Nominal response model in MIRT

[Jonas Dockx]

Last week I've been trying to fit some nominal response models (NRM, Bock, 1972) with both MIRT & Mplus. Both do this well, with the MIRT-package having the advantage in producing nice plots of the estimated response probabilities conditional on the latent variable. However, I seem to be on the wrong track in interpreting the ak0, ak1, ak2, ... and d0, d1, d2,... parameter values in MIRT. I was initially under the impression that the models I was fitting had the following form:

 

So I used the estimated parameter values from MIRT as this: 

However, when calculating the probabilities using these parameter values they are quite a bit off from what I see on the MIRT-plots using itemfit and what I calculate with the Mplus parameter values. The MIRT-plots using itemfit and what I calculate with the estimated Mplus parameter values are in agreement though. This makes me suspect that the model used for NRM in MIRT may not be what I thought it was. For there certainly are different ways to define such a model. Unfortunately, I cannot find any documentation of the exact NRM used within MIRT? Is there any information somewhere on the NRM used in MIRT?

[Phil Chalmers]

Hi Jonas,

What you're referring to is the classical nominal response model formulation by Bock 1972, which doesn't generalize too well to multidimensional models. mirt uses the form z = d + a1 * ak * theta, where the ak terms serve as 'scoring' coefs (indicate the ordering of the categories) while the a1 represents the overall slope parameter across all categories. 

Perhaps play around with the itemplot(shiny=TRUE) interface to get a feel for the nominal model. Also, if you use coef(model, IRTpars = TRUE) then you'll obtain this more traditional parametrization, which seems like what you're after anyway. HTH.

Phil

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