With such a dependent variable, I would look at -intreg-. If you want to
think that the effects for the different intervals differ, then you think
that the effect isn't linear in the latent variable (hours of activity per
week). If you specify the functional form you expect that effect to have,
you could make some progress along those lines, i.e. build your own
likelihood function. However, I would at least start with just -intreg- and
the assumption of a linear effect on hours of activity.
Now that I think about it, let me second the suggestion of Maarten
and others, and add a recommendation that you read the reference
manual entry on intreg. That entry shows (a) how to test the
appropriateness of the intreg model, e.g. you can do a contrast
between oprobit and intreg, and (b) if intreg is problematic, it
suggests transforming the dv, e.g. take the logs of the interval
boundaries. If the goal is "to give different effects for
explanatory variable according to the levels in the dependent" then
taking logs or doing some other transformation of Y may accomplish this goal.
