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Markov Model Problem

B

Beanny

Member
Hi All

I want to set up a Markov-type model to model leaving rates in each year of a uni degree course.

The model should have the state space S = {1,2,3,P,W} where the numbers indicate the year of the course, P represents the completion of the course and W represents withdrawn from the course.

Transitions are possible from state 1 to 2, from 2 to 3 and from 3 to P, as long as the student passes the exams at the end of each year. Conversely, if the student fails the exam in any year they will be withdrawn from the course. This would need a discrete time model with time period of one year.

However, students may also voluntarily drop out of the course at any time. This would need a continuous time model.

The problem is: how do I combine the discrete and continuous models without making any simplifying assumptions, i.e. I want to be able to model the overall rate of leaving and hence calculate the overall probability of leaving, without treating the models separately.

I'm thinking there could be some type of Markov model (perhaps outside the syllabus) that will let me do this.

Thanks for your time.
 
Markov model

Are you sure you need to combine chain and jump? I think you might be able to do this with a Mkv chain quite happily. When you get to the end of the year, some people have moved up a level and some have gone to W. Does it matter when they went there?

In the same way, in an NCD system, some people will move down a discount level at the end of the year (December say) when they renew their policy. Does it matter that they crashed their car in February and have known for 10 months where they will end up?

John
 
Thanks for the speedy response.

I see what you mean by modelling this as a Markov chain instead. I guess the exact timings of the departures won't affect the overall results.

However, if they were important and a jump model were used instead, would this require assumptions such as contant forces of transition or distributions of the transitions being uniform over the year? This would seem unrealistic as there is likely to be a larger number of withdrawals at the time the exam results are released, compared to the rest of the year.
 
Markov model

You could have 2 states of people who have left, one for those leaving at the time of the exam results and one for people just leaving generally over the year.

I think you would still model where everyone is using a Markov chain and have the people leaving generally over the year's timing modelled as a separate uniform distribution.

John
 
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