Abstract
The purpose of this study is to investigate the relationship between the Shannon entropy procedure and the Jensen–Shannon divergence (JSD) that are used as item selection criteria in cognitive diagnostic computerized adaptive testing (CD-CAT). Because the JSD itself is defined by the Shannon entropy, we apply the well-known relationship between the JSD and Shannon entropy to establish a relationship between the item selection criteria that are based on these two measures. To understand the relationship between these two item selection criteria better, an alternative way is also provided. Theoretical derivations and empirical examples have shown that the Shannon entropy procedure and the JSD in CD-CAT have a linear relation under cognitive diagnostic models. Consistent with our theoretical conclusions, simulation results have shown that two item selection criteria behaved quite similarly in terms of attribute-level and pattern recovery rates under all conditions and they selected the same set of items for each examinee from an item bank with item parameters drawn from a uniform distribution U(0.1, 0.3) under post hoc simulations. We provide some suggestions for future studies and a discussion of relationship between the modified posterior-weighted Kullback–Leibler index and the G-DINA (generalized deterministic inputs, noisy “and” gate) discrimination index.
Highlights
Summative assessments are typically used for grading and accountability purposes, and formative assessments are often used for supporting student learning (Laveault & Allal, 2016)
When the test length was 5, 43% pattern recovery rates of the Shannon entropy (SHE) were higher than the mean of pattern recovery rates of the Jensen–Shannon divergence (JSD), and 51% pattern recovery rates of the JSD were higher than the mean of pattern recovery rates of the SHE
We complete the proof that the SHE procedure and the JSD are linearly related under cognitive diagnostic model (CDM)
Summary
Summative assessments are typically used for grading and accountability purposes, and formative assessments are often used for supporting student learning (Laveault & Allal, 2016). Cognitive diagnosis assessment (CDA) can be regarded as a kind of formative assessments because it is intended to promote assessment for learning to modify instruction and learning in classrooms by providing the formative diagnostic information about students’ cognitive strengths and weaknesses (Jang, 2008; Leighton & Gierl, 2007). Computerized adaptive testing (CAT) has become a popular mode of many summative and formative assessments (Quellmalz & Pellegrino, 2009). SAGE Open cognitive diagnostic computerized adaptive testing (CD-CAT) is a popular mode of online testing for cognitive diagnosis, as it can help one make informed decisions about the steps in instruction for each student and greatly facilitate individualized learning (Chang, 2015) and provide many benefits to support formative assessments (Gierl & Lai, 2018).
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