Markov model for the online multichannel attribution problem

Davide Altomare, David Loris
2016-12-07
R-package ChannelAttribution for the online multichannel
attribution problem.
Introduction
Advertisers use a variety of online marketing channels to reach consumers and they want to know the
degree each channel contributes to their marketing success. It’s called the online multi-channel attribution
problem. In many cases, advertisers approach this problem through some simple heuristics methods that
do not take into account any customer interactions and often tend to underestimate the importance of
small channels in marketing contribution.
R-package ChannelAttribution (https://cran.r-project.org/web/packages/ChannelAttribution/index.html) provides a
function that approaches the attribution problem in a probabilistic way. It uses a k-order Markov
representation to identifying structural correlations in the customer journey data. This would allow
advertisers to give a more reliable assessment of the marketing contribution of each channel. The approach
basically follows the one presented in F. Anderl, I. Becker, F. v. Wangenheim, J.H. Schumann (2014):
Mapping the customer journey: a graph-based framework for attribution modeling. Differently for them,
we solved the estimation process using stochastic simulations. In this way it is possible to take into account
conversion values and their variability in the computation of the channel importance. The package also
contains a function that estimates three heuristic models (first-touch, last-touch and linear-touch
approach) for the same problem.
The following paragraph is a gentle introduction to Markov model. It also contains some considerations on
heuristic models.
Markov Model
Consider the following example in which we have 4 states: (START), A, B, (CONVERSION) and 3 paths
recorded:
PATH CONVERSIONS
(START) -> A -> B -> A -> B -> B -> A -> (CONVERSION) 1
(START) ->A -> B -> B -> A -> A -> (CONVERSION) 1
(START) -> A -> A -> (CONVERSION) 1
TOTAL 3
For every couple of ordered states we count the number of directed edges:
EDGE ARROW.COUNT
(START) -> A 3
(START) -> B 0
A -> A 2
A -> B 3
A -> (CONVERSION) 3
B -> A 3
B -> B 2

B -> (CONVERSION) 0
TOTAL 16
From the table we can calculate the transition probabilities between states:
EDGE ARROW.COUNT TRANSITION.PROBABILITIES
(START) -> A 3 3/3
(START) -> B 0 0
TOT (START) 3
A -> A 2 2/8
A -> B 3 3/8
A -> (CONVERSION) 3 3/8
TOT A 8
B -> A 3 3/5
B -> B 2 2/5
B -> (CONVERSION) 0 0
TOT B 5
Now we have all the information to plot the Markov Graph:
This kind of Markov Graph is called First-Order Markov Graph because the probability of reaching one state
depends only on the previous state visited.
From the Graph, or more clearly from the original data, we see that every path leads to conversion. Thus
the conversion rate of the Graph is 1.
Now we want to define a measure of channel importance using the relationship between states described
by the Graph.
Importance of channel A can be defined as the change in conversion rate if channel A is dropped from the
Graph, or in other terms if channel A becomes a NULL state.
A NULL state is an absorbing state so if one reaches this STATE can’t move on.

This Graph simplifies to
In previous Graph it’s easy to see that if channel A becomes a NULL state there is no way of reaching
conversion from START state. So conversion rate of this Graph is 0. The conversion drops from 1
(conversion of the original Graph) to 0. Thus importance of channel A (defined as the change in conversion
rate) is 1.
In similar way we define the importance of channel B as the change in conversion rate if channel B is
dropped from the Graph, or in other terms if channel B becomes a NULL state.

This Graph simplifies to:
In previous Graph we see the probability of reaching conversion from START state is 0.5. Conversion drops
from 1 (conversion rate of the original Graph) to 0.5. Thus the importance of channel B (defined as the
change in conversion rate) is 0.5.
Once we have the importance weights of every channel we can do a weighted imputation of total
conversions (3 in this case) between channels.
CHANNEL CONVERSIONS
A 2 [ =3 x 1/(1+0.5) ]
B 1 [ = 3 x 0.5/(1+0.5) ]
TOTAL 3
Now let’s go back to the original data:
PATH CONVERSIONS
(START) -> A -> B -> A -> B -> B -> A -> (CONVERSION) 1
(START) ->A -> B -> B -> A -> A -> (CONVERSION) 1
(START) -> A -> A -> (CONVERSION) 1
TOTAL 3
We see that if we use a first-touch or last-touch approach, all the conversions are assigned to channel A,
despite the important work of channel B in “conversion game” is clear from the data.
The channel attribution problem can be viewed as a football match, to better understand how different
approaches work. So channels can be viewed as players, paths are game actions and conversions are goals.
Markov Model analyses relationships between game actions to understand the role of the player in scoring.
While heuristic approach analyzes one action (path) at the time.
So last-touch approach rewards only players who scored, while first-touch approach rewards only players
who started the action. Linear approach rewards with the same credit to every player who took part the
action, while time-decay approaches gives subjective weights to every player who took part the action.
As we have seen Markov Model require as inputs paths and total conversions and does not require
subjective assumptions, differently from heuristic approaches.

Package ChannelAttribution
In the following example we will show how ChannelAttribution can be used for the multichannel
attribution problem.
Load libraries and data:
library(ChannelAttribution)
library(reshape2)
library(ggplot2)
data(PathData)
Estimate heuristic models:
H=heuristic_models(Data,'path','total_conversions',var_value='total_conversion_value')
Estimate Markov model:
M=markov_model(Data, 'path', 'total_conversions', var_value='total_conversion_value')
Plot total conversions:
R=merge(H,M,by='channel_name')
R1=R[,(colnames(R)%in%c("channel_name","first_touch_conversions","last_touch_conversions","linear
_touch_conversions","total_conversion"))]
colnames(R1)=c('channel_name','first_touch','last_touch','linear_touch','markov_model')
R1=melt(R1,id="channel_name")
ggplot(R1, aes(channel_name, value, fill = variable)) +
geom_bar(stat="identity", position = "dodge") +
ggtitle("TOTAL CONVERSIONS")+
theme(axis.title.x = element_text(vjust=-2))+
theme(axis.title.y = element_text(vjust=+2))+
theme(title = element_text(vjust=2))+
theme(text = element_text(size=16)) +
theme(plot.title=element_text(size=20)) +
ylab("")

Plot total value:
R2=R[,(colnames(R)%in%c("channel_name","first_touch_value","last_touch_value","linear_touch_value
","total_conversion_value"))]
colnames(R2)=c('channel_name','first_touch','last_touch','linear_touch','markov_model')
R2=melt(R2,id="channel_name")
ggplot(R2, aes(channel_name, value, fill = variable)) +
geom_bar(stat="identity", position = "dodge") +
ggtitle("TOTAL VALUE")+
theme(axis.title.x = element_text(vjust=-2))+
theme(axis.title.y = element_text(vjust=+2))+
theme(title = element_text(vjust=2))+
theme(text = element_text(size=16)) +
theme(plot.title=element_text(size=20)) +
ylab("")
ChannelAttribution Tool
ChannelAttribution can be used through a user-friendly graphical interface without interfacing with R-code. Channel
Attribution Tool can be found at https://adavide1982.shinyapps.io/ChannelAttribution.
ChannelAttribution Tool can be also used locally through package ChannelAttributionApp.
library(ChannelAttributionApp)
CAapp()

Markov model for the online multichannel attribution problem

Markov model for the online multichannel attribution problem

More Related Content

What's hot (20)

Viewers also liked (16)

Similar to Markov model for the online multichannel attribution problem (20)

Recently uploaded (20)

Markov model for the online multichannel attribution problem