Gabriel Katz writes:

I am currently working on estimation of a latent class via MCMC. The model is an extension of a latent class model for binary data (e.g., Berkoff, Mechelen and Gelman, 2000), for longitudinal data. Specifically, I am analyzing roll-call votes for N legislators over T rollcalls, and am trying to define unobserved indicator variables for legislators (with three latent classes) and rollcalls (two latent classes). The main difficulty I face is that, unlike in standard hierarchical latent class models for longitudinal data (e.g., Vermunt), the structure of the two sets of latent indicators (for legislators and rollcalls) is non-nested. I have not come across with any paper dealing with this kind of non-nested structure, and have doubts about the identification of the two sets of indicator variables. In addition, dealing with the the label-switching problem in this context seems particularly difficult. I was wondering whether you could recommend me relevant literature on Bayesian estimation of this kind of models.

My (brief) reply: We discuss non-nested models in chapter 14 of the ARM book, but I don’t have experience with this specific model. My generic advice for this sort of identification problem is to fit the full, nonidentified model and then define uniquely identified summaries, for example by fixing the signs of the differences between certain selected legislatures.