Markov Chain first order applied to attribution modelling
$begingroup$
Based on this article I'm using within R the Channel Attribution package to leverage on the Markov Chain in order to attribute conversion between several marketing channels. However, the computation made by hand the outcome of the program are not corresponding, so I'm wondering what of the markov chain manual computation is not performing as it should be.
On one point the author suggested:
"When using one-order Markov chains, a subsequence of the same channels in a path (duplicates) can be reduced to one channel (for example C2 in the path C1 → C2 → C2 → C2 → C3 can be reduced to C1 → C2 → C3). Because, mathematically, it doesn’t matter how many times each C2 goes through the loop with itself in the transition matrix, it will be in the C3 state finally. Therefore, we will obtain different transition matrices but the same Removal Effect for channels with or without subsequent duplicates ".
Now, I utilized another data set to validate the package result. Specifically:
If I take the example in the picture, where I simulated an hypothetical set of paths, with both number of conversions and not conversions represented in the coloured cells (in the green and red cells respectively)
Doing the math by hand I get the following transition probabilities for the 1st order Markov chain (I also compute looping probability for google channel as in the article it is stated that mathematically the removal effect should be the same):
However, when I do the calculation by hand to get the removal_effect and the total_conversions, I do not get the same results of the package for each channel.
According to the theory and the example in the article, the total probability of conversion of the model should be = $(1times 0.1008times 0.5455times 0.1261) + (0.1765times 0.2605times0.0323) +(0.2605times0.3226times0.1818) + 0.1261=0.1498$
Then the removal effects:
$text{google}= 1-(0/0.1498)=1$
$text{facebook}=1- ( (0.0015+0.1261)/0.1498)=0.1482$
$text{instagram}=1-((0.0069+0.1261)/0.1498)=0.1121$
Then to compute the share of conversion, let's say of google
$text{share of google}=frac{1}{1+0.1482+0.1121}=0.7935 times 20 text{conversions} =15.87$
However, the attribution channel package in R give me different results as per below
I think I'm missing something in my calculation respect to what the code does or maybe it is expected in computing the Removal effects.
Could anyone with some experience with Markov chains help in identifying what is not right in the manual computation?
Many thanks D
markov-chains matrix-calculus markov-process
edited Dec 13 '18 at 10:59
Vee Hua Zhi
759224
asked Dec 13 '18 at 10:35
davide cortellinodavide cortellino
11
$endgroup$
add a comment |
$begingroup$
Based on this article I'm using within R the Channel Attribution package to leverage on the Markov Chain in order to attribute conversion between several marketing channels. However, the computation made by hand the outcome of the program are not corresponding, so I'm wondering what of the markov chain manual computation is not performing as it should be.
On one point the author suggested:
"When using one-order Markov chains, a subsequence of the same channels in a path (duplicates) can be reduced to one channel (for example C2 in the path C1 → C2 → C2 → C2 → C3 can be reduced to C1 → C2 → C3). Because, mathematically, it doesn’t matter how many times each C2 goes through the loop with itself in the transition matrix, it will be in the C3 state finally. Therefore, we will obtain different transition matrices but the same Removal Effect for channels with or without subsequent duplicates ".
Now, I utilized another data set to validate the package result. Specifically:
If I take the example in the picture, where I simulated an hypothetical set of paths, with both number of conversions and not conversions represented in the coloured cells (in the green and red cells respectively)
Doing the math by hand I get the following transition probabilities for the 1st order Markov chain (I also compute looping probability for google channel as in the article it is stated that mathematically the removal effect should be the same):
However, when I do the calculation by hand to get the removal_effect and the total_conversions, I do not get the same results of the package for each channel.
According to the theory and the example in the article, the total probability of conversion of the model should be = $(1times 0.1008times 0.5455times 0.1261) + (0.1765times 0.2605times0.0323) +(0.2605times0.3226times0.1818) + 0.1261=0.1498$
Then the removal effects:
$text{google}= 1-(0/0.1498)=1$
$text{facebook}=1- ( (0.0015+0.1261)/0.1498)=0.1482$
$text{instagram}=1-((0.0069+0.1261)/0.1498)=0.1121$
Then to compute the share of conversion, let's say of google
$text{share of google}=frac{1}{1+0.1482+0.1121}=0.7935 times 20 text{conversions} =15.87$
However, the attribution channel package in R give me different results as per below
I think I'm missing something in my calculation respect to what the code does or maybe it is expected in computing the Removal effects.
Could anyone with some experience with Markov chains help in identifying what is not right in the manual computation?
Many thanks D
markov-chains matrix-calculus markov-process
edited Dec 13 '18 at 10:59
Vee Hua Zhi
759224
asked Dec 13 '18 at 10:35
davide cortellinodavide cortellino
11
$endgroup$
add a comment |
$begingroup$
Based on this article I'm using within R the Channel Attribution package to leverage on the Markov Chain in order to attribute conversion between several marketing channels. However, the computation made by hand the outcome of the program are not corresponding, so I'm wondering what of the markov chain manual computation is not performing as it should be.
On one point the author suggested:
"When using one-order Markov chains, a subsequence of the same channels in a path (duplicates) can be reduced to one channel (for example C2 in the path C1 → C2 → C2 → C2 → C3 can be reduced to C1 → C2 → C3). Because, mathematically, it doesn’t matter how many times each C2 goes through the loop with itself in the transition matrix, it will be in the C3 state finally. Therefore, we will obtain different transition matrices but the same Removal Effect for channels with or without subsequent duplicates ".
Now, I utilized another data set to validate the package result. Specifically:
If I take the example in the picture, where I simulated an hypothetical set of paths, with both number of conversions and not conversions represented in the coloured cells (in the green and red cells respectively)
Doing the math by hand I get the following transition probabilities for the 1st order Markov chain (I also compute looping probability for google channel as in the article it is stated that mathematically the removal effect should be the same):
However, when I do the calculation by hand to get the removal_effect and the total_conversions, I do not get the same results of the package for each channel.
According to the theory and the example in the article, the total probability of conversion of the model should be = $(1times 0.1008times 0.5455times 0.1261) + (0.1765times 0.2605times0.0323) +(0.2605times0.3226times0.1818) + 0.1261=0.1498$
Then the removal effects:
$text{google}= 1-(0/0.1498)=1$
$text{facebook}=1- ( (0.0015+0.1261)/0.1498)=0.1482$
$text{instagram}=1-((0.0069+0.1261)/0.1498)=0.1121$
Then to compute the share of conversion, let's say of google
$text{share of google}=frac{1}{1+0.1482+0.1121}=0.7935 times 20 text{conversions} =15.87$
However, the attribution channel package in R give me different results as per below
I think I'm missing something in my calculation respect to what the code does or maybe it is expected in computing the Removal effects.
Could anyone with some experience with Markov chains help in identifying what is not right in the manual computation?
Many thanks D
markov-chains matrix-calculus markov-process
edited Dec 13 '18 at 10:59
Vee Hua Zhi
759224
asked Dec 13 '18 at 10:35
davide cortellinodavide cortellino
11
$endgroup$
Based on this article I'm using within R the Channel Attribution package to leverage on the Markov Chain in order to attribute conversion between several marketing channels. However, the computation made by hand the outcome of the program are not corresponding, so I'm wondering what of the markov chain manual computation is not performing as it should be.
On one point the author suggested:
"When using one-order Markov chains, a subsequence of the same channels in a path (duplicates) can be reduced to one channel (for example C2 in the path C1 → C2 → C2 → C2 → C3 can be reduced to C1 → C2 → C3). Because, mathematically, it doesn’t matter how many times each C2 goes through the loop with itself in the transition matrix, it will be in the C3 state finally. Therefore, we will obtain different transition matrices but the same Removal Effect for channels with or without subsequent duplicates ".
Now, I utilized another data set to validate the package result. Specifically:
If I take the example in the picture, where I simulated an hypothetical set of paths, with both number of conversions and not conversions represented in the coloured cells (in the green and red cells respectively)
Doing the math by hand I get the following transition probabilities for the 1st order Markov chain (I also compute looping probability for google channel as in the article it is stated that mathematically the removal effect should be the same):
However, when I do the calculation by hand to get the removal_effect and the total_conversions, I do not get the same results of the package for each channel.
According to the theory and the example in the article, the total probability of conversion of the model should be = $(1times 0.1008times 0.5455times 0.1261) + (0.1765times 0.2605times0.0323) +(0.2605times0.3226times0.1818) + 0.1261=0.1498$
Then the removal effects:
$text{google}= 1-(0/0.1498)=1$
$text{facebook}=1- ( (0.0015+0.1261)/0.1498)=0.1482$
$text{instagram}=1-((0.0069+0.1261)/0.1498)=0.1121$
Then to compute the share of conversion, let's say of google
$text{share of google}=frac{1}{1+0.1482+0.1121}=0.7935 times 20 text{conversions} =15.87$
However, the attribution channel package in R give me different results as per below
I think I'm missing something in my calculation respect to what the code does or maybe it is expected in computing the Removal effects.
Could anyone with some experience with Markov chains help in identifying what is not right in the manual computation?
Many thanks D
markov-chains matrix-calculus markov-process
markov-chains matrix-calculus markov-process
edited Dec 13 '18 at 10:59
Vee Hua Zhi
759224
asked Dec 13 '18 at 10:35
davide cortellinodavide cortellino
11
edited Dec 13 '18 at 10:59
Vee Hua Zhi
759224
asked Dec 13 '18 at 10:35
davide cortellinodavide cortellino
11
edited Dec 13 '18 at 10:59
Vee Hua Zhi
759224
edited Dec 13 '18 at 10:59
Vee Hua Zhi
759224
edited Dec 13 '18 at 10:59
Vee Hua Zhi
759224
759224
asked Dec 13 '18 at 10:35
davide cortellinodavide cortellino
11
asked Dec 13 '18 at 10:35
davide cortellinodavide cortellino
11
asked Dec 13 '18 at 10:35
davide cortellinodavide cortellino
11
11
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