Given multi-level data, I'm interested in estimating member-level outcomes when only group-level outcomes, along with both group- and member-level predictors, are known. I'm lacking in statistical terminology, so I'll explain with an example:
We'd like to estimate the likelihood that a given high school student will be granted college admission. In this case, "groups" will be schools and "members" will be students. We have:
- Aggregated, group-level data on the dependent variable (total number of accepted/rejected applications from each high school)
- Aggregated, group-level independent variables for each school (number of students who have taken at least three advanced/honors courses, distribution of GPA, number of students in the top 10% of standardized test scores, etc.)
- The same independent variables at the member/individual level (for each student, whether he/she has taken at least three advanced/honors courses, actual GPA, whether they scored in the top 10% on a standardized test, etc.)
What we're lacking, however, is member-level outcome data on college admission (for each student, whether he/she was admitted to college).
Intuitively, I get the sense that some estimation may be made for group members even in absence of this individual-level outcome data: we may see, for instance, that schools with high proportions of students taking at least three advanced/honors courses have correspondingly high acceptance rates. It makes sense that, knowing this, a student's likelihood of being granted college admission should be positively influenced by whether he/she has taken at least three advanced/honors courses (possibly along with other, group-level effects).
Is it possible, then, to model group-level outcomes and apply those models to individual cases to estimate individual-level probabilities? If so, what terminology describes this type of model? Any pointers to literature on this topic would be appreciated as well.