Assessing Item-Level Fit for the DINA Model. (October 2015)

• Record Type: Journal Article
• Authors: Wang, Chun; Shu, Zhan; Shang, Zhuoran; Xu, Gongjun
• Is Part Of: Applied psychological measurement. Volume 39:Number 7(2015)
• Page Start: 525
• Page End: 538
• Publication Date: 2015-10
• Subjects: DINA model -- chi-square index -- power-divergence index -- posterior predictive model checking -- false positive rate -- correct detection rate; Psychometrics -- Periodicals; Psychological tests -- Periodicals; Psychology, Applied -- Periodicals; 150.1519505
• DOI: 10.1177/0146621615583050
• Languages: English
• ISSNs: 0146-6216

Abstract

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.