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Title: Multiple-choice log-linear cognitive diagnostic model framework and its application Authors:  Kentaro Fukushima - The University of Tokyo (Japan) [presenting]
Kensuke Okada - The University of Tokyo (Japan)
Abstract: Polytomous response models have attracted attention in the literature on diagnostic classification models (DCMs) for efficiently extracting diagnostic information on the levels of learners. In addition, the DCMs for multiple-choice items in which each option has its own Q-vector make effective use of observed information in distractors to infer the attribute mastery status of examinees. A novel framework of DCMs for multiple-choice items is proposed from a unified perspective. This framework is derived from the log-linear cognitive diagnostic model (LCDM) in binary DCMs and is hereby referred to as multiple-choice LCDM (MC-LCDM). It expresses models by the main effects and interactions of attribute mastery states and elements of Q-vectors. Existing DCMs for multiple-choice can be interpreted as the combinations of these effects in the proposed framework by introducing appropriate parameter constraints. In addition, novel sub-models can be derived within the framework based on rational assumptions. Essentially, these reduced models are suitable for empirical analysis with a modest sample size since they can save the number of parameters used without sacrificing the empirical adequacy of the model. Moreover, real data illustration of several sub-models within the proposed framework is likewise provided to demonstrate the applicability and interpretability of the proposal.