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Thanks, I checked several books as well as Kenny's website, they never discussed this exact issue of comparing just-identified and overidentified models.
@TrungDung I used Mplus software and created plots manually. The above plot used thinning of 100 and it didn't help either. Do you think it's fine to have an autocorrelation of .6 or higher? The closer look at the chains shows estimates between .8 and 1.6 for different chains, which is quite a lot substantively.