# How do Causal Directed Acyclic Graphs (DAGs) work in Marketing Mix Modeling:

Correlation vs causation is a huge marketing measurement problem that traditional methods often fail to account for and can lead to biased conclusions and misguided budget allocation.

This is where Directed Acyclic Graphs (DAGs) come into play. DAGs offer a powerful, visual approach to mapping out and clarifying causal relationships to help marketers and econometricians make more informed decisions.

This article will explain what DAGs are, how to build them, and how to apply them in marketing – with a particular example around media spend analysis that we have seen marketing teams struggle with.

## What is a Causal DAG?

In the realm of causal inference, Directed Acyclic Graphs (DAGs) are tools for helping you visualize and understand intricate webs of causal relationships. A DAG, fundamentally, is a graphical representation consisting of nodes (representing variables) and directed edges (arrows indicating causal influence) with the critical constraint that there are no cycles—no variable can indirectly cause itself. This acyclic property ensures clarity in mapping out the direction of causation without the risk of circular reasoning.

But let’s bring to our marketing context: DAGs work as a preliminary step before diving into quantitative analysis. They allow marketers to explicitly state their assumptions about what influences what.

For example, think of a simple model where seasonality affects sunscreen sales. If you draw an arrow from a node labeled “Season” to another labeled “Sales,” you can visually capture this assumption.

This directional arrow shows the assumed causation and makes it clear that changes in the season are expected to influence sales levels.

Without this clarity, running a regression analysis might show a strong correlation between season and sales, but the model alone cannot determine the direction of the relationship. DAGs help bridge this gap by including the marketer’s knowledge in the model and making sure that the directionality of causation is appropriately considered.

DAGs also guard against the risk of “causal salad,” where marketers might include all possible variables in a model without considering their interrelationships. This indiscriminate inclusion can introduce significant bias and lead to incorrect conclusions. With a DAG you can identify mediators—variables that transmit the effect of one variable onto another—and decide how to appropriately include them in the model.

## Practical Marketing Examples of DAGs

For example, imagine you are a marketer trying to evaluate the effectiveness of TV advertising on sales. Naturally, you would include TV spend as a variable in your model. Additionally, you might consider other factors such as seasonality, which also impacts sales. Here, a DAG helps by clearly laying out these relationships: an arrow from “Season” to “Sales” indicates that seasonality affects sales, and an arrow from “TV Spend” to “Sales” shows the direct impact of TV advertising on sales.

A common question we’ve gotten is whether to include web sessions in the model, assuming that higher TV spend increases web traffic, which in turn boosts sales. In this case, the DAG would have arrows from “TV Spend” to “Web Sessions” and from “Web Sessions” to “Sales.” This setup reveals that web sessions are a mediator in the relationship between TV spend and sales.

However, including web sessions directly in the statistical model can lead to under-crediting. If web sessions are included without acknowledging their mediating role, the model might attribute most of the increase in sales to web sessions rather than TV spend. This misattribution occurs because one of the pathways through which TV spend impacts sales—driving web traffic—is captured separately, thus diminishing the apparent effect of TV spend.

To handle this correctly, the DAG provides a visual and conceptual framework that reminds the analyst of the mediating role of web sessions. This understanding allows for a more sophisticated approach, such as modeling the mediating effect explicitly or adjusting the interpretation of the results to account for the indirect pathway.

Ultimately, DAGs help marketers to extract true causal effects from their data. They provide a structured, visual framework to represent and analyze the mechanisms driving marketing outcomes so you can make better-informed decisions.

## Constructing a Causal DAG

Creating a causal DAG is an important step in understanding and mapping out the relationships between variables before diving into quantitative analysis.

### Steps to Create a DAG:

• Identifying Key Variables:
• The first step in constructing a DAG is to identify the key variables relevant to the context. For a marketing model, these could include variables like TV spend, seasonality, sales, etc.
• Establishing Directional Arrows:
• Once the key variables are identified, the next step is to draw arrows that represent the assumed causal relationships between these variables. Following the previous example, if you believe that TV spend increases web sessions and that web sessions increase sales, you would draw an arrow from “TV Spend” to “Web Sessions” and another from “Web Sessions” to “Sales.” These arrows indicate the direction of causality based on your assumptions or established knowledge.

As you think and possibly construct DAGs, it’s important to remember that building a DAG is a qualitative exercise. The focus at this stage is not on the data but on the underlying mechanisms that generate the data. Each arrow in the DAG represents an assumption about how the world works, either based on empirical evidence, marketing science literature, or intuitive understanding.

This qualitative nature is what makes DAGs so powerful. They work as a clear, visual representation of your understanding of the causal relationships in your model and are setting the stage for more robust and accurate quantitative analysis.

## Recap

1. Causal DAGs (Directed Acyclic Graphs) are very useful tools for visualizing and understanding causal relationships in marketing.
2. They help clarify which variables influence others, preventing misattributions and biases in analysis.
3. Constructing a DAG involves identifying key variables and establishing directional arrows to represent causal assumptions.
4. Practical applications, such as analyzing TV spend impact on sales, demonstrate the importance of recognizing mediators.
5. Segmenting audiences within DAGs allows for more accurate and actionable insights into marketing effectiveness for different customer groups.