I was wondering whether someone has a suggestion on how to create a unidimensional IRT model where item pairs (on symptoms) are conditional so that the one item asks about the presence of a symptom (Yes/No) and the other about the severity of the endorsed item (on a 5-step scale).
Conceivably reporting a symptom but rating the lowest severity could be indistinguishable on the latent trait from the "No" response, but how can I test this?
If I combine the item pairs into items with 6 response options, will a nominal model do the trick? Or -- assuming that symptom and severity items measure the same thing -- should I just use all variables in a Graded Response Model, accepting the systematic missingness, and compare a parameters for the item pairs? In the latter case the dependence isn't modelled in any way.
Thank you all for your thoughtful responses. I'm summarizing what I learned in case someone later stumbles upon this discussion.
I believe latent response modelling is a way of making explicit our assumptions about how the world and our "instruments" interact, and in addition to make them plausible. Latent models can also be argued to simplify our data, in finding the common factor driving responses. Furthermore, for science to be replicable and cumulative, we have to operationalize and quantify, even though it may currently be inferior to intuitive understanding.
Most of the literature suggested was unfortunately not applicable, as it pertained to, for instance, (1) local dependence between items, but not missingness dependent on the other item, (2) "hierarchical" as in second-order latent factor models, or (3) multidimensional IRT models (MIRT).
Phil Chalmers, the author of the mirt package for R, responded on the forum for that tool:
"I think you are correct that merging these two-stimulus questions into one is the best approach to avoid the use of NA's. Otherwise, the MAR assumption would be violated if the dataset contained NA's where participants reported no symptoms present (i.e., it is more likely to see an NA for low participants than high participants, which violates independence). I think an ordinal/graded model should be just fine; no need for a nominal model unless you are really worried about category ordering and wanted to verify."
I tried the nominal model, and the order between strongly disagree vs. disagree re distress was indeed indistinguishable for many items, suggesting that they could be collapsed, and a graded model applied.
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