The literature review encompasses several different topics that, when combined, create a holistic proposal for an effective Marketing Mix Model.
To get a holistic picture on Marketing Mix Models, we started by looking at Hierarchical Marketing Mix Models with Sign Constraints, Chen, Hao, et al. (2021), which gave us an overview on the complications of building a MMM. We found that, “first, besides being affected by marketing activities, sales volume is also affected by many non-marketing factors, such as prices, holidays, seasonality, etc.”
We also learned that marketing activities have different responses to others and is something we need to account for. An example where we can see this difference would be looking at a promotional sale vs TV advertising. In addition, when creating a model, we have to take into account carry over effects, i.e. Adstock. Adstock is the lag effect that we see when looking at high level and lower level marketing, where a TV ad might prep a consumer and an Instagram ad leads to the sale. For this, we can take into account the lag by using targeted rating points. Essentially, we are looking at the percentage of the target audience sees our advertisements, Chen, Hao, et al. (2021). We can do this by calculating TRP \[TRP = \frac{I}{A}\] where \(I\) stands for impressions and \(A\) stands for intended target audience. Another important topic discussed was the idea of saturation, the concept that the relationship between spend and revenue has a limit. In an ideal world, the relationship between advdertising spend and revenue would be linear, but that is not the case in our world. As we will see in some later literature, the relationship typically follows an s or a c curve. For saturation, the paper suggests we use a Weibull transformation to find the limits, Chen, Hao, et al. (2021).
In Challenges And Opportunities In Media Mix Modeling, a Google published paper, the article informs on the current methodologies for Marketing Mix Models and discusses challenges and solutions for them. The article warned about bias that comes from targeting certain peeople in advertising. For example, in some of the audiences we use for Meta, we target specific people who have made Samsung purchases in the past. So a model created with this data would not be general but would apply to the audiences that we have selected. Chan, D., & Perry, M. (2017).
To correct for this, we can use the search/audience volumes since, “query volume can be used in a MMM to make the estimate of paid search impact be more causal,” from Chen et al. (2017) and quoted in Chan, D., & Perry, M. (2017). The paper also recommends to test with simulated data as it, “allows for more control of the conditions of the marketing environment, and provides a flexible and inexpensive environment from which to conduct virtual experiments.”
The article also gives us a general regression model. \[y_t = F(x_{t-L+1},...x_t,z_{t-L+1},...z_t;\Phi) \space t=1,...T,\]
Now, we will look at some literature around the penalized models. Penalized models are important for advertising data as there is the potential for collinearity within our data, Assaf, A. George, et al. (2019). Before we do create a penalized model, we first should make sure there is collinearity, we can do this by “The test can be made more formal by” using a Kolmogorov-Smirnov test for testing the equality of the two distributions,” Assaf, A. George, et al. (2019).
We then looked at Machine learning advances for time series forecasting. There have been several advances in penalized models over the years, starting from Ridge Regression to Least Absolute Shrinkage and Selection Operator (LASSO) and Adaptive LASSO to Elastic net, which was proposed as a way to combine the strengths of Ridge Regression and Lasso. Masini, R. P., Medeiros, M. C., & Mendes, E. F. (2023)
When researching MMM, a common method we came across for modelling was Vector Autoregressive Models (VAR Model) for Multivariate Time Series, the eponymous name for our next article. In it Zivot, Eric, and Jiahui Wang (2003), discuss how it is a useful way to forecast multivariate time series data, for which, our model will be looking at. We will look at Months, channels, and Product categories, which all in all will be made easier by utilizing a VAR model. We can combine the power of the penalized models and versatility of the VAR model by running a VAR Estimation with the Adaptive Elastic Net Furman, Yoel. (2014). “Unlike competing methods, this estimator preserves the standard structural-VAR toolkit but at the same time leads to accurate forecasts,” Furman, Yoel. (2014). For this, we can utilize the Elastic Net vector autoregression package found in R.
As mentioned before, advertising data deals with several issues that need to be corrected to build out the best model. We can begin by looking at adstock issues, the best way to resolve adstock issues is to transform the data, and for this we will look at Adstock transformations, Joseph, Joy V. (2006). Since our team deals with lower funnel conversions, we benefit from higher level tactics are performed by other teams. “The usual approach to account for saturation is to transform the advertising variable to a non-linear scale for example log or negative exponential transformations. It is this transformed variable that is used in the sales response models,” Joseph, Joy V. (2006). We can also experiment with some of the other method the author proposes, such as a Simple Decay-Effect Model, Log Decay Model, Negative Exponential Decay Model, or a Logistic (S-Curve) Decay Model.
Another issue for marketers is Endogeneity. Endogeneity is essentially where the estimated effect of a marketing variable on the dependent variable is distorted due to correlation between one or more independent variables. Ebbes, P., Papies, D., van Heerde, H.J. (2022). For example, the price of ice cream could be increased on hotter days that leads to more sales, but if the person modelling wasn’t familiar with this strategy, temperature would become part of the error and the price raises would be associated with higher sales. In our own data, we often add a new channel when launching a product, if this were not known, then it could be assumed that the new channel led other channels to increase sales. We can first test for endogeneity by using the Hausman test after adding in as many exogenous variables as we can with our business knowledge.
After testing, the best way to account for Endogeneity is to experiment with random spend changes, but, since we are not able to experiment with our data, there are two methods we could employ. The first is instrumental variables (IVs), “to address the endogeneity problem, a popular approach is to find one or more additional variables… which correlate with the price variable but not with the unobserved determinants of sales (that are part of the error term),” Ebbes, P., Papies, D., van Heerde, H.J. (2022). In the case of the ice cream vendor, we could add cost as an IV. For Advertising, we can add in a column for estimated audience size each month. The second method is to use the REndo package, which address endogeneity without external instrumental variables. It builds on the work of several papers to address endogeneity, Gui, (2020).
Next we will look at Demographic information around the platforms that we use. For this, we will use With our knowledge of Samsung, we know that we are attracted to Men who are older than 25 the most but are trying to be more familiar with younger people and women. We will only look at the social media we advertise on, so Facebook, Instagram, Snapchat, YouTube, and TikTok.
We can initially see that Facebook actually caters to age groups and more likely to women than men and has the second highest percentage of adults using it. Instagram also favors women, but also favors younger people. Snapchat favors people under 30 and females but only 25% of the population uses it. YouTube sees the highest usage with 81% of the population using it and is fairly split between men and women using it. When looking at how many people use a social media site daily, 70% of people who use Facebook use it daily, 59% use it daily for both Instagram and Snapchat, and 54% of users for YouTube use it daily. “Social Media Fact Sheet.” (2021). For our Search Engine Result Page (SERP) ads, we use Google and Bing, Google makes up 84.69% of all SERP searches, while Bing makes up 8.85%, Bianchi, Tiago. (2023).
Another important factor when looking at Marketing Mix is adding in macroeconomic factors. By adding in external data to our trends we are factoring in exogenous factors that otherwise would have existed as a part of the error. “Companies use this external data to augment their decision-making, better meet customer needs, predict supply and demand, and more,” Brown, Sara. (2021).
For us, it is important to look at the macroeconmic trends that are affecting the country. We will look a the sources of data given public access by the Federal Reserve Econonmic Data website. We will add in the data and test for correlation and if there is any multicollinearity we will prune to the columns that have the most impact on the model. We will begin by adding in Consumer Sentiment as disclosed by the University of Michigan, Real Disposable Personal Income, Average Price of Gasoline, and Inflation, consumer prices for the United States, Wagner, Rich. (2021).
Finally, we will look at some Meta published tools that are created specifically for time series forecasting and MMMs. The interest in using Meta for the MMM is that it is a useful tool to pass off to other teams who might not have the expertise in creating, optimizing, and maintaining a custom made MMM solution. The beauty of Robyn is that it will automatically create all of the transformations for you and even recalculate each month so that model drift is limited. It even has the ability to show you predicted and actual overtime. In a business environment, this is an easy way to create a model, allow for a more junior team member to maintain the model and check in every now and then to make sure the model is still accurate.
We will begin by looking at Nevergrad an open source platform for black-box optimization. Nevergrad is a population control algorithm that fixes a bias found in other population control methods and has proven robust for noisy optimization of continuous variables, Pauline Bennet, Carola Doerr, Antoine Moreau, Jeremy Rapin, Fabien Teytaud, and Olivier Teytaud (2021). Ultimately, it is a tool used to find the optimal model, in Robyn, it is used to find the best model fit, “Analysts Guide to MMM” (2021). For our case, it will also be used for the adstock transformation to find the best hyperparameters.
Next, let’s take a look at Prophet, Meta’s tool for time series forecasting and used for that purpose in Robyn. Prophet is a Meta open source code for forecasting time series data, and has been included in the Robyn code to decompose the time series data into trends, seasonality and holidays. “Analysts Guide to MMM” (2021). It will automatically break our time series data into the components for us. Unlike other time series models, prophet allows us to create a multivariate model and allows for us to easily add in holidays/promotions. “Analysts Guide to MMM” (2021).
Finally, let’s take a look at Robyn, Meta’s ML-powered and semi-automated Marketing Mix Modeling (MMM) open source package. Robyn aims to reduce human bias in the modeling process, esp. by automating modelers decisions like adstocking, saturation, trend & seasonality as well as model validation. Moreover, the budget allocator & calibration enable actionability and causality of the results, Facebookexperimental. (2021). For us, it uses the two tools above as well as runs auto ridge regression in order to regularize multi-collinearity and prevent overfitting.
“Analysts Guide to MMM.” (2021). Robyn, https://facebookexperimental.github.io/Robyn/docs/analysts-guide-to-MMM.
Assaf, A. George, et al. (2019). “Diagnosing and Correcting the Effects of Multicollinearity: Bayesian Implications of Ridge Regression.” Tourism Management, vol. 71, pp. 1–8., https://doi.org/10.1016/j.tourman.2018.09.008.
Bianchi, Tiago. (2023).“Global Search Engine Desktop Market Share 2023.” Statista, 24 Feb. 2023, https://www.statista.com/statistics/216573/worldwide-market-share-of-search-engines/.
Brown, Sara. (2021). “Why External Data Should Be Part of Your Data Strategy.” MIT Sloan, https://mitsloan.mit.edu/ideas-made-to-matter/why-external-data-should-be-part-your-data-strategy.
Chan, D., & Perry, M. (2017). Challenges and opportunities in media mix modeling.
Chen, A., Chan, D., Perry, M., Jin, Y., Sun, Y., Wang, Y. & Koehler, J. (2017). Bias correction for paid search in media mix modeling. Forthcoming on https:// research.google.com.
Chen, Hao, et al. (2021) “Hierarchical Marketing Mix Models with Sign Constraints.” Journal of Applied Statistics, vol. 48, no. 13-15, pp. 2944–2960., https://doi.org/10.1080/02664763.2021.1946020.
Ebbes, P., Papies, D., van Heerde, H.J. (2022). Dealing with Endogeneity: A Nontechnical Guide for Marketing Researchers. In: Homburg, C., Klarmann, M., Vomberg, A. (eds) Handbook of Market Research. Springer, Cham. https://doi.org/10.1007/978-3-319-57413-4_8
Ebbes P, Wedel M, Boeckenholt U, Steerneman A (2005). “Solving and Testing for Regressor- Error (In)Dependence When no Instrumental Variables Are vailable: With New Evidence for the Effect of Education on Income.” Quantitative Marketing and Economics, 3(4), 365–392.
Facebookexperimental. (2021). “Facebookexperimental/Robyn: Robyn Is an Experimental, Automated and Open-Sourced Marketing Mix Modeling (MMM) Package from Facebook Marketing Science. It Uses Various Machine Learning Techniques (Ridge Regression, Multi-Objective Evolutionary Algorithm for Hyperparameter Optimisation, Gradient-Based Optimisation for Budget Allocation Etc.) to Define Media Channel Efficiency and Effectivity, Explore Adstock Rates and Saturation Curves. It’s Built for Granular Datasets with Many Independent Variables and Therefore Especially Suitable for Digital and Direct Response Advertisers with Rich Dataset.” GitHub, https://github.com/facebookexperimental/Robyn.
Furman, Yoel. (2014). “VAR Estimation with the Adaptive Elastic Net.” SSRN Electronic Journal, https://doi.org/10.2139/ssrn.2456510.
Gui, Raluca,(2020). REndo, v2.4.8.
Joseph, Joy V. (2006). “Understanding Advertising Adstock Transformations.” SSRN Electronic Journal, https://doi.org/10.2139/ssrn.924128.
Masini, R. P., Medeiros, M. C., & Mendes, E. F. (2023). Machine learning advances for time series forecasting. J Econ Surv, 37, 76– 111. https://doi.org/10.1111/joes.12429
Pauline Bennet, Carola Doerr, Antoine Moreau, Jeremy Rapin, Fabien Teytaud, and Olivier Teytaud. (2021). Nevergrad: black-box optimization platform. SIGEVOlution 14, 1, 8–15. https://doi.org/10.1145/3460310.3460312
“Social Media Fact Sheet.” (2021). Pew Research Center: Internet, Science & Tech, Pew Research Center, 5 Apr. 2023, https://www.pewresearch.org/internet/fact-sheet/social-media/.
Wagner, Rich. (2021) “Council Post: External Data: The Key to Building Predictive Models That Help Navigate Uncertainty.” Forbes, Forbes Magazine, https://www.forbes.com/sites/forbestechcouncil/2021/09/30/external-data-the-key-to-building-predictive-models-that-help-navigate-uncertainty/?sh=1568640a348f.
Zivot, Eric, and Jiahui Wang. (2003). “Vector Autoregressive Models for Multivariate Time Series.” Modeling Financial Time Series with S-Plus®, pp. 369–413., https://doi.org/10.1007/978-0-387-21763-5_11.