how to understand dichotomized issues

[mikedecr]

Hi there,

I'm doing some similar modeling for a project of mine, and I'm curious how you manage ordered items. It looks like the following function creates indicators from ordered variables

dgo/R/dichotomize_item_responses.r

Line 4 in 2961b5b

# For item response variables with K ordered levels, make K - 1 indicators for

but I'm just curious how to understand how this reacts with modeling of item parameters. Seems plausible that a set of K-1 indicators might have correlated item parameters between any two levels k and k', but it looks also like you have independent priors for all items. Am I understanding this correctly? I'm curious about how to deal with ordered multichotomous items in my own situation so just wondering how you view this in the broader picture. Thanks!

[devincaughey]

Hi Mike!

Sorry for the delayed and brief reply. From what I can tell, your understanding of what dgirt does is perfectly correct. You are also correct to note that its approach treats the discrimination parameters corresponding to different levels of the same item as a priori independent. This is probably not optimal, but it generally works fine in practice because there is usually more than enough information to estimate the discrimination parameters quite precisely. An alternative way to handle polychotomous ordered variables is implemented in the mgirt branch of dgo, which implements an ordinal version of the group-level IRT model. (Ordinal IRT is equivalent to forcing all levels of the same variable to have the same discrimination parameter.) Chris Warshaw's and my article with Tom O'Grady uses this model (see here for replication files). We have continued to work on this approach in the modgirt_dev branch, which theoretically subsumes and could ultimately replace the dichotomous version of the model implemented in the master branch.

Hope this helps!
Devin