Figuring out causation from event data? Suppose I have event data showing these things:


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*users who signed up

*users who signed up and then went on to do main important activity

*users who signed up and then went on to invite a coworker


This event data contains the timestamp of these events. I am wondering: would inviting a coworker cause the main important activity? Should we emphasize inviting a coworker as part of the onboarding flow?
Short of running an a/b test where we build a feature to invite coworkers as part of an onboarding flow, can you figure out causation from the historical data?
I can see correlation but I really want to know causation.
 A: Since no true randomized experiment was done here, it's difficult if not impossible to determine causation from observational data.  However, there are some causal inferential methods you can use to maybe provide evidence that the relationship is causative.  Propensity score analysis is the first thing that comes to mind.  If you have a rich source of "pre-treatment" covariates, you may be able to gain some insight and provide evidence for causal effects through various causal inference techniques such as propensity score (PS) analysis.  In PS analysis, if you can show that those who where invited versus those who were not invited are "balanced" with regard to all possible confounding covariates (i.g. they looks the same), then you can use the propensity scores to match/weight/stratify/adjust your data with the propensity scores to help determine if the invitations were the causal factor (in reality thought, this isn't possible since you can't measure all known/unknown possible confounders).  There are are other causal inference analyses such as interrupted time-series, difference-in-differences methods, instrumental variables, regression discontinuity designs, stratification, etc. that might might be appropriate for your study, but it's difficult to tell based on what little information you've provided us.  I'd recommend reading up on some of these methods and seeing if any of them might be suitable for your situation.
