Kinshuk Jerath, CMU

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Customer-Base Analysis Using Aggregated Data
(Or The Joys of RCSS)

• Kinshuk Jerath, CMU
• Peter S. Fader, Wharton (www.petefader.com)
• Bruce G. S. Hardie, LBS

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Customer-Base Analysis
Track the purchasing of a cohort of customers
and make predictions about their future
purchasing (collectively and individually)
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The Pareto/NBD Model(Schmittlein, Morrison, and
Colombo 1987)

• Transaction Process
• While active, number of transactions made by a
  customer follows a Poisson process with
  transaction rate ?
• Transaction rates are distributed gamma(r,a)
  across the population
• Dropout Process
• Each customer has an unobserved lifetime of
  length t, which is distributed exponential with
  dropout rate µ
• Dropout rates are distributed gamma(s,ß) across
  the population
• Astonishingly good fit and predictive performance

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Tracking Cumulative Repeat Transactions
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Conditional Expectations
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The Pareto/NBD works very well given
individual-level (disaggregate) data.
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Barriers to Disaggregate Data

• Many firms may not (be able to) keep detailed
  individual-level records
• Corporate information silos make data integration
  difficult
• Wariness given high-profile stories on data loss
• Data protection laws (with bans on trans-border
  data flows)
• General weaknesses with the firms information
  systems capabilities
• Anonymizing (and other statistical disclosure
  control methods) costly and potentially
  ineffective

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Repeated Cross-Sectional Summary Data
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Proof of Concept Tuscan Lifestyles
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Tuscan Lifestyles Data
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Proof of Concept Tuscan Lifestyles
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Tuscanizing the Pareto/NBD
Under the Pareto/NBD, for a specific individual,
given ? and µ
For a randomly chosen individual
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Tuscanizing the Pareto/NBD
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Augmenting the Model

• Assume a fraction of customers make exactly one
  extra purchase in the first year

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Model Fit
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Cohort Comparison Heterogeneity
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Future Projections
E(CLV) for lt50 cohort 46 E(CLV) for 50
cohort 89
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Do We Need All Five Years of Data?

• Calibrate the model on years 1-3 only, predict
  for years 4 and 5.

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Customer-Base Analysis Using Repeated
Cross-Sectional Summary (RCSS) Data

• Under more general conditions, what is the
  information loss by aggregating data?
• Under what conditions can a model built using
  aggregated data accurately mimic its
  individual-level counterpart?
• How much aggregated data is required to do this
  job well?

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Forward-looking vs. backward-looking histograms
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Summary of Results

• Using three or more quarters always matches
  disaggregate performance in terms of
• In-sample LL
• Out-of-sample histogram predictions
• This is true both for backwards-looking and
  forward-looking approaches to creating
  histograms
• Validated across extensive simulations and a
  real-world dataset

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Other Desirable Properties

• Just the percentage of total customers in each
  bucket is sufficient dont even need actual
  numbers
• Data can be aperiodic (they just have to be
  repeated)
• Histograms can be of different time lengths,
  e.g.,
• 3-month 6-month 4-month
• Histograms can be missing, e.g.,
• Qtr. 1, , Qtr. 3, Qtr. 4
• Data management/storage benefits

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Which Data Structure Would You (and Your
Customers) Prefer to Use?
or