Imagine you are a data scientist at a startup that sells custom T-shirts designed by Generative AI. The marketing team approached you and asked you to investigate how various channels – Facebook Ads, Google Ads, email, and organic video (e.g. YouTube) – led to a customer conversion. Now, how would you use statistical analysis to attribute which channel(s) led to customer conversions?

A naive assumption is to calculate the probability of conversion for each conversion P(conversion | Facebook Ads), P(conversion | Google Ads), and such. However, in the real world, prospects don’t behave that way. They interact with a combination of channels before converting. And, this is called multi-touch attribution modeling (MTA). The other dimension you may want to consider is how the user may interact with various pages within the eCommerce website before converting. Your attribution modeling will need to account for that as well.

💡Understanding attribution modeling will help you solve interview and real-life cases that deal with the following problems:

How effective is the current funnel in converting users?
Which channels and/or pages cause friction points for conversion?
How should the marketing budget be allocated across channels to maximize conversion?

For instance, at Meta’s marketing data scientist interview will assess attribution model given that this is a core framework in marketing analytics and modeling. Other companies such as Uber, DoorDash, Figma and such should know how to conduct attribution modeling.

✍️ Case Framework

Let’s follow-up on the example laid out in the introduction. Given that you are a marketing data scientist at an eCommerce startup, how would you determine which touchpoint (channel, page) in the user funnel can be attributed with conversion?

You want to walk through the attribution case with the following procedure👇

Clarify the problem
Scope the data and discuss data preparation
Propose methodology
Discuss business impact

1. Clarify the problem

You can start with the following questions to constrain the problem.

What are all the channels and pages a user can interact with before converting?
What is the granularity of data I have for attribution modeling? Is it user-event data, or is it aggregated?

2. Scope the data and discuss data preparation

Let’s look at the following user activity that tracks all the touchpoint of a user. Whenever a user interacts with any of the marketing displays on YouTube, Google Ads, and such, the event is logged. In addition, their in-app and browser activities are stored as well.

User ID	Email	Timestamp	Event
A	johndoe@email.com	09-22-2023 14:22:33	Facebook Ad
A	johndoe@email.com	09-22-2023 14:22:33	Google Ad
A	johndoe@email.com	09-22-2023 14:22:33	Page Visit A
A	johndoe@email.com	09-23-2023 08:22:33	Page Visit B
A	johndoe@email.com	09-23-2023 14:22:33	Converted
B	jennifer@gmail.com	09-22-2023 14:22:33	Page Visit B
B	jennifer@gmail.com	09-22-2023 14:22:33	Checkout
B	jennifer@gmail.com	09-22-2023 14:22:33	Converted
…	…	…	…

Depending on how you apply attribution modeling, your data preparation method will vary.

3. Propose methodology

Now, let’s look at three different approaches to attribution modeling:

📕 Rule-Based
📘 Logistic Regression
📙 Markov Chain

📕 Approach 1 – Rule-Based Attribution Modeling

This is the simplest approach. You merely compute the attribution weight of a given surface based on fixed assumptions. These are first-click (first touch) attribution, last-click (last touch) attribution, equal weights (linear) attribution, and time decay attribution.

Imagine that a user interacted with various channels in the following sequence before conversion – YouTube → Google Ad → Facebook Ad → Page A → Page B → Conversion. Now what’s the attribution weight applied to each touchpoint?

1. First-Click (First Touch) Attribution:

This model attributes the entire conversion value to the first interaction. YouTube would receive 100% of the credit for the conversion since it is the first touchpoint. While simple and easy to use, this model doesn’t consider the impact of subsequent interactions. It might be best suited for businesses focusing on broad brand awareness and outreach.

2. Last-Click (Last Touch) Attribution:

This model gives all the credit for the conversion to the last interaction. Page B gets 100% of the conversion credit in your example. Although straightforward, it overlooks the contribution of earlier stages in the customer journey, often undervaluing initial awareness and consideration stages.

3. Equal Weights (Linear) Attribution:

Every touchpoint receives equal credit for the conversion. YouTube, Google Ad, Facebook Ad, Email, Page A, and Page B each receive 1/6 (or approximately 16.67%) of the conversion credit. his method acknowledges every touchpoint but does not consider the unique influence of each channel. It’s useful if all interactions are considered equally influential.

4. Time Decay Attribution:

More recent interactions receive more credit than earlier ones. Using a time decay model, Page B would receive the most credit since it’s closest to the conversion, followed by Page A, Email, Facebook Ad, Google Ad, and YouTube. The exact percentage split depends on the decay factor selected. This model acknowledges that closer interactions to conversion are usually more significant but may still undervalue the importance of initial awareness-building touchpoints.

Drawback:

It’s over-simplification of the true weights applied to each display. You don’t have a proper understanding of how the weights should be assigned in a multivariate manner as it’s often done with assumptions about customers’ journey. This could be quantified using machine learning approaches – logistic regression and Markov chain.

📘 Approach 2 – Logistic Regression

Logistic Regression is a statistical method that allows you to examine the relationship between one dependent binary variable and one or more independent variables. In the case of attribution modeling, logistic regression helps to assign conversion probabilities to each touchpoint.

Step-by-Step Demonstration:

Data Preparation:
- Set up your dataset where each row represents an individual customer journey that ends in conversion or non-conversion.
- Encode the channels (YouTube, Google Ad, Facebook Ad, Email, Page A, Page B) as binary variables (1 if interacted, 0 if not).
- The dependent variable will be “Conversion” (1 for conversion, 0 for non-conversion).

Example of Dataset Structure:

YouTube	Google Ad	Facebook Ad	Email	Page A	Page B	Conversion
1	1	1	1	1	1	1
0	1	0	1	1	0	0
1	0	1	1	1	1	1
…	…	…	…	…	…	…

Run Logistic Regression:
- You can use statistical software like R, Python (with libraries such as StatsModels, SciKit-Learn), or SPSS.
- Fit the logistic regression model using the binary channel variables as predictors and Conversion as the outcome variable. The equation is the sum of indicator variables of the predictors in question.
  - Y(conversion) ~ Ind(YouTube) + Ind(Google Ad) + Ind(Facebook Ad) + Ind(Email) + Ind(Page A) + Ind(Page B) + B0
Interpretation:
- Look at the coefficients of the logistic regression output.
- The coefficients represent the log odds of conversion associated with each channel.
- Transform these coefficients into odds ratios to interpret the relative contribution of each channel to conversion. Assess for statistical significance of each predictor. Presume that the significance level is 0.05.

Example of Logistic Regression Output:

| Predictor   | Coefficient | Odds Ratio | P-Value    ||-------------|-------------|------------|------------|| YouTube     | 0.5         | 1.65       | 0.04       || Google Ad   | 0.3         | 1.35       | 0.02       || Facebook Ad | 0.2         | 1.22       | 0.08       || Email       | 0.4         | 1.49       | 0.03       || Page A      | 0.1         | 1.11       | 0.10       || Page B      | 0.6         | 1.82       | 0.03       |

Interpretation:

Coefficient: The log odds of conversion. Positive values mean that the channel positively influences conversion, while negative values mean the opposite.
Odds Ratio: This is the exponentiated coefficient. An odds ratio of 1 means no effect, greater than 1 means a positive effect on conversion, and less than 1 means a negative effect.
P-Value: This is the probability of the observing the effect or more extreme (odds ratio) of a given predictor assuming that the odds ratio is 1.0 (meaning that there is no effect). Typically, if this p-value is less than 0.05, then the predictor is deemed statistically significant.

In the example output:

Page B has the highest positive influence on conversion with an odds ratio of 1.82.
YouTube, Google Ad, Facebook Ad, and Email also positively contribute to conversion but to a lesser extent. However, Facebook Ad is not statistically significant which suggests that the observed effect is questionable. Either there is no effect in conversion, or more data may be required.
Page A has the least influence on conversion with an odds ratio of 1.11, and no statistical significance.

Drawback:

Susceptible to multicollinearity. When you have predictors that are collinear in a regression model, the coefficient estimations become unreliable as the standard errors of the estimates inflate.
Ignores transition property. Two groups of users converted, but one group followed the path which is Google Ad → Facebook Ad → Converted where as the other group followed the path of Facebook Ad → Google Ad → Converted. Both touched Google and Facebook Ad, yet the conversion rate differs. Clearly the sequence of their interaction matters. The logistic regression model ignores this.

📙 Approach 3 – Markov Chain

A Markov Chain Attribution Model allows you to analyze the sequential interaction of channels in a customer’s journey. In this model, each channel represents a state, and transitions between states are modeled probabilistically.

Basics of Markov Chain

Markov chain is composed of state and transition probabilities. The state probability is no more than the probability of a particular display visited (e.g. P(Page A)). The transition probability is the probability of a particular display visited given that another page was displayed (e.g. P(Page B | Email)). Think of conditional probability, except the prior condition is the state that the user was on in the prior step of the user journey.

Step-by-Step Demonstration:

Data Preparation:
- You need a dataset where each row represents a sequence of channels that a user interacted with before conversion. Ensure data is in the form of a list of sequences.
- Example: [‘YouTube’, ‘Google Ad’, ‘Facebook Ad’, ‘Email’, ‘Page A’, ‘Page B’, ‘Conversion’].
Transition Matrix Creation:
- Calculate the transition probabilities between all channels. Count the number of transitions from one channel to another and divide by the total transitions from the initial channel.
- Create a matrix where each cell [i, j] represents the probability of transitioning from channel i to channel j.
Removal Effect Calculation:
- Compute the removal effect of each channel. This means simulating what would happen if a channel were removed from all paths, then measuring the difference in conversion probabilities.
- The removal effect is calculated as (Original Conversion Probability - Conversion Probability without Channel) / Original Conversion Probability.
Attribution Calculation:
- The attribution value of each channel is computed as the sum of removal effects for that channel divided by the sum of removal effects for all channels.

How to Interpret:

Channels with higher attribution values have a more significant impact on driving conversions.
The attribution values derived from the Markov Chain Model can help understand the sequential influence and synergy between different channels.

Example:

Suppose you calculated the removal effects as follows:

| Channel     | Removal Effect ||-------------|----------------|| YouTube     | 0.15           || Google Ad   | 0.20           || Facebook Ad | 0.25           || Email       | 0.10           || Page A      | 0.15           || Page B      | 0.15           |

Then, compute the attribution value by normalizing the removal effects. For YouTube, it would be 0.15 / (0.15 + 0.20 + 0.25 + 0.10 + 0.15 + 0.15) = 0.15 / 1.00 = 15%.
Repeat this for all channels to get the attribution values.

💬 Interview Questions

[Uber] Suppose that Uber wants to increase sign-ups to Uber One, a $9.99 monthly membership that provides 10% ride discounts to riders. How should Uber allocate the marketing budget across various marketing channels (e.g. push notification, in-app banner, social media Ads) that promote Uber One sign-ups?
[Square] Suppose we want to identify friction point on the merchant sign-up funnel, how do we identify where the merchant is dropping off in the funnel when there are up to 7 different pages a prospect may visit before purchasing the Square terminal?

[Marketing] Attribution Modeling

Unlock now by joining.