I have many predictor variables (100+) and many outcome variables (10+). I am attempting to optimise which predictor variables to use when modelling my outcome variables. I am using R for the analysis and the outcome variables must be modeled separately using the
My issue is that the GLMs should all use the same predictor variables, and so when I am choosing which variables to use, I have to take all models into consideration and not just one. Since there are so many predictor variables, I am using backward selection for simplicity. If I were optimising a single model, I would minimise the AIC. However, since I have more than one model, I can't minimise the AIC for just one of them as the AIC for the others might be really high.
My question is this: When optimising more than one model, what value should I minimise at each iteration?
I believe I read somewhere that you are to take the sum of the AICs, but I can't find where I read that (sources would be incredibly helpful). I have a niggling feeling however that it might be beneficial to minimise the product of the AICs as that would reduce influence of any outlying values (this boils down to minimising the arithmetic vs geometric mean)
P.S. If anyone can suggest a different information criterion (such as BIC, etc.), how to use it in this case and why it is superior I would be more than happy to have the feedback.