I’m fielding a query from a colleague who is interested in modeling survivorship over time as a function of a latent trait that is estimated as a random effect.
As an example, imagine that we first estimate the latent ability of person j in the context of an item-response model. Estimated as a random effect in rstan, can that θ then be inserted into a likelihood function predicting survivorship (as a discrete-time event history model). Using brms code for shorthand (and excluding other predictors), that model would look something like:
brm (survival ~ theta[j], family = bernoulli)
where “theta” is the random effect for person j.
This modeling strategy would put a beta parameter on theta[j], which is not something I have seen often. Are there pitfalls to this approach?
(This assumes that the IRT model and the event history model are estimated simultaneously in the context of a single rstan model.)