I have a large dataset on children's test scores through time (so test scores nested in child).

The test scores are integer-valued from 0 to 15. Like many test scores, the scores I have are skewed & cannot be transformed adequately into a normal distribution. The obvious option to me was to categorise the scores and carry out a ML ordinal regression- but then I wondered whether a ML poisson regression might also be appropriate, as I could see that the scores were perhaps "counts" of the questions the children got right, all done in the same time frame, and the scores are integers.

I've consulted some textbooks, but the only examples I've come across are "counts of events" based, and I've also not come across others using Poisson regression in this way. One potential problem I thought that may exist was that the "counts" may not be independent from each other, in that getting one question correct might directly increase the probability of getting the next one correct. However, after much thought, I decided this is unlikely as the physical task of answering a question correctly will not make you answer the next one correctly (i.e., it should solely be dependent on other covariates like IQ or school attendance).

Could I use a Poisson multilevel regression in this context? Any advise on this issue would be greatly appreciated.