Does this cross-lagged panel model account for non-independence of observations? I have estimated a cross-lagged panel model using Stata's SEM builder as I am concerned about potential reverse causation. Each individual has measures of mh and pf at three timepoints, and so we would expect that these measures are correlated within each individual over time. I have correlated the error terms as per other examples I have seen. See diagram:

(A) Does the cross-lagged panel model I have specified account for the non-independence of observations within each individual?
(B) If yes, what is the statistical reasoning behind this? And if not, how can I change the model to account for non-independence?

This is an excellent question, and the answer is not very well understood by many researchers. Your model includes contemporaneous correlations among measured variables, but it does not account for any stable factors. To do this you need to have a latent variable for each data variable series. The implications and meaning of such Between-person parts of CLPMs is discussed extensively in Zyphur et al. (2020) parts one and two (here and here).
