Even if you believe every group has a different coefficient, I would also
estimate the pooled model and use interactions to test whether the
coefficients really are different across groups. If you only estimate
separate models for each group, you are unable to test the assumption
(unless you simply eyeball coefficients and make an ad hoc decision).
There are some other issues to consider (e.g., is it appropriate to assume
the same error structure for the different groups?) but the pooled model
seems a place to start, at least in my area of research and perhaps in
yours as well.
Hope this helps.
Sam
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