I have GBs of Event-Based Data. How do I figure out causation? I have a lot of event-based data about users of our website. For example, data in the format (verb, timestamp). There's about 10 or so different verbs (call them A, B, C, etc).
I'm interested in figuring out different events' contribution to a users' decision to purchase a membership.
i.e.
P(chance to buy in a given month) = A * contribution-of-a + B * contribution-of-b +  ...
This is a tricky problem because some things might happen many times (user makes a friend) and some things might happen rarely (user uploads a level). I'm also trying to establish causation instead of just correlation.
It seems like this problem has a lot of degrees of freedom. Is it even possible in theory to solve? How do other companies optimize this? What is the statistics technique that I should Google for?
Is this what a Singular Value Decomposition is for?
 A: That's not what SVD is for.  However it does look like a reasonable application for a logistic regression model though, perhaps with a rate events correction if people don't often buy things.
Before launching into that you might want to think about how the verbs could relate to purchase decisions.  Three basic questions might be: a) do A, B, C, etc. have independent effects on purchasing probability or might they operate together?  If they do, this suggests an additive specification.  b) Is it the case that more (or less) of each verb matters, or is it more of one verb than another?  If the latter, this affects how you code your users' behaviour, e.g. in ratios, counts, proportions etc. c) Do they purchase different things and does this matter? This may affect whether it is more helpful to model buying something, or buying Y rather than Z, and consequently what the dependent variable(s) might be.
Any statistical package will fit such a model for you. The key is knowing what it's telling you when it's finished, and here more importantly whether it fits well enough to be trusted for prediction: On this latter question, consider what you might do with a positive prediction, and thus how much it might cost to do that thing.  ROC curves are useful here.
To the causal question. Some of the commenters claim that you won't necessarily get causal information from this model fitting exercise.  That's correct.  However you can run experiments within your website to see if randomly selected users will change their purchasing behaviour.  You might even stratify by verb combination if you get the idea that some people are more susceptible than others to the manipulation.  That's really the final test of whether some regularity thrown up in the fitted model actually corresponds to a cause of purchasing behaviour rather than simply a correlate.
