We tried the following code: ... VARIABLE: NAMES ARE it1-it40; CATEGORICAL ARE it1-it40; ANALYSIS: TYPE = GENERAL; ESTIMATOR = MLR; LINK = LOGIT; MODEL: th1 BY it1-it20* (p1-p20); th2 BY it21-it40* (p21-p40); th0 BY th1-th2* (lamb); th1-th2@.5 [th1-th2@0]; [th0@0]; th0@1; ....
But constraining [th0@0] and th0@1 is not what we want! We want to freely estimate those parameters while constraining mean(threshold) = 0, var (threshold) = 1, and th1-th2@*.5 (ev) such that ev = 1-lamb^2 (i.e., constrain the residual variance).
We tried adding a model constraint line for the latter:
MODEL: th1-th2@*.5 (ev); MODEL CONSTRAINT: ev = 1-lamb^2;
but Mplus complained and forced all of the item loadings to be 1. We would appreciate if you could give us some advice on this issue.