On the Link between Cognitive Diagnostic Models and Knowledge Space Theory

Heller, Jürgen; Stefanutti, Luca; Anselmi, Pasquale; Robusto, Egidio

doi:10.1007/s11336-015-9457-x

Cited by 64 publications

(54 citation statements)

References 37 publications

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“…However, in the other six spaces the correspondence between competence states and performance states is many‐to‐one. In

C_{3}

, for instance, both competence states ∅ and { d } are mapped to the performance state ∅, whereas both competence states { a } and { a , d } are mapped to performance state {1} (the reader interested in the conditions that a skill function must satisfy to have a one‐to‐one correspondence between competence and performance states is referred to Heller, Stefanutti, Anselmi, & Robusto, , ).…”

Section: A Simulation Studymentioning

confidence: 99%

The assessment of knowledge and learning in competence spaces: The gain–loss model for dependent skills

Anselmi

Stefanutti

Chiusole

et al. 2017

Brit J Math & Statis

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The gain-loss model (GaLoM) is a formal model for assessing knowledge and learning. In its original formulation, the GaLoM assumes independence among the skills. Such an assumption is not reasonable in several domains, in which some preliminary knowledge is the foundation for other knowledge. This paper presents an extension of the GaLoM to the case in which the skills are not independent, and the dependence relation among them is described by a well-graded competence space. The probability of mastering skill s at the pretest is conditional on the presence of all skills on which s depends. The probabilities of gaining or losing skill s when moving from pretest to posttest are conditional on the mastery of s at the pretest, and on the presence at the posttest of all skills on which s depends. Two formulations of the model are presented, in which the learning path is allowed to change from pretest to posttest or not. A simulation study shows that models based on the true competence space obtain a better fit than models based on false competence spaces, and are also characterized by a higher assessment accuracy. An empirical application shows that models based on pedagogically sound assumptions about the dependencies among the skills obtain a better fit than models assuming independence among the skills.

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“…However, in the other six spaces the correspondence between competence states and performance states is many‐to‐one. In

C_{3}

Section: A Simulation Studymentioning

confidence: 99%

The assessment of knowledge and learning in competence spaces: The gain–loss model for dependent skills

Anselmi

Stefanutti

Chiusole

et al. 2017

Brit J Math & Statis

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“…It is beyond the scope of this paper to examine the use of numbers to describe behaviors in greater detail, but the interested reader may wish to explore the work of Tatsuoka classifying learners using cognitive task analyses employing rule space (Tatsuoka, 2009), the use of partially ordered set theory (Tatsuoka & Ferguson, 2003), and related methods that describe knowledge spaces (e.g., Heller, Stefanutti, Anselmi, & Robusto, 2015).…”

Section: Numbers As Points On a Linementioning

confidence: 99%

Is Learning Data in the Right Shape?

Kelly

2017

Learning Analytics

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ABSTRACT:In this short thought-piece, I attempt to capture the type of freewheeling discussions I had with our late colleague, Mika Seppälä, a research mathematician from Helsinki. Mika, not being a psychometrician or learning scientist, was blissfully free from the design constraints that experts sometimes ingest, unwittingly. I also draw on delightful conversations with the German research mathematician, Heinz-Otto Peitgen, a polyglot whose work includes advances in medical imaging and explorations in fractal geometry for K-12 students. Together, they taught me to reconsider foundational assumptions about learning, how to describe it, and how to grow it. Accordingly, I use this set of papers as a prompt for examining assumptions that numerical precision ensures scientific insight, that linear models best capture growth in learning, and that relaxing a fixation with time (exemplified by the reification of pre-and post-testing) might open up new topologies for describing, predicting, and promoting learning in its myriad manifestations.

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“…It was only recently that Robusto (2015, 2016) showed that a particular class of CDMs is equivalent to probabilistic KST models. To be more precise, they proved that the multi-strategy DINA model (MS-DINA; de la Torre & Douglas, 2008) is equivalent to the so-called CBLIM (Heller et al, 2015), a competence-based extension of the basic local independence model (BLIM; Falmagne, 1989;Doignon & Falmagne, 1999), which is the predominant probabilistic model in KST. This includes identifying popular CDMs as submodels of the CBLIM: the DINA model (E. H. Haertel, 1984Haertel, , 1989Haertel, , 1990) is equivalent to the conjunctive CBLIM, and the DINO model (Templin & Henson, 2006) is equivalent to the disjunctive CBLIM.…”

Section: Introductionmentioning

confidence: 99%

Complete Q-Matrices in General Attribute Structure Models

Heller¹

2019

Preprint

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In cognitive diagnostic assessment a property of the Q-matrix, usually referred to as completeness, warrants that the cognitive attributes underlying the observed behavior can be assessed uniquely. Characterizations of completeness were first derived under the assumption of independent attributes, and are currently under investigation for interdependent attributes. The dominant approach considers so-called attribute hierarchies, which are conceptualized through a partial order on the set of attributes. The present paper corrects and extends previously published results on this issue obtained for conjunctive attribute hierarchy models. Drawing upon results from knowledge structure theory it provides novel sufficient and necessary conditions for completeness of the $Q$-matrix, not only for conjunctive models on attribute hierarchies, but also on more general attribute structures.

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On the Link between Cognitive Diagnostic Models and Knowledge Space Theory

Cited by 64 publications

References 37 publications

The assessment of knowledge and learning in competence spaces: The gain–loss model for dependent skills

The assessment of knowledge and learning in competence spaces: The gain–loss model for dependent skills

Is Learning Data in the Right Shape?

Complete Q-Matrices in General Attribute Structure Models

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