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I am trying to understand how a regression of a categorical variable which is also a predictor of a latent variable is modeled. Letting Y be the latent variable formed by LS1LS5, if I include the autoregression “LS2 ON LS1” with parameter beta, does Mplus include it in the model as follows? LS2* = lambda2 nu + beta LS1 + epsilon2, such that Pr(LS2 >= k  nu, LS1) = F[(tau_ik – beta LS1 – lambda2 nu)theta_2^{1/2}] In particular I’m concerned about whether beta*LS1 enters into the probability function, because the predicted factor scores do not change when I change the fixed value of beta (“LS2 ON LS1@1” vs. “LS2 ON LS1@3” holding all other parameters constant). ANALYSIS: ESTIMATOR IS WLSMV; PARAMETERIZATION = THETA; MODEL: Y by LS1LS5 @1; LS2 ON LS1 @ 1; ! LS2 ON LS1 @ 3; [LS1$1LS5$1 @ 3]; [LS1$2LS5$2 @ 2]; [LS1$3LS5$3 @ 1]; [LS1$4LS5$4 @ 0]; [LS1$5LS5$5 @ 1]; [LS1$6LS5$6 @ 2]; [Y@0]; Y@1; 


You are correct in your assumption of the modeling when your estimator is ML. In contrast, with WLSMV "LS1" is replaced by its latent response variable "LS1*". I assume your "nu" is the factor (eta). Regarding the factor scores, Appendix 11 of the Tech appendix for Version 2 (see our web site) shows that conditional independence of y  eta is assumed. Therefore the factor scores cannot be computed correctly for your model using WLSMV. You can try ML or you can rewrite the model by letting a new factor influence the two items that you want to have related beyond the original factor. 

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