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ERIC Number: EJ1109308
Record Type: Journal
Publication Date: 2014-Dec
Pages: 15
Abstractor: As Provided
ISSN: EISSN-2330-8516
The Log-Linear Cognitive Diagnostic Model (LCDM) as a Special Case of The General Diagnostic Model (GDM). Research Report. ETS RR-14-40
von Davier, Matthias
ETS Research Report Series, Dec 2014
Diagnostic models combine multiple binary latent variables in an attempt to produce a latent structure that provides more information about test takers' performance than do unidimensional latent variable models. Recent developments in diagnostic modeling emphasize the possibility that multiple skills may interact in a conjunctive way within the item function, while individual skills still may retain separable additive effects. This extension of either the conjunctive deterministic-input-noisy-and (DINA) model to the generalized version (G-DINA) or the compensatory/additive general diagnostic model (GDM) to the log-linear cognitive diagnostic model (LCDM) is aimed at integrating models with conjunctive skills and those that assume compensatory functioning of multiple skill variables. More recently, a result was proven mathematically that the fully conjunctive DINA model, which combines all required skills in a single binary function, may be recast as a compensatory special case of the GDM. This can be accomplished in more than one form such that the resulting transformed skill-space definitions and design (Q) matrices are different from each other but mathematically equivalent to the DINA model, producing identical model-based response probabilities. In this report, I extend this equivalency result to the LCDM and show that a mathematically equivalent, constrained GDM can be defined that yields identical parameter estimates based on a transformed set of compensatory skills.
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Publication Type: Journal Articles; Reports - Research
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A