Is it possible to fit a Graded Response Model in Stata?

[Jose Vila]

I've been reading about Item Response Theory during the past few weeks and I'd like to use it to examine how my scales are functioning. The response categories are ordinal. If I understood well, the Graded Response Model is particularly appealing because it is more flexible than other alternatives such as the Partial Credit Model or the Rating Scale Model, providing different "difficulty" parameters per category within each item, and different "discrimination" parameters for each item. Moreover, I'm confident that the response categories are ordered (expressing different degrees of agreement with a statement) so cumulative logit rather than adjacent category models seem adequate. (I might be wrong in various parts of this reasoning though!).

1) Is there a way to fit Graded Response Models in Stata 13, maybe using the gsem command or gsem builder? If so, can anyone shed light on how to do it and how to process the outputs to draw Category Response Curves, Item Information Functions and Standard Error of Measurement function for the scale?

2) If it is not possible to do it with gsem, is it possible to do it with gllamm? In this article it is explained how to fit PCM and RSM but not Graded Response Models. This post suggests it is possible to do it with the thresh() option, in order to relax the proportional odds assumption/constraint, but I have no clue about what to put inside the thresh() option. It seems I have to define equations for the thresholds; any clues about what it means or how to do it would be much appreciated.

3) My final question is a conceptual one: If I understood well, the Graded Response Model gives a "discrimination" parameter for each item and C-1 "difficulty" parameters for the C response categories. Is there a model which provides different "discrimination" parameters for each response category as well? Would this be a nominal model? Why is it reasonable to constrain discrimination parameters to be equal for different response categories of an item? (maybe this is not really a "constraint"?)

4) Can anyone explain the difference between the Graded Response Model and a Generalised Graded Response Model?

[Dimitriy V. Masterov]

Cross-posted at http://stats.stackexchange.com/quest...model-in-stata.

[Nick Cox]

Otherwise put, our policy on cross-posting is that you are asked to tell us about it. This is explicit in the FAQ Advice all members are asked to read before posting.

[Jose Vila]

My apologies, I didn´t read the FAQ Advice (just read it!)

[Mike Lacy]

A Google search on /Stata "graded response"/ yield 248 hits, of which one promising one might be:
http://journals.lww.com/optvissci/Ab...ory_to.10.aspx

[Jose Vila]

Many thanks Mike, the paper you suggested is very interesting indeed. Luckily, my case is simpler because I don't have several time points, so I guess that if I use gllamm I will have to model my data as having two levels (persons and their responses) instead of three. In addition, I'm mostly interested in finding out whether the scales we used allow to discriminate well across the entire range of the latent trait, or where do they fail to do so.

This reading confirms some of my preliminary ideas: an advantage of using a graded response model is that it is based on cumulative logits instead of adjacent category logits (as in Partial Credit and other Rasch models), which seems to be more efficient. Also, they use the gllamm command, which confirms that it is possible to fit complex IRT models with this command.

On the other hand, it also leaves me a bit more confused with respect to the differences between various IRT models. They say they use a "restricted graded response model", and by the word "restricted" it seems they mean that "threshold steps" (the distance between categories within each item along the latent variable) is constrained to be equal across all items. In this context, they have just one "difficulty parameter" per each item, which gives the overall position of the categories of each item. But, strikingly for me, they do not have "discrimination parameters" in their model (slopes, conceptually equivalent to factor loadings). Other authors, such as Bryce B. Reeve, say that the "graded response model" is characterised by allowing discrimination parameters to vary across items (unlike the partial credit and rating scale models).

I guess that finding out exactly which IRT model(s) are best for my purposes will be helpful. I'm pressuming that I want to have discrimination parameters in my model, but I'll be happy to hear arguments for not needing them! In the meanwhile, I'll see if Mark Wilson's "On Choosing a Model for Measuring" paper helps me clarifying this. In my first post, I was assuming that I rather use a very flexible model instead of models which impose restrictions, specially given that I have a large sample. Any guidance in this regard will be much appreciated.

[Philip Matthews]

Jose, in case it might be of help: a very useful (and technically thorough) account of various IRT models is to be found in de Ayala, R. J. The Theory and Practice of Item Response Theory. The Guilford Press, New York, 2009. Chapter 8 discuss the graded response model and its relation to other models.

[Jose Vila]

Thanks Philip! I was wondering which book to get, that one looks like a good candidate.