Dear Brian,
Estimating seperate logistic regressions for each group is equivalent
of estimating a single logistic regresion with dummy variables for
each group and interactionterms of each group dummy with all other
explanatory variables. So the `seperate logistic regression model' is
larger (uses more degrees of freedom) than only adding the dummies
for group membership.
One followup comment: You can pretty much always think of subgroup models
that you could run. You could run separate models by gender; by race; by
religion; and then you could run separate models by various joint
characteristics, e.g. white male Catholics, white female Catholics,
etc. But if you just do that automatically, you can easily be overwhelmed
with numbers and create samples that are so small that nothing comes up
significant (or you start finding across-group differences just by chance
because you are estimating so many parameters). So in general, I wouldn't
start estimating subgroup models unless I had good theoretical reasons for
doing so.
