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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:

  1. 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.

  2. 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.

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  1. Depends on the nature of the question. Adjusting for an observed lag has advantages such as allowing for real-time prediction and estimating more easily interpretable effects. One confusing bit is that a latent variable usually considers 2 or more manifest / endogenous variables. Here s(t-1, i) is the only such variable. However, if s(t-1, i) is measured with error, an instrumental variables model might improve precision by considering s*(t-1,i) as a latent lagged effect.

  2. They are really quite similar, in fact the two models are too nearly equivalent to be worth conducting separate analyses. Focus on the scientific question of the model and choose either the logistic regression or SEM as a prespecified analysis.

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  • $\begingroup$ Thank you; I will do a SEM. However, just in case, for #2 I would like to clarify that the distinction I am interested is between using s* or s as the lag (not between using dynamic panel model estimation vs SEM). $\endgroup$ – HRD27891 Aug 29 '17 at 21:20

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