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.