I am wondering what good ways to model cause/effect relationships in timeseries events are. My data consists of events with a timestamp. Some of those events are already known to be effects and some are potential causes.
A concrete example: A person records the types of foods they consume along with time and also stomach issues along with the time they occur. I want to predict which food will (likely) cause a stomach issue. I know that there is some domain knowledge required (eg. when food will be digested and for how long it will stay in the intestine and so on, but let's assume that those parameters are known to some extend or can be estimted well).
My modeling approach was to use a logistic regression (ie, model the food consumed in chosen time interval (eg. 1 hour) and 1/0-encode it in a vector with columns for food types and a 0 or 1 target for the classes: "issues" or "no issues". The resulting internal coefficients should be an approximate of the certainty of a specific food to cause the issues.
However, I am wondering if there are any better ways to model this as my data is pretty noisy and the amount is low (just a few weeks). Also, since some foods are often consumed together there is a high correlation between individual food types and the data set can be imbalanced (lots of "issue" targets, low "no issue" targets).
Any suggestions on how this can be improved are appreciated.
