How to obtain Item Information Curves for the Partial Credit Model?

Question

I have estimated a Partial Credit Model in Stata following Zheng, X. and Rabe-Hesketh, S. (2007) "Estimating parameters of dichotomous and ordinal item response models using gllamm".

I'd like to compute Item Information Curves but I can't figure out how to do it from what I found in Google or in other StackExchange posts.

a) In Ayala's "the theory and practice of IRT" book, pg 200, it is explained that the item information function in the PCM model is obtained as the weighted sum of category information functions. But in the formula for item information function I don't see where do I sum across item category options.

b) Is the item information formula for the Partial Credit model valid for the 2-paramenter version (Generalized Partial Credit Model)? If not, what is the formula for this?

Any guidance would be much appreciated.

Answer 1

Just found out the answer to my questions... In case anyone cares:

a) It seems to me that the "p_xj" element in Ayala's pg 200 formula for item information in the PC model should instead be "p_jk" (as in this paper). In this way, it is clear how the probabilities of choosing each k response category of item j conditional on zeta enters in the equation. It is very likely, however, that I am just misreading Ayala's formula and it does say the same as the referred paper.

b) The formula for the item information under the GPC model is slightly different from the formula for the PC model, as shown in the referred paper. It basically involves multiplying the item information that you would obtain with the PC formula by a², where "a" is the discrimination parameter of the relevant item.