Suppose you have a classroom of 10 students. Over the course of 50 weeks, a teacher administers a set of 15 tests to each of the 10 students. Some students are absent during some of the weeks, and other times, some students are not able to complete the same test within the one week. For example, student 1 may do test 5 in week 25, but student 2 may do test 5 in week 24.
The student either passes or fails each exam (so the outcome is binary).
The motivation of the study is to determine the probability of any new student who enters the study, they will pass or fail a certain test, conditioning on what they have done in the past. For example, what is the probability of a student passing test 7 in week 32 given they have completed: test 6 in week 31 (and failed), test 5 in week 26 (passed), did not do test 4, test 3 in week 15 (and passed), etc..
I believe this is a multivariate longitudinal study with missing data? Any suggestions on what this type of experiment is called?