This paper showed how violation of assumption of the MRM would result in spurious latent class specification. Using MRM, more classes would be specified if the data is requiring for an IRT model with additional parameter, such as discrimination and guessing parameter. However, theses classes are spurious and it is caused by the misspecification of the model.
To investigate the effect of misspecification of model, this paper used both empirical and simulated studies. Additional parameters in the model, the magnitude of the parameter, and the number of misfit items would lead to detection of spurious latent classes. In other words, it is important to select an appropriate model for the data, otherwise, unexpected results would appear without obvious symbol in the criterions. And the explanation and implication from the results would cause dramatic impacts on practitioners and examinees.
Q:
How to determin which mixture model should be used when analyzing real data?
Future:
1. Investigate the method to correct the MRM when assumption is violated, or when the data could not fit the RASCH model.
2. Find out whether other more sensitive criterion could be used for model selection and detect whether the class numbers is incorrect.
3. What would be the results if other RASCH family models are used to generate the data, instead of dichotomous response.