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Uplift modeling, also known as incremental modeling, true lift modeling, or net-lift modeling is a predictive modeling technique that directly models the incremental impact of a treatment (such as a direct marketing action) on an individual’s behavior. Uplift modeling has applications in customer relationship management for up-sell, cross-sell and retention modeling. It has also been applied to personalized medicine. Unlike the related Differential Prediction concept in psychology, Uplift modeling assumes an active agent.
All of your marketing effort are about Return on Investment (ROI), ultimately, unless you are a non-profit. But, are you maximizing your ROI? There are at least three ways to calculate profit per sale (profit(sale)):
Profit of Product or Service (Margin)
Net Present Value (NPV)
Life Time Value (LTV)
If marketing is your business, you may have heard the term "Uplift" when referring of class of predictive models. Uplift refers to a more common term, “incremental lift”. This lift is based on the difference in the responses from a control group and a treatment group:
R_{treat} – R_{control}
The ROI for a direct mail (DM) campaign, for example is calculated by:
ROI = (N ´ profit(sale) ´ (R(treat) – R(control)) – cost(DM))/cost(DM)
In order to improve ROI, incremental response is required to be maximized, equivalent to Increasing R(treat) and meanwhile Reducing R(control).
Here is the current situation in most marketing organization from a modeler’s eyes. For direct marketing, a contact is delivered through DM channel such as DM, DEM or OBTM. Customers who are most likely to respond or churn will be selected for the targeting. The most popular modeling solutions are:
Ordinary logistic model, built to score customers’ propensities of product acquisition or service activation
Survival model, built to score how likely and when a customer is going to churn
Most often, we name them either Propensity model or Response model, or Churn model
However, a big assumption is made: a Direct Marketing campaign will achieve maximal Incremental Response when a group of the highest scored customers is targeted.
A Propensity/Response model itself is not going to tell marketers which customers are most likely to contribute to the incremental campaign response. An alternative statistical model is needed, targeting the customers whose propensities of response are dramatically driven by “touching” customers with a promotion. There are primarily four types of customers we deal with went planning a marketing campaign, as depicted below.
We want to pay attention to the “Persuadables”, those consumers who will only buy if they receive an offer. What spend marketing dollars on those who are going buy anyway, those who do not want to receive your offer, or those who will not ever consider your offer?
This is something we can accomplish using an Uplift model. Before I do that, however, do not get your hopes up. Uplift models are hard to construct and even harder to maintain—they are not a "cure all" solution to marketing problems.
Uplift modeling uses a randomized scientific control to not only measure the effectiveness of a marketing action but also to build a predictive model that predicts the incremental response to the marketing action. It is a data mining technique that has been applied predominantly in the financial services, telecommunications and retail direct marketing industries to up-sell, cross-sell, churn and retention activities.
This kind of modeling is not for the faint at heart. It is a bold approach that requires an understanding of the underlying data, precision is preparing the response data, tremendous modeler judgment, and adept salesmanship. Uplift modeling does not begin with an experimental design, though that is required. Rather, it begins with raising awareness with the client, progresses through proactive measuring uplift for marketing campaigns as they occur, until at last there is sufficient confidence in our ability to predict uplift.
The uplift of a marketing campaign is usually defined as the difference in response rate between a treated group and a randomized control group. This allows a marketing team to isolate the effect of a marketing action and measure the effectiveness or otherwise of that individual marketing action. Honest marketing teams will only take credit for the incremental effect of their campaign.
The uplift problem can be stated as follow, given the following:
n_{1}+⋯+ n_{U} = n
find a treatment assignment
f: P→J
So that the total return
∑ R_{if(i)} for i=1…N
is maximized, subject to the constraints that the number of cases assigned to treatment j is not to exceed.
n_{j},(j =1,..,U)
Example: Marketing action case
Solution to the maximization problem, can be reached with a sum does not involve f, so maximizing total return is equivalent to maximizing the first term:
∑ (R_{i}_{1}-R_{i}_{2}) over (i∈(f=1))
As for to the solution to the problem when we consider only the responses to treatment 1, to attain the maximum return:
The difference R_{i}_{1}-R_{i}_{2} is called net lift, uplift, incremental response, differential response, etc.
If we consider only the response to treatment 1, and base targeting on a model built out of responses to previous marketing actions, we are not proceeding as if to maximize ∑ R_{if(i)} for i=1…N. Such maximization would not yield the maximum return. We need to consider the return from cases subjected to no marketing action. Now, consider a model with a binary response, e.g., Yes = 1, No = 0. Then the netlift is:
Prob(1)=exp(score_{1} )/(1+exp (score_{1} ) );
Prob(0)=exp(score_{0} )/(1+exp (score_{0} ) );
netlift = Prob(1)–Prob(0),
where Prob(1) is the probability of a response equal to 1, Prob(0) is the probability of a response = 0, score_{1} is the model scores for responses equal to 1, and score_{0} is the model scores for responses equal to 0. The incremental response lift, with all initial vales set to 0, can be obtained using the following pseudo code:
prob1 = exp(score_1)/(1+exp(score_1));
prob0 = exp(score_0)/(1+exp(score_0));
n
etlift = prob1 – prob0;
if treatment flag = 1 then
mail total = mail total + 1;
if response = 1 then
mail response = mail response + 1;
expected netlift mailed = expected netlift mailed + netlift;
expected anyway mailed = expected anyway mailed + prob(0);
expected mail response = expected mail response + prob(1);
end;
else do;
nomail totoal = nomail total + 1;
if response = 1 then nomail
response = nomail response + 1;
end;
The associated probabilities and netlift pseudo code is:
if last pentile;
empirical prob mail = mail response/mail total;
empirical prob nomail = nomail response/nomail total;
empirical netlift = empirical prob mail - empirical prob nomail;
percent gain = 100* empirical netlift/ empirical prob nomail;
empirical expected buyanyway mailed = mail total* empirical prob nomail;
empirical expected netlift = mailresp - empirical expected buyanyway mailed;
The table below shows the details of a campaign showing the number of responses and calculated response rate for a hypothetical marketing campaign. This campaign would be defined as having a response rate uplift of 5%. It has created 50,000 incremental responses (100,000 - 50,000).
Group | Number of Customers | Responses | Response Rate |
Treated | 1,000,000 | 100,000 | 10% |
Control | 1,000,000 | 50,000 | 5% |
Traditional response modeling typically takes a group of treated customers and attempts to build a predictive model that separates the likely responders from the non-responders through the use of one of a number of predictive modeling techniques. Typically this would use decision trees or regression analysis. This model would only use the treated customers to build the model. In contrast uplift modeling uses both the treated and control customers to build a predictive model that focuses on the incremental response. To understand this type of model it is proposed that there is a fundamental segmentation that separates customers into the following groups (Lo, 2002):
The only segment that provides true incremental responses is the Persuadables. Uplift modeling provides a scoring technique that can separate customers into the groups described above. Traditional response modeling often targets the Sure Things being unable to distinguish them from the Persuadables.
The Two-Model approach requires us to build two logistic models as follows:
Logit(P_{test}(response | X, treatment =1)) = a + b*X + g*treatment
Logit(P_{control}(response | X, treatment=0) ) = a + b*X
We then calculate the uplift score by taking difference of two scores
Score = P_{test}(response | X, treatment =1) – P_{control}(response | X, treatment =0)
Advantages
Uses standard logistic regression modeling techniques
Easy to implement and maintain
Disadvantages
Does not fit he target directly (i.e. incremental response)
Introduces modeling errors twice
Sensitive to predictive variable selections and parameter estimations
Build two logistic models
Logit(P(reponse|X) = a + b*X + g*treatment + l* treatment *X
Now we calculate the uplift score by taking difference of two scores
Score = P(response|X,treatment =1) - P(response|X,treatment =0)
Advantages
Uses standard logistic regression modeling techniques
Better robustness comparing to two model approach
Effect modifications due to treatment
Disadvantages
Does not fit the target directly (i.e. Lift)
Increases modeling complexity due to assumptions of Non-linearity
Needs trade-off between significances and sizes of parameter estimations due to turning treatment on/off
Random Forest
Uplift Random Forests estimate personalized treatment effects (a.k.a. uplift) by binary recursive partitioning. The algorithm and split methods are described in Guelman et al. (2013a, 2013b). In short, an ensemble of B trees are grown, each built on a fraction ν of the training data3 (which includes both treatment and control records). The estimated personalized treatment eﬀect is obtained by averaging the predictions of the individual trees in the ensemble.
It is one of the most accurate learning algorithms available. For many data sets, it produces a highly accurate classifier.
The sampling, motivated by Friedman (2002), incorporates randomness as an integral part of the ﬁtting procedure.
Adds an additional layer of randomness, which further reduces the correlation between trees, and hence reduces the variance of the ensemble.
Disadvantages
The main limitation of the Random Forests algorithm is that a large number of trees may make the algorithm slow for real-time prediction.
For data including categorical variables with different number of levels, random forests are biased in favor of those attributes with more levels. Therefore, the variable importance scores from random forest are not reliable for this type of data.
Majority of direct marketing campaigns are based on purchase propensity models, selecting customer email, paper mail or other marketing contact lists based on customers’ probability to make a purchase. Simulation-Educators.com offers training courses in modeling and simulation topics. The following is an example of a of standard purchase propensity model output for a mailing campaign for such courses.
Scoring Rank | Response Rate | Lift |
1 | 28.1% | 3.41 |
2 | 17.3% | 2.10 |
3 | 9.6% | 1.17 |
4 | 8.4% | 1.02 |
5 | 4.8% | 0.58 |
6 | 3.9% | 0.47 |
7 | 3.3% | 0.40 |
8 | 3.4% | 0.41 |
9 | 3.5% | 0.42 |
10 | 0.1% | 0.01 |
Total | 8.2% |
Table 1. Example of standard purchase propensity model output used to generate direct campaign mailing list at Simulation-Educators.com
This purchase propensity model had a ‘nice’ lift (rank’s response rate over total response rate) for the top 4 ranks on the validation data set. Consequently, we would contact customers included in top 4 ranks. After the catalog campaign had been completed, we conducted post analysis of mailing list performance vs. control group. The control group consisted of customers who were not contacted, grouped by the same purchase probability scoring ranks.
Mailing Group | Control Group | ||
Scoring Rank | Response Rate | Response Rate | Incremental Response Rate |
1 | 26.99% | 27.90% | -0.91% |
2 | 20.34% | 20.90% | -0.56% |
3 | 10.70% | 10.04% | 0.66% |
4 | 8.90% | 7.52% | 1.38% |
Total | 16.70% | 16.55% | 0.15% |
Table 2. Campaign Post analysis
As shown the table 2, the top four customer ranks selected by propensity model perform well for both mailing group and control group. However, even though mailing/test group response rate was at decent level – 16.7%, our incremental response rate (mailing group net of control group) for combined top 4 ranks was only 0.15%. With such low incremental response rate, our undertaking would be likely generating a negative ROI. What was the reason that our campaign shown such poor incremental results? The purchase propensity model did its job well and we did send an offer to people who were likely to make a purchase. Apparently, modeling based on expected purchase propensity is not always the right solution for a successful direct marking campaign. Since there was no increase in response rate over control group, we could have been contacting customers who would have bought our product without promotional direct mail. Customers in top ranks of purchase propensity model may not need a nudge or they are buying in response to a contact via other channels. If that is the case, the customers in the lower purchase propensity ranks would be more ‘responsive’ to a marketing contact. We should be predicting incremental impact – additional purchases generated by a campaign, not purchases that would be made without the contact. Our marketing mailing can be substantially more cost efficient if we don’t mail customers who are going to buy anyway. Since customers very rarely use promo codes from catalogs or click on web display ads, it is difficult to identify undecided, swing customer based on the promotion codes or web display click-throughs. Net lift models predict which customer segments are likely to make a purchase ONLY if prompted by a marketing undertaking. Purchasers from mailing group include customers that needed a nudge, however, all purchasers in the holdout/control group did not need our catalog to make their purchasing decision. All purchasers in the control group can be classified as ‘need no contact’. Since we need a model that would separate ‘need contact’ purchasers from ‘no contact’ purchasers, the net lift models look at differences in purchasers in mailing (contact) group versus purchasers from control group. In order to classify our customers into these groups we need mailing group and control group purchases results from similar prior campaigns. If there are no comparable historic undertakings, we have to create a small scale trial before the main rollout.
Segments used in probability decomposition models:
Contacted Group | Control Group | |
Purchasers prompted by contact | A | D |
Purchasers not needing contact | B | E |
Non Purchasers | C | F |
Figure 2. Segments in probability decomposition models
Standard purchase propensity models are only capable of predicting all purchasers (combined segments A and B). The probability decomposition model predicts purchasers segments that need to be contacted (segment A) by leveraging two logistic regression models, as shown in the formula below (Zhong, 2009).
P(A I AUBUC) = | P(AUB I AUBUC) x | (2 - 1/P(AUB I AUBUE)) |
Probability of purchase prompted by contact | Probability of purchase out of contact group | Probability of purchaser being in contact group out of all purchasers |
Scoring Rank | Contact Group Response % | Control Group Response % | Incremental Response Rate |
1 | 18.8% | 12.9% | 5.9% |
2 | 7.8% | 5.4% | 2.4% |
3 | 6.9% | 4.5% | 2.5% |
4 | 4.3% | 3.6% | 0.7% |
5 | 3.9% | 3.5% | 0.4% |
6 | 4.1% | 4.1% | 0.0% |
7 | 3.7% | 4.0% | -0.2% |
8 | 4.7% | 4.1% | 0.6% |
9 | 5.0% | 6.7% | -1.7% |
10 | 11.0% | 15.7% | -4.7% |
Table 3. Post analysis of campaign leveraging probability decomposition model for Simulation-Educators.com
Scoring Ranks 1 thru 6 show positive incremental response rates. The scoring ranks are ordered based on the incremental response rates.
Because uplift modeling focuses on incremental responses only, it provides very strong return on investment cases when applied to traditional demand generation and retention activities. For example, by only targeting the persuadable customers in an outbound marketing campaign, the contact costs and hence the return per unit spend can be dramatically improved (Radcliffe & Surry, 2011).
One of the most effective uses of uplift modeling is in the removal of negative effects from retention campaigns. Both in the telecommunications and financial services industries often retention campaigns can trigger customers to cancel a contract or policy. Uplift modeling allows these customers, the Do Not Disturbs, to be removed from the campaign.
The first appearance of true response modeling appears to be in the work of Radcliffe and Surry (Radcliffe & Surry, 1999). Victor Lo also published on this topic in The True Lift Model (Lo, 2002), and more recently Radcliffe (Radcliffe, Using Control Groups to Target on Predicted Lift: Building and Assessing Uplift Models, 2007). Radcliffe also provides a very useful frequently asked questions (FAQ) section on his web site, Scientific Marketer (Uplift Modelling FAQ, 2007). Similar approaches have been explored in personalized medicine (Cai, Tian, Wong, & Wei, 2009). Uplift modeling is a special case of the older psychology concept of Differential Prediction. In contrast to differential prediction, uplift modeling assumes an active agent, and uses the uplift measure as an optimization metric.
Authored by: Jeffrey Strickland, Ph.D. Jeffrey Strickland, Ph.D., is the Author of Predictive Analytics Using R and a Senior Analytics Scientist with Clarity Solution Group. He has performed predictive modeling, simulation and analysis for the Department of Defense, NASA, the Missile Defense Agency, and the Financial and Insurance Industries for over 20 years. Jeff is a Certified Modeling and Simulation professional (CMSP) and an Associate Systems Engineering Professional (ASEP). He has published nearly 200 blogs on LinkedIn, is also a frequently invited guest speaker and the author of 20 books including:
Connect with Jeffrey Strickland Contact Jeffrey Strickland
Comment
Great to see acknowledgements for Nicholas Radcliffe and Patrick Surry in this paper. The implementation conceived by them (and others as part of a team at Edinburgh University) was implemented in Quadstone, which on acquisition by Portrait Software International Limited was renamed Portrait Miner and Portrait Uplift. The product is still 'out there'. Portrait was acquired by Pitney Bowes in 2010.
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