I’m trying to perform a multi-group factor analysis where the number of response categories differs between groups (G1: 4 response options; G2: 8 response options). Obviously the standard multi-group set up does not allow different response scales. On the other hand, the “known-class” option gives ML estimates for both groups. However, the results look weird as some (non existing) thresholds in the group with the 4 point response options where fixed by the program to some arbitrary values. Mplus gives me the following warning:
ONE OR MORE PARAMETERS WERE FIXED TO AVOID SINGULARITY OF THE INFORMATION MATRIX. THE SINGULARITY IS MOST LIKELY BECAUSE THE MODEL IS NOT IDENTIFIED, OR BECAUSE OF EMPTY CELLS IN THE JOINT DISTRIBUTION OF THE CATEGORICAL VARIABLES IN THE MODEL. THE FOLLOWING PARAMETERS WERE FIXED: 14 15 16 21 22 23 28 29 30 34 36 37 20 27 13 33
I’m wondering whether the results for the freely estimated thresholds given by the program are trustworthy. In order to check the results I have analyzed the 4 point group separately. After I have fixed the thresholds to those values estimated in the multi-group analyses the loglikelihood did not change too much as compared to a model where I have freely estimated the threshold parameters. The loglikelihoods where not the same, however. Are there any other possibilities to conduct such multi-group factor analyses with categorical indicators in Mplus?