We are performing three individual LCAs at 3 measurement points (9 categorical items), and find the that a 3 class solution fits the data best at all measurement points. The classes look similar.
We want to perform a test of measurement invariance on these 3 classes over 3 measurement points now. However, we are unable to find examples of MPLUS syntax for this (neither in the videos/tutorials nor in the forum). Our understanding is that checking for measurement invariance is required in order to then perform LTA and predict class change by covariates.
Do you know of an example syntax? Or would you even recommend a different approach?
Measurement invariance is shown in Example 8.14, for example, by the equality of the thresholds. To test these equalities, use MODEL TEST. One should not do difference testing with mixtures because the classes will change.