These parameters are not the same so if they would be identified if they are free, a modificaton index will be given for them. For example, a reciprocal interaction model would have both a ON b and b ON a.
Y2, Y3 and Y4 are correlated, and our rationale suggests that Y2 -Y4 better be used as indicators of an underlying latent construct rather than being separately used in the equation 1. We run the following (model 2)
Y1 = f(X1, eta) eta BY Y2, Y3, Y4 eta ON X5
where Y1 is binary and Y2 -Y4 are ordered categorical. X’s are vector of strictly exogenous variables.
Model 2 uses x5 which is not part of Model 1, so the models are difficult to compare.
In Model 2 y2-y4 are correlated even conditional on the covariates. This is because you have a residual variance in eta. The default for Model 1 should give residual correlations for the y's as well so I don't understand how you get non-zero MI's for those correlations. But if your Model 1 indeed has zero residual corr's for the y's, Model 1 is therefore quite different from Model 2.