Assessing Item-Level Fit for the DINA Model

• Activity Number: 152
• Type: Invited
• Date/Time: Monday, August 10, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Mental Health Statistics Section
• Author(s): Chun Wang* and Gongjun Xu
• Companies: University of Minnesota and University of Minnesota
• Keywords: chi-square index ; power-divergence index ; posterior predictive model checking ; cognitive diagnosis model ; DINA model

Abstract

This research focuses on developing item level fit checking procedures in the context of diagnostic classification models (DCM), and more specifically for the DINA model. Although there is a growing body of literature discussing model fit checking methods for DCM, the item level fit analysis is not adequately discussed in literature. This study intends to take an initiative to fill in this gap. Two approaches are proposed, one stems from classical goodness-of-fit test statistics coupled with the EM algorithm for model estimation, and the other is the Posterior Predictive Model checking (PPMC) method coupled with the MCMC estimation. For both approaches, the chi-square statistic and a power divergence index are used, along with Stone's (2000) method for considering uncertainty in latent attribute estimation. An extensive simulation study with varying test length, type of misspecification, proportion of misspecification, and correlation level among attributes, is carried out. Results show that both approaches are promising if Stone's correction is imposed, but the classical goodness-of-fit approach has a much higher detection rate than the PPMC method.