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A diagnostic tree model for polytomous responses with multiple strategies
Author(s) -
Ma Wenchao
Publication year - 2019
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.12137
Subject(s) - rubric , polytomous rasch model , tree (set theory) , set (abstract data type) , computer science , scheme (mathematics) , machine learning , artificial intelligence , item response theory , mathematics , statistics , data mining , psychometrics , arithmetic , mathematical analysis , programming language
Constructed‐response items have been shown to be appropriate for cognitively diagnostic assessments because students’ problem‐solving procedures can be observed, providing direct evidence for making inferences about their proficiency. However, multiple strategies used by students make item scoring and psychometric analyses challenging. This study introduces the so‐called two‐digit scoring scheme into diagnostic assessments to record both students’ partial credits and their strategies. This study also proposes a diagnostic tree model ( DTM ) by integrating the cognitive diagnosis models with the tree model to analyse the items scored using the two‐digit rubrics. Both convergent and divergent tree structures are considered to accommodate various scoring rules. The MMLE / EM algorithm is used for item parameter estimation of the DTM , and has been shown to provide good parameter recovery under varied conditions in a simulation study. A set of data from TIMSS 2007 mathematics assessment is analysed to illustrate the use of the two‐digit scoring scheme and the DTM .