This research focuses on developing item-level fit checking procedures in the context of diagnostic classification models (DCMs), and more specifically for the “Deterministic Input; Noisy ‘And’ gate” (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 Expectation-Maximization algorithm for model estimation, and the other is the posterior predictive model checking (PPMC) method coupled with the Markov chain Monte Carlo estimation. For both approaches, the chi-square statistic and a power-divergence index are considered, along with Stone’s method for considering uncertainty in latent attribute estimation. A simulation study with varying manipulated factors is carried out. Results show that both approaches are promising if Stone’s method is imposed, but the classical goodness-of-fit approach has a much higher detection rate (i.e., proportion of misfit items that are correctly detected) than the PPMC method.
Bibliographical noteFunding Information:
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This project is partially supported by 2010 CTB/McGraw-Hill R&D research grant.
© 2015, © The Author(s) 2015.
Copyright 2015 Elsevier B.V., All rights reserved.
- DINA model
- chi-square index
- correct detection rate
- false positive rate
- posterior predictive model checking
- power-divergence index