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  • Sequential Logit or similar with multiple paths / transition possibilities

    I have 10 different states of interest.
    People have a set number of chronic conditions. In the simplest model, I am interested in how people transition from one disease count to the next.
    People can have x = {0,1,...,9} number of conditions. People can move 0-1-2-3-4-5, but also 0-1-4-5, or 0-4-2-3-5 (because their disease count can decrease in a particular version of the example that allows for recovery).

    A sequential logit, as is, does not seem appropriate because people have to move through specified paths (e.g. 0:1 2 3; 1:2 3; 2:3).
    If I want to model the transition probabilities between each state, is there some joint procedure available? It would seem to me that there are 1024 (2^10) possible transitions to estimate in this case?

  • #2
    The reversion of the sequencing makes your model more tricky.
    What if you recode the transitions and use multinomial logit?
    For example, the transition from 0 to 1 is 1, the transition from 1 to 2 is 2, the transition from 0 to 2 is 3. But also, the reverse, that is, the transition from 2 to 1 is 3, the transition from 2 to 0 is 4, and so on. I guess you then could use multinomial logit (or a form of logit depending on categorical (not ordered) data. However, as you note, this will increase the number of alternatives considerably.
    May I ask, since you aim to estimate transition probabilities, does your dataset allow you to track individuals over time?

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    • #3
      Sorry missed that detail. Yes, it is a panel dataset with multiple possibilities of states within ID across t.

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