I am interested in fitting a dynamic panel model in the form of a random effects logistic regression logit P(s(t,i) = 1) for time t and subject i. The regression equation for this logistic equation is to include lagged values: so it would be P(s(t,i) = 1) = BX + u(i) + s(t-1,i). U(i) are the patient level random effects, and s(t-1,u) is response at prior time. Two questions in this regard:
Would you find it better to include s(t-1,i), the actual value at time t-1 as the lag, or s*(t-1,i) which would be the underlying latent value as the lag, using the latent value formulation in a logistic regression.
I am planning to re-express this dynamic panel model into a SEM model and estimate it using Full Information Maximum Likelihood. It seems to me expressing the logistic regressions in the latent value formulation is the approach that will best fit in a SEM context. I am not sure the other approach (actual values) is possible or desirable. Thank you very much for your insight.