I am working with a data set to model student performance with various variables from the class/school/district/provincial level. Student performance is extremely low though--~70% of reading performance scores are 0.

I have no experience working with non-parametric models, but assume I should use one for this non-normal distribution. I am playing around with a logit model and using a above/below threshold for student performance.

What other models should I explore with this kind of data?