remember things. So, it’s completely wrong not to incorporate in our models the time period while the ad yet lives in our brains! Of course, the impact of ads is the strongest when we see, read or hear them, but we can also think about them later and they can drive our behavior as customers for weeks after the initial contact with ads. Hence, the question is, *how to include this time period of the delayed impacts of ads in our calculations?*

These are the questions I’ll try to answer in this chapter. In the previous article, I used linear regression to model the impact of each marketing channel on our Imagined Company revenue. But, if you have read carefully, each week’s ad spend had an impact only on revenue achieved in that week. And now, I want to integrate the cases described in the previous two paragraphs into our model. How to do that? The answer is in one single word: **ADSTOCK - **the measure of carry-over and lag effect of marketing activities!

I have no intention of bothering you about who coined the term and about all historical stories, you can easily find these facts somewhere else. I will only guide you on how to include a delayed effect of your marketing activities into your model in the simplest possible way. The process is simple, let us suppose that *40% (or 0.4, which is called ‘adstock rate’) of our advertising activities are carried over from one week to another*. Then, *if I spent $1,000 in the first week*, I expect *the impact of $400 to be carried over to the next week*, and *the impact of $160 to be carried over to the third week*, etc.

“A picture is worth a thousand words”, someone once said, and I have nothing to add but to agree! Suppose we spent $1,000 on marketing activities in a week1, and we spent nothing in the following 11 weeks. *Did our activity in the week1 have an impact on our revenue in the following weeks? *We said that the answer is **YES**, but the impact diminishes and disappears after a few weeks. But, the higher the adstock rate, the delayed impact of our activity in the first week last longer, furthermore, with *the adstock rate of 0.8*, our initial $1,000 had some impact on the customers *even after 12 weeks*, while with *the adstock rate of 50%*, the impact *became negligible after 8 weeks*, and with the *adstock rate of 20%*, the impact *faded away after 4 weeks*!

OK, it looks great, but one thing is not clear. Why would we stop spending on advertising after week one? A more common situation is that we continue to spend on marketing activities. What to do then? Let us suppose that we spent $1,000 on ads every week. How to do adstock transformations in that case?

The procedure is described in the following steps (with the adstock rate of 0.8):

- in the first week, we spent $1,000 and we have nothing to transform.
- In the second week, we spent $1,000 but we have 0.8 $1000=$800 of impact from the prior week, hence, our transformed variable is $1,000+$800=$1,800
- In the third week, we also spent $1,000, but now
*we have 0.8*$1,800=$1,440 from the prior week, hence, our transformed spend is $1,000+$1,440=$2,440 - Repeat the same for each of the weeks from 4 to 12
- For those who are familiar with math, the formula of transformation is:

*A(t)=Spend(t)+adstock_rate A(t-1)*

The t denotes **the ordinal of the time period **(day, week, month…), and A is **adstock**, transformed spend variable.

The tabular view and the appropriate chart are given below:

It is not hard to conclude that the adstock rate transforms our spend series into a new series of higher values. The higher the adstock rate, the higher the new series values are.

Let us consider our simulated dataset again, and try to repeat all steps from the MMM part 2, but this time, with adstock transformations of *Google spend*, *Facebook spend* and *TV spend* with independent adstock rates. **How to guess the real adstock rates for all of the media?** Adstock rates for digital media are usually smaller, about (0.0-0.3), while adstock rates for TV are highest (0.3-0.8). I’ll set the initial adstock rate for Google and Facebook to be 0.15, and 0.50 for TV. We shall see if we need to change these rates and why.

Let us compare the first 10 rows of our variables before and after the transformation:

And, as we can see, transformed variables are generally higher than untransformed spends (except the first row!) Again, the picture(s) tell(s) us more:

As we could expect, the TV variable has changed the most, since its adstock rate is set to be the highest - 50%, and the impact of the first week is spread over the more than 10 next weeks.

### Back on the modeling, again

We transformed our spend variables to include their impact on the following week's revenue. The next step can be multiple linear regression again, but now, we use transformed spends instead of row values. The result is given in the following table:

In comparison with the model with row spends, *R-squared is higher *(0.92), which is good because it is one measure of accuracy. Also, I calculated one more indicator of accuracy - MAPE, which is equal to 3.9% - lower than the prior model. We want lower errors! Also, the baseline is significantly lower, from $4,700 which is reduced to about $1,870. Its contribution is partly attributed to our marketing channels with spending, which is a much more likely situation, there is no sense to assume that advertising impact has to be instantaneous.

In the next table, you can read the distribution of the revenues generated by all variables:

Each of the spend variables increases its effect share in comparison to the prior model, TV even doubled its impact on the revenue (16%), since it has the highest adstock rate! Facebook generated nearly 45% of the total revenue, and Google videos generated 26%. ROI of each spend channel is given by:

which can be shown through the following charts:

Most of our revenue is driven by marketing activities, adstock helped us to estimate the contribution of each channel better! And at the end, we have an actual/predicted chart, where we can see that the new model better explains dips and spikes in our revenue, with a MAPE of only about 4%!

### That’s all folks?

Honestly, no, not even close… Many questions are still open. Among the most important ones are:

- If Facebook ROI is the highest, why then I shouldn’t invest all my money into Facebook ads? My model suggests investing any amount into Facebook ads and I’ll get more than 7 times higher in return.
- Are adstock rates we choose “the real ones”? Is it OK just guess some values, as I did, or there is a better solution?
- Does the constant baseline fit “the real situation”? Or the baseline depends on the general trend in my business and even seasonality?
- How to deal with multicollinearity, what to do when my spend variables are correlated to each other?
- Should I trust my model at all?

In the next chapter, I’ll try to answer the first question, at least. All of the questions require a deep understanding of statistics and machine learning concepts, but one old wise says (attributed to Albert Einstein, but I really doubt he said that):*” If you can't explain it simply, you don't understand it well enough”!*

## What are your YouTube ad questions?

In the meantime though, what questions do YOU have about YouTube ads?

Let us know in the Comments section below, and we’ll make sure to cover your question in an upcoming post.

Have a nice day!

The VidTao Team

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Please keep talking about this, Dobrojan!

Where is part 4?

Hello, Antonio! I work on it, will be announced soon.