How to proceed when collapsing ordinal items with levels that got no answer?

Question

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?

Answer 1

With 9 levels, you can probably treat the indicators as continuous unless there is significant kurtosis in them. If you are modeling the variables as ordinal, then it doesn't matter how you collapse (i.e., if you are preserving symmetry); the ordinal nature of the data means that it's the order of the categories that matters, not the label assigned. You throw away information when you collapse categories, but as long as there is enough information about the participants in other items, your inference should be approximately correct no matter how the binning is done. You don't need all the indicators to be on the same scale; some can have more and different categories than others. It's not the category labels that matter, it's the relative ordering of units for each item.