Tuesday, May 22, 2012

CLV Episode 3: Predictive Models

What drives profit?

The previous two sections, Time Series and Segment Migration, address the problem of future profitability through trends and migration.   Predictive Modeling approaches tackle the problem head on.  That is, they use all possible information to predict the profitability figure itself.  This class of techniques requires the most data and has the greatest risk/benefit profile.   It can be very good or be very wrong.   Predictive modeling is excellent for interpolation within the boundaries of a problem, but it can be suspect when trying to extrapolate to areas – like the future – where it hasn’t seen any data. 

All the ideas presented here look like the following:

where the x's are the different variables used and 'B' is their respective contribution to profit 'y'.

These approaches can be applied to individual customers, segments or across the enter customer database depending on objectives and business needs.

Direct Estimation
The easiest method to imagine is to predict profitability directly from a combination of factors – customer characteristics, behavior, market conditions, etc.   This is an extension of the Time Series model shown in the first chapter.

Since we’re dealing with time series, a subset of variables should be the consumer’s previous behavior and profitability.  It is common to see ‘lagged profit’, ‘lagged growth in profit’ or ‘lagged transactions’ in such a model.    Future profit is simply a recursive set of estimates each one period further in the future using the last period’s estimates.   

This approach works given sufficient history of profitability data.  How far in the future one can predict is often a function of how far back one can go to create the baseline trend.
Drivers First
Profit is often an outcome of a distinct set of behaviors and characteristics.  Thus, it may make more sense to estimate those factors first and then derive profitability from them.   This is particularly true if product margins and the cost to serve vary substantially over customer segments and product lines.

Profit only exists if a consumer is still a customer.  So, if retention or churn is an issue then focusing on the probability of future purchasing makes sense as a first step.   In this scenario, factors like cross-buying might help since it is often assumed that the more products a customer buys, the more loyal they are.  

An issue with driver estimation is that one model begets another.   For instance, to use cross-buying we need to estimate not only the likelihood of doing so but its relationship to overall profitability.  For instance, it is known that consumers with high customer service costs; heavy promotion usage and a history of revenue reversal actually are more unprofitable the more they buy.

This approach works when profitability varies greatly by things the business can influence.  The challenge then becomes one of estimating all the inputs in the future and keeping those relationships straight.

Marketing Influence
A special extension of the driver estimation procedure is to explicitly model the impact of marketing on the propensity to purchase in the first place.  Whether this is a marketing mix model approach or an assessment of direct contact is a function of the kind of business involved.

This approach fits scenarios with the following logic:

•    Marketing is allocated to people deemed worthy of investment; i.e. it isn’t random.
•    Marketing directly impacts the probability of a purchase
•    Profitability is a function of purchasing and level of marketing conducted

These statements imply that three separate models are required using transaction and marketing contact information.  Each builds on the previous one by using one set of predictions as inputs to the next model.  

This approach is the most theoretically sound and directly accounts for marketing activity. On the flip side it has substantial data and analytic requirements to implement. It has been shown to do a better job than some of the time series suggestions. 

Dealing with Uncertainty
Usually in predictive modeling we’re interested in interpretation rather than estimation.  As a result we tend to ignore the little ‘e’ at the end of the equation listed above.   The error term represents variance we can’t explain and is assumed to average out to be zero and not related to anything else in the model.  Thus, it has little value to the business in terms of explaining what’s going on.  

However, in forecasting the future that little e implies that there isn’t one predicted profitability but rather a whole bunch of them that vary in amount depending on the size of the error term.  Plus, if we do use some nested form of models where one set of outputs is used later as inputs it is quite possible that the individual error terms play off one another creating huge swings in profitability. 

So, like the migration suggestions above it is recommended that any predictive model that estimates the future be run thru a number of scenarios that change the error term.  Here’s an example of the distribution of Customer Lifetime Value from a research paper entitled “Will the Frog change into a Prince."

While the most likely lifetime value for this individual customer is around $200,000 the long tail of high values just might influence the marketing investment or customer support decisions.

Summary and Recommendations
Given scarce marketing resources, it makes sense to focus them on the most important or valuable customers.   Targeting customers who will be profitable is probably the most efficient way to spend marketing dollars.   To do so requires the creation of Customer Lifetime Value based on future behavior and potentially marketing investments.

This series covered a wide range of methods from the simple, na├»ve approach of ‘most recent’ to contemporary advances from academics.   Since the future is unknowable sometimes the simplest models work best.  There is no single, best approach – it all depends.

1.    Define the objective, appetite for risk and uses of Customer Lifetime Value
  • Time Series: stable, abrupt changes not expected, direct marketing not in play
  • Segment Migration: different groups exist that behave very differently, marketing influences medium to long term, market structure may change
  • Predictive Modeling: large number of known drivers, one of which is direct marketing contact
2.    Define multiple techniques for estimating and simulating the future and ‘average the results’

And remember: Forecasts are always wrong, what is interesting is why.

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