for a prospective study of parameters affecting student's success in graduate school I am looking at a population of about 1500 med students. I have performed a cluster analysis (using Gower's universal similarity index and average linking) showing that students fall into 3 main groups (at ~ 0.2), each with several subgroups (at ~ 0.8). Clustering correlates poorly with study success and with any of the other parameters.
Normally, I'd perform a PCA in the hope of uncovering hidden variables that determine clustering. However, about 1/3 of the students fail the course at various time-points, so that there are a lot of missing data. To make matters worse, student performance at various exams (e.g., NBME Step1 and Step2) is only weakly correlated (r^2 ~ 0.3), so "filling" the table with calculated values would be questionable. Unfortunately, standard PCA reacts "poorly" to missing data.
I should add that the parameters are a mix of nominal, binary, ordinal and rational variables.
Any help would be much appreciated.