The paper demonstrated that the traditional mixture Rasch model would suffer getting spurious latent class when data does not follow mixture model. The mixture Rasch model is exploratory method, so three simulation studies were conducted to investigate when and why spurious latent class(es) emerge. Program WINMIRA 2011 was used for parameter estimation and AIC, BIC, and SBIC for model comparison.
Simulation one was conducted to show the fit the data generated from 2PLM by MRM would generate spurious latent class, but more sample size and items are required. Author conjectured the phenomena is caused by underfit items. Simulation two was conducted to investigate the need of items required to cause spurious latent class. High discrimination items would lead to spurious latent class, so it needs to consider the reverse condition when mixture 2PLM fits to data generated by MRM model. Two-class solution were obtained in all conditions. So no spurious latent class would occur.
Questions:
1. The underfit items were found out under the assumption that the MRMR with fewer latent classes is the true model. But we never know the true model. Although it is evident the spurious latent class exists, selecting the underfit items is critical.
2. The paper just showed us the potential of spurious latent class. Is it no solution to develop new model to prevent this problem?
3. It notes that MRM fits to data generated by 2PLM would lead spurious latent class. In practice, why not fit data by 2PLM or 3PLM initially instead of by MRM?
4. Large sample size is required to see striking evidence when non-Rasch items exist, what can we do with small data set in case?
5. When data were actually generated by MRM, assumed some items are of high discrimination parameter, is it possible to generate spurious latent class even we use the right model, MRM?