develop minimum adequate model with correlated predictors

Question

Could someone guide me what should my approach be regarding what predictors to include if they are correlated and how to develop my minimum adequate model. For e.g. lets say I have 10 predictors some of which are strongly correlated. When developing a model (say a Poisson GLM), do I include only those predictors that are uncorrelated in my model

or

can I include all 10 predictors in the model (irrespective of correlation structure) and use a variable selection approach or drop function which will automatically select the important predictors based on AIC values

or

first select only the uncorrelated predictors for the model and then use the variable selection or drop function to further remove predictors that are not important to the response

Answer 1

It is not a problem to include correlated predictors, as long as the association is not too strong (multi-colinearity). The approach using information criteria should do just fine, as it allows you to compare non-nested models. In R, you may find the MuMIn package helpful.