Passage-related local item dependence and spurious latent classes in the mixture Rasch model : a simulation study

Abstract

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] Mixture Rasch models, which are often used to investigate response strategy difference, differential item functioning, and test speediness, have gained much attention in educational and psychological research recently. Although these models show promise in more in-depth understanding of the latent variables being measured, the determination of the number of latent classes remains a challenging issue. This problem becomes more serious when one of the key underlying assumptions, local item independency is violated. The current simulation study examined the performance of mixture Rasch models in deciding the correct number of latent classes when passage-related local item dependence is present. Three information-based indices, the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Integrated Completed Likelihood (ICL) are used in this study for selecting number of latent classes under a variety of conditions. Results indicate that the ICL selects the correct number of latent classes at all conditions despite the fact that the assumption of local item independence is violated. The BIC is moderately effective under certain conditions. The AIC tends to select the more complex model under most conditions and is considered to be least effective for this use. Among four manipulating factors, the level of testlet effects appeared to be the most influential cause for overextracting latent classes based on the AIC and BIC. The impacts of other factors vary according to which information-based index is used.