incorporating regularity into models of noncontractual customer-firm relationships
DESCRIPTION
Presentation of a newly derived stochastic prediction model for customer lifetime values, which is able to incorporate regularity within the transaction patterns.TRANSCRIPT
MotivationRegularity
Model DevelopmentEmpirical Application
Summary
Incorporating Regularity into Models ofNoncontractual Customer-Firm Relationships
M. Platzer T. Reutterer
Marketing DepartmentVienna University of Economics
and Business Administration
May, 2009
M. Platzer, T. Reutterer Regularity within Purchase Timings
MotivationRegularity
Model DevelopmentEmpirical Application
Summary
Outline
1 Motivation
2 Regularity
3 Model Development
4 Empirical Application
5 Summary
M. Platzer, T. Reutterer Regularity within Purchase Timings
MotivationRegularity
Model DevelopmentEmpirical Application
Summary
A Simple ExampleNoncontractual SettingsStochastic ModelsNBD Assumptions
A Simple Example: Aunt Betty
Aunt Betty buys cookies for her favorite nephews at the end ofevery month at Mr. Baker’s local store. She adheres to thiscustom as long as Mr. Baker can recall back in time.
But recently Mr. Baker noticed that Aunt Betty has not been tohis shop since 35 days!
Mr. Baker immediately concluded that something terrible musthave happened...
M. Platzer, T. Reutterer Regularity within Purchase Timings
MotivationRegularity
Model DevelopmentEmpirical Application
Summary
A Simple ExampleNoncontractual SettingsStochastic ModelsNBD Assumptions
A Simple Example: Aunt Betty
Aunt Betty buys cookies for her favorite nephews at the end ofevery month at Mr. Baker’s local store. She adheres to thiscustom as long as Mr. Baker can recall back in time.
But recently Mr. Baker noticed that Aunt Betty has not been tohis shop since 35 days!
Mr. Baker immediately concluded that something terrible musthave happened...
M. Platzer, T. Reutterer Regularity within Purchase Timings
MotivationRegularity
Model DevelopmentEmpirical Application
Summary
A Simple ExampleNoncontractual SettingsStochastic ModelsNBD Assumptions
A Simple Example: Aunt Betty
Aunt Betty buys cookies for her favorite nephews at the end ofevery month at Mr. Baker’s local store. She adheres to thiscustom as long as Mr. Baker can recall back in time.
But recently Mr. Baker noticed that Aunt Betty has not been tohis shop since 35 days!
Mr. Baker immediately concluded that something terrible musthave happened...
M. Platzer, T. Reutterer Regularity within Purchase Timings
MotivationRegularity
Model DevelopmentEmpirical Application
Summary
A Simple ExampleNoncontractual SettingsStochastic ModelsNBD Assumptions
A Simple Example: Aunt Betty
Aunt Betty must have changed her buying behavior !!!
M. Platzer, T. Reutterer Regularity within Purchase Timings
MotivationRegularity
Model DevelopmentEmpirical Application
Summary
A Simple ExampleNoncontractual SettingsStochastic ModelsNBD Assumptions
A Simple Example: Aunt Betty
But if Mr. Baker knows it,
why don’t our models know?
M. Platzer, T. Reutterer Regularity within Purchase Timings
MotivationRegularity
Model DevelopmentEmpirical Application
Summary
A Simple ExampleNoncontractual SettingsStochastic ModelsNBD Assumptions
Noncontractual SettingsIn noncontractual customer relationships organizations can notobserve directly whether a customer is still active. Hence, thestatus is a latent variable and other indicators need to be usedto assess activity.
M. Platzer, T. Reutterer Regularity within Purchase Timings
MotivationRegularity
Model DevelopmentEmpirical Application
Summary
A Simple ExampleNoncontractual SettingsStochastic ModelsNBD Assumptions
Stochastic Models for Noncontractual Settings
Pareto/NBDby Schmittlein, Morrison, and Colombo, 1957BG/NBDby Fader, Hardie, and Lee, 2005CBG/NBDby Hoppe and Wagner, 2007
All of these models share Ehrenberg’s well-known andwidely-accepted NBD assumptions.
M. Platzer, T. Reutterer Regularity within Purchase Timings
MotivationRegularity
Model DevelopmentEmpirical Application
Summary
A Simple ExampleNoncontractual SettingsStochastic ModelsNBD Assumptions
NBD Assumptions1 Interpurchase times for an active customer follow an
exponential distribution with rate parameter λ.2 Heterogeneity in λ follows a Gamma distribution across
customers.
M. Platzer, T. Reutterer Regularity within Purchase Timings
MotivationRegularity
Model DevelopmentEmpirical Application
Summary
A Simple ExampleNoncontractual SettingsStochastic ModelsNBD Assumptions
NBD Assumptions
Concerns regarding Exponential Distribution
Mode zero: The most likely time of purchase is immediatelyafter a purchase. No dead period.
Memoryless Property: No regularity within timing patterns.Succeeding interpurchase times are assumed to beuncorrelated.
M. Platzer, T. Reutterer Regularity within Purchase Timings
MotivationRegularity
Model DevelopmentEmpirical Application
Summary
A Simple ExampleNoncontractual SettingsStochastic ModelsNBD Assumptions
NBD Assumptions
Concerns regarding Exponential Distribution
Mode zero: The most likely time of purchase is immediatelyafter a purchase. No dead period.
Memoryless Property: No regularity within timing patterns.Succeeding interpurchase times are assumed to beuncorrelated.
M. Platzer, T. Reutterer Regularity within Purchase Timings
MotivationRegularity
Model DevelopmentEmpirical Application
Summary
A Simple ExampleNoncontractual SettingsStochastic ModelsNBD Assumptions
NBD Assumptions
ImplicationsNBD-based models only consider recency and frequencywhen assessing the activity status of a customer.Thus, these models know nothing about regularity andsubsequently they all (mis)interpret Aunt Betty’s 35-dayinactivity simply as a ‘longer than average’ but still unsuspiciousintertransaction period.
M. Platzer, T. Reutterer Regularity within Purchase Timings
MotivationRegularity
Model DevelopmentEmpirical Application
Summary
A Simple ExampleNoncontractual SettingsStochastic ModelsNBD Assumptions
NBD Assumptions
Is the customer still active at time T ?
-× ×× × ×× ×t0 t1 t2 t3 t4 t5 t6 T
-× × × × × × ×t0 t1 t2 t3 t4 t5 t6 T
Figure: Regular vs. random timing pattern with identical recency andfrequency.
M. Platzer, T. Reutterer Regularity within Purchase Timings
MotivationRegularity
Model DevelopmentEmpirical Application
Summary
A Simple ExampleNoncontractual SettingsStochastic ModelsNBD Assumptions
Regularity
Thus, regularity is crucial!
M. Platzer, T. Reutterer Regularity within Purchase Timings
MotivationRegularity
Model DevelopmentEmpirical Application
Summary
MeasuresErlang-k
Regularity
But what is regularity, and how can it be measured?
The observed timings can fall anywhere between totallyrandom patterns and ‘clockwork-like’, deterministic patterns.
A regularity measure for a given timing pattern should thereforeindicate the location between these two extremes.
M. Platzer, T. Reutterer Regularity within Purchase Timings
MotivationRegularity
Model DevelopmentEmpirical Application
Summary
MeasuresErlang-k
Regularity
MeasuresVariability Ratio (=variance/mean) of the IPTsShape parameter of a fitted Gamma distribution toindividual IPTsShape parameter of a fitted Gamma distribution to all IPTs
M. Platzer, T. Reutterer Regularity within Purchase Timings
MotivationRegularity
Model DevelopmentEmpirical Application
Summary
MeasuresErlang-k
Erlang-k
A relatively easy-to-handle alternative to the exponentialdistribution for modeling regularity within the IPTs is the familyof Erlang-k distributions.
Erlang-k is equivalent to the Gamma distribution with its shapeparameter being fixed to some specified integer k , whichdetermines the assumed degree of regularity.
The exponential distribution equals the Erlang-1 distribution.
M. Platzer, T. Reutterer Regularity within Purchase Timings
MotivationRegularity
Model DevelopmentEmpirical Application
Summary
MeasuresErlang-k
Erlang-k
Figure: Erlang-k Distributions with Sampled Timing Patterns
M. Platzer, T. Reutterer Regularity within Purchase Timings
MotivationRegularity
Model DevelopmentEmpirical Application
Summary
IdeaReplace the exponential distribution from the stochasticmodels for noncontractual settings with the more generalErlang-k distribution.
The Gamma mixture of Erlang-k distributions will result in theCondensed Negative Binomial Distribution (cf. Chatfield andGoodhardt, 1973).
M. Platzer, T. Reutterer Regularity within Purchase Timings
MotivationRegularity
Model DevelopmentEmpirical Application
Summary
The CBG/CNBD-k Model1 Interpurchase times for an active customer follow an
Erlang-k distribution with rate parameter λ.2 Heterogeneity in λ follows a Gamma distribution across
customers.3 At time zero and directly after each transaction customers
drop out with probability p.4 Heterogeneity in p follows a Beta distribution across
customers.5 Parameters λ and p are distributed independently of each
other.6 The observation period starts out with a transaction at time
zero.
M. Platzer, T. Reutterer Regularity within Purchase Timings
MotivationRegularity
Model DevelopmentEmpirical Application
Summary
The CBG/CNBD-k Model1 Interpurchase times for an active customer follow an
Erlang-k distribution with rate parameter λ.2 Heterogeneity in λ follows a Gamma distribution across
customers.3 At time zero and directly after each transaction customers
drop out with probability p.4 Heterogeneity in p follows a Beta distribution across
customers.5 Parameters λ and p are distributed independently of each
other.6 The observation period starts out with a transaction at time
zero.
M. Platzer, T. Reutterer Regularity within Purchase Timings
MotivationRegularity
Model DevelopmentEmpirical Application
Summary
The CBG/CNBD-k Model1 Interpurchase times for an active customer follow an
Erlang-k distribution with rate parameter λ.2 Heterogeneity in λ follows a Gamma distribution across
customers.3 At time zero and directly after each transaction customers
drop out with probability p.4 Heterogeneity in p follows a Beta distribution across
customers.5 Parameters λ and p are distributed independently of each
other.6 The observation period starts out with a transaction at time
zero.
M. Platzer, T. Reutterer Regularity within Purchase Timings
MotivationRegularity
Model DevelopmentEmpirical Application
Summary
The CBG/CNBD-k Model1 Interpurchase times for an active customer follow an
Erlang-k distribution with rate parameter λ.2 Heterogeneity in λ follows a Gamma distribution across
customers.3 At time zero and directly after each transaction customers
drop out with probability p.4 Heterogeneity in p follows a Beta distribution across
customers.5 Parameters λ and p are distributed independently of each
other.6 The observation period starts out with a transaction at time
zero.
M. Platzer, T. Reutterer Regularity within Purchase Timings
MotivationRegularity
Model DevelopmentEmpirical Application
Summary
The CBG/CNBD-k Model1 Interpurchase times for an active customer follow an
Erlang-k distribution with rate parameter λ.2 Heterogeneity in λ follows a Gamma distribution across
customers.3 At time zero and directly after each transaction customers
drop out with probability p.4 Heterogeneity in p follows a Beta distribution across
customers.5 Parameters λ and p are distributed independently of each
other.6 The observation period starts out with a transaction at time
zero.
M. Platzer, T. Reutterer Regularity within Purchase Timings
MotivationRegularity
Model DevelopmentEmpirical Application
Summary
The CBG/CNBD-k Model1 Interpurchase times for an active customer follow an
Erlang-k distribution with rate parameter λ.2 Heterogeneity in λ follows a Gamma distribution across
customers.3 At time zero and directly after each transaction customers
drop out with probability p.4 Heterogeneity in p follows a Beta distribution across
customers.5 Parameters λ and p are distributed independently of each
other.6 The observation period starts out with a transaction at time
zero.
M. Platzer, T. Reutterer Regularity within Purchase Timings
MotivationRegularity
Model DevelopmentEmpirical Application
Summary
Empirical Application
DMEF Contest: Data21,166 donors53,998 donations4.7 years of observation
DMEF Contest: TaskPredict the donations for theupcoming 2 years on andisaggregated level.
M. Platzer, T. Reutterer Regularity within Purchase Timings
MotivationRegularity
Model DevelopmentEmpirical Application
Summary
Empirical Application
Figure: Worst Estimates of a ‘Classic’ Model
M. Platzer, T. Reutterer Regularity within Purchase Timings
MotivationRegularity
Model DevelopmentEmpirical Application
Summary
Empirical Application
Figure: Observed Regularities
M. Platzer, T. Reutterer Regularity within Purchase Timings
MotivationRegularity
Model DevelopmentEmpirical Application
Summary
Empirical Application
Thus, CBG/CNBD-2 seems to be the better choice!
M. Platzer, T. Reutterer Regularity within Purchase Timings
MotivationRegularity
Model DevelopmentEmpirical Application
Summary
Empirical Application
Results
LogLik MSLE RMSE Corr SUMRegression Model - .086 .642 .644 -31%
Pareto/NBD -245,674 .098 .653 .628 +22%BG/NBD -245,833 .096 .651 .640 +19%
CBG/NBD -245,702 .096 .650 .639 +19%CBG/CNBD-2 -242,738 .083 .632 .660 -11%CBG/CNBD-3 -243,924 .082 .637 .663 -24%
MSLE = mean squared logarithmic errorRMSE = root mean squared errorCorr = CorrelationSUM = Error on Aggregated Level
M. Platzer, T. Reutterer Regularity within Purchase Timings
MotivationRegularity
Model DevelopmentEmpirical Application
Summary
Summary
ConclusionIncorporating regularity improves predictability on adisaggregated level in noncontractual settings.
This finding can be possibly generalized to all kind of predictivemodels that condense past transaction records to recency andfrequency.
M. Platzer, T. Reutterer Regularity within Purchase Timings
MotivationRegularity
Model DevelopmentEmpirical Application
Summary
For Further Reading I
M. Platzer.Stochastic Models of Noncontractual ConsumerRelationships.Master Thesis, 2008.
Malthouse, E.The Results from the Lifetime Value and Customer EquityModeling Competition.Journal of Interactive Marketing, 23(3):272-275, 2009.
M. Platzer, T. Reutterer Regularity within Purchase Timings
MotivationRegularity
Model DevelopmentEmpirical Application
Summary
For Further Reading II
C. Chatfield and G.J. Goodhardt.A Consumer Purchasing Model with Erlang Inter-PurchaseTime.Journal of the American Statistical Association,68(344):828-835, 12 1973.
D. Hoppe and U. Wagner.Customer Base Analysis: The Case for a Central Variant ofthe Betageometric/NBD Model.Marketing - Journal of Research and Management,2:75-90, 2007.
M. Platzer, T. Reutterer Regularity within Purchase Timings