Please see Chapter 3.2 from this article: http://www.turn.com.akadns.net/sites/default/files/whitepapers/TURN_Tech_WP_Data-driven_Multi-touch_Attribution_Models.pdf
Here, a method is described by which the influence of online-marketing-channels/campaigns (for example: "Display" as a channel for Display-Ads, "SEA" as a channel for Search-Engine-Ads etc.) on a binary criterion (for example: 1 = positiv User = User buys a product in online-store vs. 0 = negative User = User does does not buy a product in online-store) can be calculated. The described method is described as more easy and simple than conducting a logistic regression.
With the first equation, you can calculate for every channel the share of positive users (=users who had contact to this channel AND bought the product) on all users which had contact to this channel:
Example: 1000 Users had contact to the channel "Display" and 400 of them bought the product. Hence, the probability for this channel is 0.4 (=400/1000 = 400/(400 + 600))
For considering overlapping between channels, you use equation two, which includes the second-order interaction term:
What i am not understanding and at which point i need your help is the following: For calculation the contribute of each channel to the buy-probability (= C(xi); and this is what is important, because every marketer wants to know, which online marketing channel/campaign "works" and converts a internet-user to a buyer of the product) the following equation is used:
What does mean "The contribution of channel i is then computed at each positive user level" and what does mean "for a particular user"? With equation 1 and 2 we have calculated terms on a aggregated level and suddenly, in equation 3, they talk about calulation on "User level". What does this mean? And what is "N"? When i have 3 channels in total, is N = 2 (3 channels - 1 = 2 channels)? This "user level"-thing is irritating. I thougt i have to calculate for a specific channel - for example: channel "Display" - the terms according to equation 1 and 2 and just enter this terms in equation 3, and then i get C(display) = [myresult] But is it really so easy?