## Causal Design Pattern I: Instrumental Variable #### Problem: Suppose we want to measure the causal effect of an intervention on Product A on the sales of Product B, such as adding a [[Recommender system]] to the Product A's page. The challenge is that we don't know how much of the observed increase in sales of Product B after adding the recommender is due to the recommendations, and how much is due to customers' existing interest in buying the two products together. Technically, the IV design pattern can address the following situations: 1. [[Bias]] is expected due to omitted confounding variables (e.g., because they are unobserved). This is discussed in detail in [[Confounding by intention]]. 2. Bias is expected because the predictors are believed to have measurement error. 3. Bias due to reverse or simultaneous causation (between the outcome and predictors). #### Solution: Use a variable (to serve as an instrumental variable) that affects visits to Product A's page but not on the sales of Product B. This way, the causal effect of the intervention on the sales of Product B can be *reasonably* isolated from the joint sales of Products A and B that are due to other reasons, such as customers' existing demand. See [[Data and conceptual model]] for an example. #### Requirements: The instrumental variable should have an effect on the recommender (e.g., more views of the recommendation on Product A's page) but not on the sales of Product B. The former is called the relevance criterion and the latter is called the exclusion restriction. These are discussed in [[Data centricity in the IV pattern]] in more detail. #### Challenges: For various reasons, the design pattern may not work as intended. An example is a case where Products A and B are highly complementary. If the instrumental variable not only affects the sales of Product A, but also creates an intention to purchase Product B along with Product A (regardless of the intervention), the causal effect cannot be isolated. This would be a violation of the exclusion criterion. #### Mathematical background explained using DAGs: If you are quantitatively savvy, see [[Confounding by intention]] for a summary of the design pattern along with the challenges described above. > [!info]- Last updated: September 4, 2024