I have the observed means for class j, school m and subject k (some schools have less classes and less exams/students), and additionally the number of students and exams for each of them. I want the distribution of individual scores for class j and school m. I don’t care about the outcomes from specific students (there can be imbalances across students in terms of number of exams taken). I only care about the variation of these individual scores, and the variation in higher levels of the hierarchy.
I am approaching this with a mixture because this distribution of Y_{jm} is clearly multi-modal given by the different subjects.