BayesiaLab Webinar Series
Causal Counterfactuals for Contribution Analysis
Explaining a Misunderstood Concept with Bayesian Networks
Thursday, May 30, 2019, 11a.m. – 12 p.m. (CST, UTC-6)
Attribution and contribution often appear in a similar context and are both concepts that are closely related to causality. In general, attribution identifies a source or cause of something observed. In marketing, attribution has a somewhat special meaning and often refers to the origin of a consumers’ journey towards an outcome. Thus, observed outcomes are attributed to specific prior touchpoints, such as website visits or ad clicks (Julian, 2013). Conversely, events of that kind can be considered “drivers” of outcomes.
Contribution has been proposed as a broader concept that involves a broader range of marketing drivers, on- and offline, and how they lead to a desired outcome (ibid.). As such, contribution is certainly a causal concept, too. The amount of contribution represents the degree of influence of one driver and compares it to any other drivers.
Definition of Contribution
Despite its intuitive appeal, contribution is an elusive concept that lacks a formal definition in the sciences, in general, and in marketing, in particular. To operationalize contribution, we propose to distinguish between two types, which we shall call Type 1 and Type 2 Contribution. Both types rely on computing the difference between factual and counterfactual outcomes corresponding to factual and counterfactual conditions of drivers.
A factual outcome is simply an actual observation of a target variable. Associated with a factual outcome are drivers at their observed, factual levels. A counterfactual outcome is the result of drivers being set to hypothetical, counterfactual conditions. This begs the question of how we can determine the counterfactual outcome. We must infer it, of course, with a causal model or, alternatively, with a model that facilitates causal inference.
A New Example
The definition of Contribution and its calculation is ultimately very simple, even though its description turns out to be rather verbose. To keep our explanation and notation manageable, we introduce a very simple domain as an example. In fact, we make up the new example purely for our convenience. As creators, we define the “laws of nature” as we like. Thus, we automatically have perfect knowledge of them. Knowing the ground truth in advance, we will more easily recognize what is happening in each step of the definition of contribution and the calculation of related measures.