Does identifiability matter for residual structure?

I’m in the process of constructing a functional data ANOVA model and I want to include both random intercept and AR(1) terms to account for within-unit correlations. I want to use this model because it contains the random-intercept model as a special case and the posterior simulations look very similar to the original data. This model is “non-identifiable” since any random intercept can roughly be modelled by the AR(1) term, but if inference is concerned only with the group means is it okay to use this model?

I don’t really care about the parameter values of the AR(1) process or the random intercept distribution, I just want to account for the correlation observed in the functional observations.

Since nobody else answered, I will give it a try, though I am not an expert.

In my opinion, non-identifiability is always a risk. At best you get a very correlated posterior and lower sampling efficiency, at worst your inferences might be nonsense for all parameters due to poor exploration (but the n_eff and Rhat diagnostics should signal that)

I would suggest you try to reformulate the model to make it identifiable but retain the flexibility you need. I didn’t get the exact form of the model from your post, so maybe if you add more details on the model and its motivation, I can try to speculate on possible steps forward.

Hope that helps

I don’t get the model, but a random intercept and AR1 effect are identified so long as there is some AR1 effect…

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