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Nested diagnostic classification models for multiple‐choice items
Author(s) -
Liu Ren,
Liu Haiyan
Publication year - 2021
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/bmsp.12214
Subject(s) - correctness , computer science , polytomous rasch model , monte carlo method , binary number , data mining , binary classification , machine learning , artificial intelligence , item response theory , algorithm , mathematics , statistics , psychometrics , arithmetic , support vector machine
This study proposes and evaluates a diagnostic classification model framework for multiple‐choice items. Models in the proposed framework have a two‐level nested structure which allows for binary scoring (for correctness) and polytomous scoring (for distractors) at the same time. One advantage of these models is that they can provide distractor information while maintaining the statistical properties of the correct response option. We evaluated parameter recovery through a simulation study using Hamiltonian Monte Carlo algorithms in Stan. We also discussed three approaches to implementing the proposed modelling framework for different purposes and testing scenarios. We illustrated those approaches and compared them with a binary model and a traditional nominal model through an operational study.