I have a general conceptual modeling question I’d like to pose. I am working with some time-series data at the month resolution going back about 20 years. I am looking into generating predictive models for total catch using one model for effort (angler-hours, month level) and another for catch-per-angler-hour (total catch per month/total angler-hours per month). While I would like to make inferences on each of these models seperately, I would also like to generate complete posterior predictive distributions for each model at each month for effort and catch-per-angler-hour seperately, then multply the individual scans together to simulate what predicted total catch would be. The basic equation is simply enough:
Catch = angler-hour x catch-per-angler-hour
However, before I proceed to writing the MS, I wanted to make sure this is appropropriate. The models both fit fine to their respective datasets, and the amalgamation seems to recreate the aggregate catch data well.
Moreover, if this is ok, should I combine them scan-wise or use some multiplicative analog to a convolution to generate the combined result?
Finally, if this is indeed appropriate, there is a third iteration of modeling I would like to add on top of this, but I am trying to be as careful as I can not to use the models inappropriately.