Customer Propensity

Defining Targeting Models

• Customer targeting typically involves three models:

  • Propensity model
  • Time-to-event model
  • Lifetime value model
• These models can be used individually or together
• A propensity model estimates the probability of a customer doing some event
• A time-to-event model estimates the number of days until a customer does some event
• A lifetime value model estimates the value of a customer

• The events in a propensity or time-to-event model include:

  • A candidate responding to an email campaign
  • A customer puchasing a specific product
  • A customer expanding to a new product
  • A customer purchasing additional units of a prduct
  • A customer changing shopping habits
  • A customer churning
• All three of these models can help determine the impact of this event

Defining Look-Alike Modeling

• A look-alike model is one of the main components of a propensity model
• A look-alike model assumes propensity is only the probability of a customer moving from one point on the life-cycle curve to another

• A look-alike model consists of the following components:

  • A response variable

    • E.g. did the customer purchase this product for the first time
    • E.g. did the customer churn
    • etc.

  • Customer profile predictors

    • E.g. income
    • E.g. gender
    • etc.

Describing a Look-Alike Model

• As a result, a look-alike model estimates the propensity of a customer using profiles of consumers who exhibited similar behavior in the past
• For example, let's say we're training a model to predict the propensity of buying a product for the first time
• Then, we can also train the model using profiles of customers who stopped buying a product for a while and then started buying it again

• The following are examples of predictors within a customer profile:

  • Household income
  • Household size
  • Behaviorial attributes
  • Email opens
  • Clicks
  • Gender
  • etc.

Preparing a Look-Alike Model

1. Ensure each row represents a single customer consisting of:

   • Some customer profile features
   • A timestamp

2. Organize each row into one of three sequential time frames:

   • An observational period
   • An optional buffer
   • An outcome period

3. Generate a response variable representing the desired event:

   • The observation period is used to generate features
   • The outcome period is used to generate the response variable
   • These two intervals may or may not be separated by a buffer

Describing an Optional Buffer

• The observational and outcome periods may or may not be separated by a buffer
• The buffer can be used to predict events in the relatively distant future
• It is not used for predicting immediate events
• For example, a model that predicts customer churn should probably be trained with the outcome intervals shifted into the future
• In other words, there should be a buffer included
• Since, it would be impractical to predict customers who are likely to churn immediately
• Because, it gives no time to perform any mitigating marketing action

Illustrating a Look-Alike Model

• As an example, suppose we're modeling a propensity to try a new product
• The training set only should include customers who did not buy the product during the observation period
• The same rule is applied for model evaluation
• Implying, a customer who already buys a promoted product is immediately excluded as a non-fit
• Now, suppose our targeting goal is to identify customers with a high propensity to try a dessert

• Let's assume that a targeting system generated a training data set with:

  • $12$ historical customers profiles
  • $5$ features
  • $1$ response representing whether the customer started buying a dessert

• Specifically, the features represent:

  • Bakery Total: The total spending in the bakery during the observation period
  • Dairy Total: The total spending on dairy during the observation period
  • Bakery Weekend: The total spending in the bakery on the weekends during the observation period
  • Dairy Weekend: The total spending on dairy on the weekends during the observation period
  • Credit: Represents either credit or cash
• The following table includes sample data trained on our model:

ID	Bakery Total	Bakery Weekend	Dairy Total	Dairy Weekend	Credit	Response
1	150	10	150	140	1	1
2	210	20	120	110	1	0
3	190	190	210	20	1	1
4	270	250	190	0	1	1
5	180	180	190	10	1	1
6	260	250	230	20	0	1
7	270	30	210	210	1	0
8	150	40	150	50	1	0
9	90	70	120	100	0	0
10	30	0	200	200	1	0
11	190	190	250	10	1	1
12	10	0	30	0	1	0

• For this example, we'll build our model using logistic regression
• The following table includes sample parameters for our model:

Parameters	Estimate
Bakery Total	0.0012
Bakery Weekend	0.0199
Dairy Total	-0.0043
Dairy Weekend	–0.0089
Credit	–0.4015

• The following table includes the final propensity scores for $5$ customers in our test set:

Bakery Total	Bakery Weekend	Dairy Total	Dairy Weekend	Credit	Propensity
10	0	50	50	1	0.26
20	20	200	200	1	0.07
150	20	100	30	1	0.37
250	20	190	30	1	0.31
250	200	190	30	1	0.94
250	200	190	30	0	0.96

Motivating Response Modeling

• A response model is a slight variation of the look-alike model
• Specifically, a response model is a propensity model measuring the impact of a campagin

• Creating a basic look-alike model will give us a basic propensity model

  • On its own, this model estimates the unconditional probability of a certain response $P(\text{R})$

• Including a treatment feature provides a more well-defined propensity model focused on measuring the effects of campaigns

  • Then, this model estimates the conditional probability of the response (or action) given a pilot campaign $P(\text{R} | \text{T})$

• The following are some examples of treatments:

  • Running a campaign
  • Sending targeted emails
  • Etc.
• Meaning, we can measure the propensity of an event (e.g. churn) after some campaign or marketing action
• This is done to measure the impact of a campaign before execution

Describing Response Modeling

• Response modeling usually conducts a pilot campaign

  • A pilot campaign tends to split the campaign group into treated responders and treated non-responders

• Specifically, response modeling includes the following steps:

  • Distributing a promotion initially to a small group of recipients
  • Collecting the responses
  • Creating a classification model that maximizes the difference between treated responders and treated non-responder
  • Calculate the difference between the control group and test group (i.e. uplift)
• This corresponds to a look-alike model trained on a population of treated profiles by using the response indicator as a training label
• This model can be used to execute a full-blown campaign
• Specificially, it can target customers with a high propensity to respond when given the treatment
• In certain cases, the model can be created by using historical data for similar campaigns without running a pilot

Defining a Disadvantage of Response Modeling

• So far, response modeling can target customers who are likely to take an action anyway, even without the treatment

• For example, suppose some customers in the control group were planning on purchasing a product, even before the campaign was run

  • Then, the campaign would look more effective than it actually is
  • And, the control group could likely outperform the test group

• Thus, basic propensity modeling only accounts for treated customers

  • It discards the information about the non-treated ones

Solving the Problem with Response Modeling

• A control group will solve the uplift issue in the pilot campaign
• This group includes randomly selected profiles of targeted and non-targeted customers

• As a result, we should observe four distinguishable groups:

  • Treatment responder: a participant who receives the experimental treatment, whose effect is being studied
  • Treatment non-responder: a participant who receives the experimental treatment, whose effect isn't being studied
  • Control responder: a participant who didn't receive the experimental treatment, whose effect is being studied
  • Control non-responder: a participant who didn't receive the experimental treatment, whose effect isn't being studied
• Now, we can accurately measure the uplift by finding the difference between the response rates in the test and control groups
• Specifically, the uplift becomes $\text{TR} - \text{CR}$

• These two probabilities $P(TR)$ and $P(CR)$ can be estimated either:

  • Using one classification model trained on a union of test and control profiles with a treatment indicated included as a feature
  • Using two separate classification models trained on the test and control groups
• For more information about model design, refer to pages $106 and$107$ of Introduction to Algorithmic Marketing

Describing Notation for Experiments

• As a reminder, a target group refers to the type of people targeted for an experiment

• Our experiment will only capture a sample of the entire target group

  • Here, our target group represents a population

• Any experiment includes a control group and a treatment group

  • Sometimes, a control group is called a placebo group
  • Sometimes, a treatment group is called an experimental group
• A control group refers to the people in an experiment who don't receive a treatment
• A treatment group refers to the people in an experiment who do receive a treatment

References

• Textbook about Algorithmic Marketing