Abstract
Bayesian networks (BNs) can be employed to cognitive diagnostic assessment (CDA). Most of the existing researches on the BNs for CDA utilized the MCMC algorithm to estimate parameters of BNs. When EM algorithm and gradient descending (GD) learning method are adopted to estimate the parameters of BNs, some challenges may emerge in educational assessment due to the monotonic constraints (greater skill should lead to better item performance) cannot be satisfied in the above two methods. This paper proposed to train the BN first based on the ideal response pattern data contained in every CDA and continue to estimate the parameters of BN based on the EM or the GD algorithm regarding the parameters based on the IRP training method as informative priors. Both the simulation study and realistic data analysis demonstrated the validity and feasibility of the new method. The BN based on the new parameter estimating method exhibits promising statistical classification performance and even outperforms the G-DINA model in some conditions.
Highlights
Cognitive diagnosis models (CDMs) are psychometric models developed mainly to assess students’ specific strengths and weaknesses on a set of finer-grained skills or attributes within a domain
The pattern classification rate (PCR) of Bayesian networks (BNs) based on the combination of ideal response patterns (IRPs) and gradient descent (GD) methods was higher than the BN based on the combination of IRP and expectation maximization (EM) method in these GDINA datasets
When comparing with the G-DINA analysis, in the four datasets generated by G-DINA, the PCR of BN–IRP–GD method was a little higher than the PCR of G-DINA if the attribute patterns of the students conformed to the uniform distribution, and the PCR of G-DINA was higher than the BN–IRP–GD method if the attribute patterns of the students conformed to the multivariate normal distribution
Summary
Cognitive diagnosis models (CDMs) are psychometric models developed mainly to assess students’ specific strengths and weaknesses on a set of finer-grained skills or attributes within a domain. Researchers have developed many kinds of CDMs for cognitive diagnostic assessment (CDA), including the rule space model (Tatsuoka, 1985), the attribute hierarchy model (AHM, Leighton et al, 2004), the deterministic inputs noisy and gate model (DINA, Junker and Sijtsma, 2001), the Deterministic Input, Noisy Output “Or” gate model (DINO; Templin and Henson, 2006), the LogLinear Cognitive Diagnosis Model (LCDM, Henson et al, 2009), the General Diagnostic Model (GDM, von Davier, 2005), the G-DINA model (de la Torre, 2011), and so on In addition to these traditional CDMs, some researchers proposed to use Bayesian networks (BNs, Pearl, 1988) in CDA (Mislevy, 1995; Mislevy et al, 1999; Almond et al, 2007, 2015; Wu, 2013; Levy and Mislevy, 2017). This method needs to introduce other models to assist the parameterization
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