I have a situation of repeated measures SEM -- two sets of a four-factor / 32-item measure. All items are censored (a). The measurement model with longitudinal measurement invariance converges fairly easily. A regression model (Time 2 factors regressed on Time 1 factors, and all regressed on a covariate) does not converge, after many attempts and variations.
With continuous indicators, I would covary residuals across time for each specific item. That, of course, isn't permitted with censored items.
Is there a way around that limitation? Any other suggestions?