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Abstract
In this paper, the slice-within-Gibbs sampler has been introduced as a method for estimating cognitive diagnosis models (CDMs). Compared with other Bayesian methods, the slice-within-Gibbs sampler can employ a wide-range of prior specifications; moreover, it can also be applied to complex CDMs with the aid of auxiliary variables, especially when applying different identifiability constraints. To evaluate its performances, two simulation studies were conducted. The first study confirmed the viability of the slice-within-Gibbs sampler in estimating CDMs, mainly including G-DINA and DINA models. The second study compared the slice-within-Gibbs sampler with other commonly used Markov Chain Monte Carlo algorithms, and the results showed that the slice-within-Gibbs sampler converged much faster than the Metropolis-Hastings algorithm and more flexible than the Gibbs sampling in choosing the distributions of priors. Finally, a fraction subtraction dataset was analyzed to illustrate the use of the slice-within-Gibbs sampler in the context of CDMs.
Highlights
Cognitive diagnosis models (CDMs) aim to provide a finer-grained evaluation of examinees’ attribute profiles
With the exception of the higher-order interaction terms when Kj∗ = 3, these results indicate that satisfactory estimates can be obtained for the DINA and G-DINA models using the slicewithin-Gibbs sampler even with sample size as small as I = 500
The estimates based on the expected a posteriori (EAP) and the corresponding standard errors (SEs) were computed for DINA and G-DINA models
Summary
Cognitive diagnosis models (CDMs) aim to provide a finer-grained evaluation of examinees’ attribute profiles. CDMs have been employed in both educational and noneducational contexts (Rupp and Templin, 2008; de la Torre et al, 2018). Several reduced and general CDMs have been proposed. Examples of the former are the deterministic inputs, noisy “and” gate (DINA; Junker and Sijtsma, 2001) model and deterministic inputs, noisy “or” gate (DINO; Templin and Henson, 2006) model; whereas examples of the latter are the generalized DINA (GDINA; de la Torre, 2011) model, log-linear CDM (Henson et al, 2009), and general diagnostic model (GDM; von Davier, 2008). When applying CDMs, a fundamental issue is model identifiability of the Q-matrix. Different identifiability conditions have been proposed, including strict identifiability (Liu et al, 2013; Chen et al, 2015; Xu, 2017) and milder identifiability (Chen et al, 2020; Gu and Xu, 2020)
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