For a research project that I am working on, I need to predict the probability of the occurrence of a certain event.
To be more precise, I need to predict the probability of a student submitting any solution to a certain assignment (Y) or not (N).
The only thing that I have to help me is data from previous years in this form:
Student 1 – Y Y Y Y N Y Y Y Student 2 – N N N Y Y Y Y N …
Each line represents one student and the columns represent the ordered list of assignments (Y- the student has submitted at leat one solution for that assignment), (N – the student hasn’t submitted any solution for that assignment)
Given a certain sequence of events, I need to calculate the probability of the next event. For instance:
If in the first three assignments the student had one of the following behavior, what will happen for assignment number 4?
Y N Y ? N N N ? Y Y Y ? …
I’ve already calculated the probabilities based on the overall occurrence of a Y or N for a given assignment. I’ve also calculated the probability of the occurrence of a Y after an N, and a Y after a Y, and so on… I’ve also developed a method to determine the probability using a Markov Chain... However, I am not sure which method is the most "scientifically fitted" for this kind of problem…
Any suggestions will be very welcome.