I am currently fitting moderated nonlinear factor analysis models to assess measurement invariance of categorical indicators. I have one latent factor with 10 categorical indicators. I am allowing the mean and variance of DEP to vary by a categorical covariate (we can use gender as an example). I am having trouble assessing measurement invariance of indicator thresholds. Currently, I am able to allow the indicator intercepts to vary as a function of the covariate with the following statement:
Item_01 ON gender
However, given ordinal indicators I would prefer to assess measurement invariance of the indicator thresholds instead of the indicator intercepts. I tried:
[item_01$1] ON gender (this is only one of the thresholds, and I would like to allow all thresholds to vary)
But the program does not appear to recognize the threshold as a parameter which can be specified along with an ON statement. Is it possible to add non-linear constraints such as this, to the item thresholds in the model?
One solution we found was to use a multiple group setup, allowing thresholds to vary across groups. However, if it were possible we would prefer to use the moderated non-linear factor analysis framework as opposed to moving into the multiple group framework.
I have added gender to the constraint statement: constraint = gender;
I labeled the threshold parameter [item_01$1] (thresh);
Finally, I added the model constraint, defining new parameters and specifying the threshold as a function of new paramters and the observed gender variable. Model Constraint: NEW (a b2); thresh = a + b2*gender;
I receive the following error: *** FATAL ERROR THIS MODEL IS NOT AVAILABLE.
Am I missing something in my code? Or is there something about the thresholds that is no allowing those to be constrained? I have other constraints on the factor loading and latent variable variance.