Abstract
The performance of the limited-information statistic M2 for diagnostic classification models (DCMs) is under-investigated in the current literature. Specifically, the investigations of M2 for specific DCMs rather than general modeling frameworks are needed. This article aims to demonstrate the usefulness of M2 in hierarchical diagnostic classification models (HDCMs). The performance of M2 in evaluating the fit of HDCMs was investigated in the presence of four types of attribute hierarchies. Two simulation studies were conducted to examine Type I error rates and statistical power of M2 under different simulation conditions, respectively. The findings suggest acceptable Type I error rates control of M2 as well as high statistical power under the conditions of a Q-matrix misspecification and the DINA model misspecification. The data of Examination for the Certificate of Proficiency in English (ECPE) were used to empirically illustrate the suitability of M2 in practice.
Highlights
Diagnostic classification models (DCMs) (Rupp et al, 2010) have demonstrated great potential for evaluating respondents with fine-grained information to support targeted interventions
For the linear hierarchical diagnostic classification models (HDCMs), because there is no available function in the CDM package, Mplus was used for the modeling according to the work by Templin and Hoffman (2013).We provided an abbreviated Mplus Syntax for the estimation of ECPE data and the R function for calculating M2 in the online Supplementary Material
We used the HDCMs to model the four fundamental attribute hierarchies and conducted two simulation studies and one empirical study to testify to the usefulness of M2
Summary
Diagnostic classification models (DCMs) (Rupp et al, 2010) have demonstrated great potential for evaluating respondents with fine-grained information to support targeted interventions. In the study by Liu et al (2016), the performance of M2 was evaluated under the log-linear cognitive diagnosis model (LCDM; Henson et al, 2009) They found that M2 has reasonable Type I error rates control when models were correctly specified and good statistical power when models or Q-matrix were misspecified, under the conditions of different sample sizes, test lengths, and attribute correlations. Their study showed that M2 is of good performance across different diagnostic model structures and is sensitive to the model misspecifications, the Q-matrix misspecifications, the misspecifications in the distribution of higher-order latent dimensions, and violations of local item independence Their findings were based on the general frameworks (e.g., LCDM) or the most common DCMs (e.g., DINA; de la Torre, 2009), which assume extremely complicated relationships among items but simple relationships among attributes. The more specific models are more suitable for practical use (Rojas et al, 2012; Ma et al, 2016), the results will be more convincing if M2 can be applied in more specific and practical conditions
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