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Evaluating the Wald Test for Item‐Level Comparison of Saturated and Reduced Models in Cognitive Diagnosis
Author(s) -
Torre Jimmy,
Lee YoungSun
Publication year - 2013
Publication title -
journal of educational measurement
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.917
H-Index - 47
eISSN - 1745-3984
pISSN - 0022-0655
DOI - 10.1111/jedm.12022
Subject(s) - wald test , type i and type ii errors , statistics , context (archaeology) , sample size determination , statistical power , sample (material) , econometrics , test (biology) , statistical hypothesis testing , nominal level , mathematics , score test , power (physics) , psychology , paleontology , confidence interval , chemistry , chromatography , biology , physics , quantum mechanics
This article used the Wald test to evaluate the item‐level fit of a saturated cognitive diagnosis model (CDM) relative to the fits of the reduced models it subsumes. A simulation study was carried out to examine the Type I error and power of the Wald test in the context of the G‐DINA model. Results show that when the sample size is small and a larger number of attributes are required, the Type I error rate of the Wald test for the DINA and DINO models can be higher than the nominal significance levels, while the Type I error rate of the A‐CDM is closer to the nominal significance levels. However, with larger sample sizes, the Type I error rates for the three models are closer to the nominal significance levels. In addition, the Wald test has excellent statistical power to detect when the true underlying model is none of the reduced models examined even for relatively small sample sizes. The performance of the Wald test was also examined with real data. With an increasing number of CDMs from which to choose, this article provides an important contribution toward advancing the use of CDMs in practical educational settings.