I have a set of 8 Likert-type items with 9 levels each. In no case do we have an item for which responses fill all possibilities and this has shown to be an issue for the SEM I'm trying to run (as well as previous imputation step).
From what I've read, in this situation one must collapse empty levels. My question is, how to go about doing this?
For example, if I'm only missing a 1 in the 1-9 scale, I would need to collapse levels 1 and 2. But should I also do that with levels 8 and 9 to preserve "symmetry"?
If instead of a 1 it was a 2 that's missing, I suppose the decision of collapsing 2 with 1 or 3 would be up to the researcher?
Also, since all these items are supposed to measure the same latent variable, do I need to set them all to the minimum number of possible levels or is it okay if I keep more levels for items that had enough answers?