I have a question as to which to use, population-average or unit-specific
parameter estimates.
I am estimating a multi-level binary logit model in which the
student-level dependent variable is graduate from high school or not and
the black-white gap is allowed to vary across schools. I then explain
this varying gap at the school level with the proportion of teachers in
the school who are black. There are a bunch of controls in the model I
won't go into for simplicity sake.
I am trying to make inferences of the following form. If I move a black
student from a school with a low proportion of black teachers (LOZ) to a
school with a high proportion of black teachers (HIZ), all else equal,
will this partially close the black-white gap (i.e., raise this student's
chance of being positive on the dependent variable, i.e., graduate)?
This seems to me to be a unit-specific question, but I am not sure.
I am also interested in inferring whether the difference between two
schools' black-white gaps in graduation rates is owing to differences in
the proportion of teachers who are black. This seems to be a
population-average question, but I am not sure.
Finally, as I am estimating lots of models on this dependent variable,
as well as many models on other dependent variables, I am loathe to
present both sets of coefficients for every single model. So, if the two
variants above are really about different types of coefficients, is it
possible to just present one set and make appropriate inferences?
SO, I have three questions. First, what is the appropriate set of
parameter estimates to answer the question about "moving a
student"? Second, what is the appropriate set of parameter estimates to
answer the question about "school differences"? Third, if each question
requires a different set of parameter estimates, but one can present only
one set, which set should one present assuming both questions are equally
important?
Any comments, guidance, answers with explanations, pointers to literature,
or any other assistance is greatly appreciated.
Thanks a bunch.
Sam
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