Hello, I am running a SEM-Modell with 5 categorical items at each timepoint, 2 timepoints of measurement and 3 latent variables (2 states and 1 trait). I would like to account for measurement invariance. Therefore I set equal factor loadings between the timepoints (congeneric model, first loading fixed to 1) and the intercepts are per default fixed to zero (thus, equal). Because I am regarding only the covariance structur (no means), it is not possible in MPlus to set the thresholds equal. Is the threshold equality neccessary to have measurement invariance? Or is the metric invariance (equal factor loadings) and scalar invariance (equal intercepts) sufficient? Thanks a lot Tony
With categorical outcomes, I would consider both thresholds and factor loadings while testing for measurement invariance. See Chapter 13 after the multiple group discussion for the models to be considered when testing for measurement invariance. Examples 5.16 and 5.17 show partial measurement invariance for categorical outcomes. These examples are for multiple groups but the same principles apply across time.
I do not believe that measurement invariance with categorical outcomes should exclude the thresholds. The s-shaped item characteristic curves that are the essence of categorical data modeling depend on both the threshold and the factor loading. Measurement invariance for categorical outcomes should consider both of these in tandem.
Your input looks correct. But check TECH1 and the results to be sure that the proper equalities are there.