I suppose this would most commonly be done via factor analysis or stepwise regression, but by and large creating a model in the absence of theory is a very bad idea. You'll find correlations and associations via whatever methods you choose, and some of them will be spurious (especially via factor analysis). So if you want the maths to do the modelling for you you're going to want to run a huge number of replications and follow up studies to show the validity of your findings. My advice is don't do it. Develop a theory then test that.

Exploratory methods are by definition intended to help develop theories and models. So EFA or similar approaches might allow one to begin the model development stage. However, there are very few things we are interested in that we have not had enough interest that some sort of theory has not been postulated.