Hi, I hope you are well. I am trying to fit a NRM model with items having 4 options using the "Nominal Are" option in Mplus. I am modeling the 3 response option with the reference one being the correct response (I have recoded the data). I am modeling the first response options' slope with a (*) and all intercepts in brackets. I have a couple of questions:
1. Am I correct in assuming that the slopes and intercepts I am getting in the output are specific of the three distractors? Do I interpret the intercepts as e.g. differences in ability between individuals who select this distractor compared to the correct response or are these intercepts mean ability levels of individuals selecting that distractor?
2. If I use a two factor model with the second factor being another group, for potentially testing differences between groups, do I need to constrain the correlation between the two factors to zero?
3. If the two factors define two different populations do I need to set for both populations the variances to one and the means to zero?
1. The parameterization and its interpretation is that of a regular multinomial logistic regression model. This is also described in chapter 4 of the new Handbook of IRT, Vol 1, edited by van der Linden. It refers back to Bock's 1972 article in Psychometrika.
2. I don't know what you mean by "the second factor being another group". Perhaps you mean a second set of items. The factor correlation does not have to be zero.
3. I don't know how two factors can define two different populations if by population you mean a set of subjects. But perhaps you refer to a population of items (an item bank).