Unlike in the dichotomous model, it seems that nominal models are oblivious to which choice is the correct answer at any given item. However, I'd like to make sure that, as $theta\to\infty$, the correct choice gets assigned the highest probability. Is there some way of setting this constrain in the common R packages (mirt, TAM)? Is there some way of passing information about the correct answer to this kind of model?

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    $\begingroup$ Sure, just fix the associated scoring coefficients required for identification such that the highest is the highest category. I'm not sure what parameterization TAM uses, but doing something like this in mirt is pretty straightforward. You might also want to look into hybrid models, like the nested-logit IRT model, which combine correct-incorrect scoring with nominal response models. $\endgroup$ – philchalmers Oct 23 '19 at 0:21

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