This document discusses marketing mix modeling and innovations in attribution modeling. It outlines challenges in modeling noisy marketing data and fitting statistical curves like s-curves. Various techniques are presented for transforming variables, detrending data, and fitting univariate and multivariate regression models. Vector auto-regression modeling is also discussed for measuring interdependencies between marketing drivers over time. The goal is to provide accurate estimates of the impact and effectiveness of different marketing investments to support strategic decision making.

1. © Absolutdata 2014 Proprietary and Confidential
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www.absolutdata.com
April 28, 2014
Our exploration into
innovations in Marketing Mix Modelling
Meet-up Data Science Oxford

2. © Absolutdata 2014 Proprietary and Confidential 2
Agenda
NLMixed & MCMC to automate the
fitting of s-curves and more
The statistical Challenges and the
curse of the s-curve
What is Marketing Mix Modeling?
VARx Modelling
Discussion




3. © Absolutdata 2014 Proprietary and Confidential 3
Strategic vs. tactical decisions
Spend
Brand Equity
Engagement
Web
Purchase
Profile
/segment
Preferences
Propensity Models
Strategic
How to spread the budget?
What campaigns?
Product design
Pricing strategy
???
Tactical
Who?
What?
When?
???
Decision support
modelling and tools

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Measurement of effectiveness & efficiency by marketing driver –
Answering key business questions
 Identify brand/s’ volume growth/decline
drivers
 Explain what is driving year over year change
in sales
 Determine relative importance & estimates
elasticity of different drivers
 Identify the competition and assesses impact
 Determine the key competitive levers that
impact/interact with own brand
 Build a robust framework for investment
decisions for short term - brands that should
be supported
 Determine an optimal realistic investment
plan for the future based on simulated
scenarios

5. © Absolutdata 2014 Proprietary and Confidential 5
Magazine
Online
Print
Radio
TV
Overall
Sales
Affiliate Clicks
Paid Search Clicks
Display Clicks
Decision
Support
Analysis
We would like to measure the direct and indirect impact of
marketing investment at a granularity relevant to planning

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Marketing mix modeling & optimization @ Absolutdata
focus on shift towards true attribution & predictive spend mix
Data
Collection
From
Disparate
Data Sources
Data Review –
Confirming
directional
movements of
prominent variables
Review past
performance to
determine
CONTRIBUTION of
each marketing
mix element
Traditional
Regression Based
Modeling
Techniques such as
OLS
DIY
Simulator
What-If
Scenario
Planning
Optimized
Media
Calendar
Objective
Function &
Constraints
Attribution &
ROI
Measurement
– Multi
channel
influence and
interactions
Advanced
Modeling
Techniques
such as
Auto
Regressive,
VARX, SEM
Added
model
granularity
at
customer
segment
and
regional
level

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In most cases the data is highly noisy
The key challenge it to find a statistically sound solution that can
help the business
The exogenous (independent) time series are highly inter-
correlated
The business requires an impact estimate for the actions
they can take in order to evaluate strategies (what if
analysis)
The business would prefer not to hear about dimension
reduction
S-curves

8. © Absolutdata 2014 Proprietary and Confidential 8
Business understanding is introduces through transformation
Ad-stock
Saturation
Effects
 Ad stock captures exponential decay
effect of GRPs - TV
 This depends on the temporal effect
of GRPs, can be done for Print, Radio
as well
 Research suggests that immediate
response generated by advertising
follows an S-curve
 It introduces three additional
parameters: saturation rate, point of
inflexion and ‘half-life’ parameter (for
carryover effect) as unknowns in the
model
 Together this captures the diminishing
return of advertising
Ad-stock impact
which depends
on the temporal
effect of GRPs
Carry-Over Effect
SampleOutput

9. © Absolutdata 2014 Proprietary and Confidential 9
Various research indicated that immediate response generated by advertising is followed
exponential decay
Ad-stock carry over is estimated and reported in terms of half-life
Current Effect
Half-Life K= Carry Over
Carry-Over Effect

10. © Absolutdata 2014 Proprietary and Confidential 10
0
200
400
600
800
1000
1200
1400
1600
1800
0 50 100 150 200 250 300 350 400 450
RevenueImpact
(ExcludingCarry-overeffect)
$ Spent per Week
Inflexion
Point
Saturation Level
Adstock Equation:
Where, X is actual spending, K is decay constant and determined by expression exp(ln(0.5)/t1/2); V as saturation
parameter and Xd as diminishing return point (point of inflexion)
S-Curve Impact Carry-over ImpactAd-stock Impact
At= 1/(1+exp(-V*(X-Xd ))) + K*At-1
Half-Life
Research suggests that immediate response generated by advertising can be modeled using an S-curve followed
by exponential decay of effect which helps capture the diminishing return of advertising
S-Curves transformation reflect the belief that Marketing spend reduces in its
effectiveness at a certain point and it impact decays over time

11. © Absolutdata 2014 Proprietary and Confidential 11
Standardize the variables
De-trend and account for seasonality effect
Fit an s-curve for each variable optimising it for regression to the residuals to the
Revenue trend
What is more appropriate from a businesswise perspective:
Univariate or Multivariate?
Standardize
the variables
Select a subset
Apply
s-curves
Fit a regression
model
explaining the
Revenue
Evaluate
quality of fit
Multivariate – optimize s-curves to work together in a particular setting
Manually optimize
Univariate –
fit a s-curve
for each
variable on
its own
Automate

12. © Absolutdata 2014 Proprietary and Confidential 12
Instead of calculating the s-curve from t=0, I concentrate on the last n lags:
I explored two sas procedures for fitting the s-curves
Fit aggregation model where S is the dependent and the residual to the Revenue trend is the
independent (no intercept for now – might need to reconsider that)
NLMIXED MCMC

13. © Absolutdata 2014 Proprietary and Confidential 13
My code – if you must
%Macro HazSThree(SVar);
S_Mue=1/(1+exp(-sV*(&SVar._lag&Nlags.-sXd))) ;
%do l=%sysevalf(&Nlags.-1) %to 0 %by -1;
S_Mue=1/(1+exp(-sV*(&SVar._lag&l.-sXd))) + sK*S_Mue;
%end;
%mend
proc nlmixed data=HAZ.Detrend MAXITER=4000 maxfunc=4000;
ods select ParameterEstimates;
parms b1=1 se=1 sV=1 sXd=0 SK=0.25;
bounds se>0;
bounds sV>0;
bounds 0<SK<1;
bounds b1>0;
%HazSThree(&HazVar.);
Mue= b1*S_Mue;
model Detrended ~ normal(mue, se);
proc mcmc data=HAZ.Detrend &MCMCOptions.;
ods select PostSummaries ;
parms b1 se
sV sXd SK
;
prior b1 ~ normal(mean = 1, var = 0.5);
prior se ~ igamma(shape = 3/10, scale = 10/3);
prior SK ~ uniform(0,1);
prior sXd ~ uniform(-2,2);
prior sV ~ uniform(0,10);
%HazSThree(&HazVar.);
Mue=b1*S_Mue;
model Detrended ~ n(mue, sd = se);
For illustrative purposes the code shown here fits only one s-cure. The solution actually fits a baseline and all the
curves

14. © Absolutdata 2014 Proprietary and Confidential 14
Vector Auto Regression (VAR)
time
Steady state
progression
Target
Sales/Signups
time
Co dependency
associationIndigenous
Web search
time
Marketing impact
& decay
Exogenous
campaigns

15. © Absolutdata 2014 Proprietary and Confidential 15
Phase I: Top down marketing mix modeling
Phase III: Reconcile
MMM & Cookie
Attribution
Phase IV:
Reporting, Simulatio
n and Optimization
Phase I: Marketing Mix
Modeling
Phase II: Cookie-
Based Attribution
Algorithm
Search
Clicks
Affiliates
Display
Impressions
TV Impacts
AffiliatesSecondary Relationships
Search
Signups
Email
Signups
Print
Signups
Signups
from
Other
Factors
Previous
Day’s
Baseline
Signups
+TV GI
Signups
Display
Signups+ + + + +
Daily
Signups=

16. © Absolutdata 2014 Proprietary and Confidential 16
Secondary attribution provides A refined view of the system
Paid
Search Clicks
Non
paid search
Cable
Total Impact
11.4%
9.0%
2.5%
3.8%
-1.0%
2.2%
-0.1%
2.6%-3.8%
-2.2%
Actual TV Attribution taking into
account indirect contribution of Search
Final Attribution 7.5% 5.7% 11.1%
SampleOutput
-0.1%

17. © Absolutdata 2014 Proprietary and Confidential 17
Applying
VARx to a BIG
number of
SKUs
How to
choose priors
We have encountered interesting challenges
Challenges
Modelling short
term and long
term effect
Cookie data
allows to not only
do attribution but
identify key
sequences

18. © Absolutdata 2014 Proprietary and Confidential 18
Incomplete sales (Target) data
We do not know what is sold when by the distributers
We sell to their stock

19. © Absolutdata 2014 Proprietary and Confidential 19
http://www.linkedin.com/groupItem?view=&gid=130238&item=233249172&type=member&commentID=5810144471664320512&trk=hb_ntf_COMMENTED_O
N_GROUP_DISCUSSION_YOU_FOLLOWED#commentID_5810144471664320512
Friends do not let friends to use Excel for statistical analysis

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Absolutdata provide analytics based solutions to address business critical issues
40% increase in profits through
Conjoint based Pricing
Optimization – A top SaaS
company
$50MM increase in revenue
by Market Mix Modeling
across 4 geographies
– A leading CPG Company
15% revenue growth through
Multi Channel Attribution
– A large ecommerce
company
$23MM increase in Customer
Loyalty and CRM marketing
revenue
– A major Hotel chain
$9MM incremental revenue
as a result of focused
promotional campaigns
created
– A major Online Retail
Discounter
Contribution of $78MM over the
last few years to their margins
– A major Retailer
We are decision scientists who help decision makers take better and informed decisions

21. Eli Y. Kling
Director - Analytics
Phone: +44 (0)7940094976
Email: Eli.Kling@absolutdata.com
LinkedIn: Uk.linkedin.com/in/elikling
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