Spurious Latent Classes in the Mixture Rasch Model
The mixture Rasch model (MRM) takes latent class into the original Rasch model. It helps to analyze and interpret some important and meaningful psychometric phenomena, such like difference in strategy use. However, spurious latent classes would be detected if responses are not from MRM but from the other models (2PL or 3PL) when data still be analyzed by MRM. In such situation, we may extract some more latent class due to some misfit items. The authors analyzed an empirical data and implemented three simulations to depict above related issues. Results for the empirical study show that MRM detected two classes after abandon under-fit items from the data. Results for the simulations illustrate that 2 or more than 2 classes of MRM have better fit than one-class Rasch model due to responses might come from other IRT models. Particularly, when sample size is sufficiently large, only one non-Rasch item with a discrimination parameter of 2.5 would result in second latent class in MRM.
Sharing, Question and Future study:
1) The design and the results of simulation 3 are not easy to catch up.
2) From equation (1), MRM is quite simple and easy to be understood. When responses not just involve item difficulty and person ability but also are related to specific latent class. We can choose MRM which add group property into item difficulty of conventional IRT models. On my opinion, latent class as this paper mentioned, it is like difference on strategy use. It seems like a specific ability belongs to person. Can we attribute it to a part of latent trait, like testlet model? Intuitively, it’s easy to do so due to the fact that item and person is opposite, no matter group property belongs to item or person, it should be no difference in aspect of mathematic. However, I’m not sure if it has distribution or scale constrain problem.