基于可达阵的多级评分最简完备Q矩阵设计  

Design of the polytomous simplest complete Q matrix based on the reachability matrix

作　　者：唐小娟 彭志霞 秦珊珊 丁树良[3] 毛萌萌[4] 李瑜[5] TANG Xiaojuan;PENG Zhixia;QIN Shanshan;DING Shuliang;MAO Mengmeng;LI Yu(School of Education,Jiangxi Normal University,Nanchang 330022,China;School of Statistics and Mathematics,Zhejiang Gongshang University,Hang Zhou 310018,China;College of Computer Information Engineering,Jiangxi Normal University,Nanchang 330022,China;School of Public Policy and Administration,Nanchang University 330036,China;Mental Health Education Center of School of Marxism,Zhejiang Gongshang University,Hang Zhou 310018,China)

机构地区：[1]江西师范大学教育学院,南昌330022 [2]浙江工商大学统计与数学学院,杭州310018 [3]江西师范大学计算机信息工程学院,南昌330022 [4]南昌大学公共政策与管理学院,南昌330036 [5]浙江工商大学马克思主义学院心理健康教育中心,杭州310018

出　　处：《心理学报》2024年第11期1634-1650,I0007-I0013,共24页Acta Psychologica Sinica

基　　金：浙江省哲学社会科学规划课题(22GXSZ001Z);江西省社会科学规划课题(22JY04);国家自然科学基金项目(31860284,62067005,61967009)。

摘　　要：Q矩阵的完备性是认知诊断模型具有可识别性的关键。多级评分含有比0-1评分更丰富的诊断信息,却鲜见多级评分完备Q矩阵的设计研究。用最少的题量获得最高判准率是测验设计者追求的目标,借鉴0-1评分完备Q矩阵的设计方法,本文提出从可达阵中获取多级评分结构化/非结构化最简完备Q矩阵(SSCQM/USCQM)的方法和算法。模拟实验得出以下结论:(1)测验含SSCQM/USCQM越多,判准率越高;(2)当列数相同时,含多个SSCQM或多个USCQM测验的判准率与含可达阵测验的判准率非常接近;(3)对于一些结构,纵使多个SSCQM/USCQM的列数少于可达阵列数,其判准率仍不低于可达阵。总之,短测验设计优先选择SSCQM;长测验设计优先选择USCQM。The identifiability of cognitive diagnosis models relies heavily on the completeness of the Q matrix.However,existing test designs primarily focus on dichotomously-scored items,neglecting the importance of polytomous cognitive diagnostic test design.Moreover,this limitation poses a significant obstacle to the advancement of cognitive diagnosis.To bridge this gap,this paper aimed to introduce novel designs for the construction of polytomous structured and unstructured simplest complete Q matrices(SSCQM/USCQM).Our proposed approach considered all ideal response patterns(IRPs)of knowledge states(KSs)on the reachability matrix as research objects,with the objective of minimizing the number of columns selected from the reachability matrix.This ensured one-to-one correspondence between the set of KSs and the set of IRPs,thereby enhancing the completeness of the SSCQM.Additionally,we derived a polytomous USCQM by considering the relationship between the SSCQM and the sub-matrix of the corresponding identity matrix while ensuring that each row contains at least one“1”.Interestingly,the construction process revealed that there were more USCQMs than SSCQMs.This innovative approach expanded the possibilities for polytomous cognitive diagnostic test design.This study focused on the design and evaluation of cognitive diagnostic tests using polytomous structured and unstructured Q matrices(SSCQM/USCQM).We conducted two studies to comprehensively examine the influence of factors such as the number of attributes,attribute hierarchies,and item parameters on the precision of the SSCQM,USCQM,and reachability matrix.In the first study,variations in attribute structures and item parameter values were investigated to understand their impact on Q matrix accuracy.On the other hand,the second study explored the effects of attribute hierarchies and the number of attributes on the precision of the SSCQM,USCQM,and reachability matrix.Both simulation studies and actual measurement data were utilized to assess the robustness and efficacy

关 键 词：多级评分 测验设计 结构化最简完备Q矩阵 非结构化最简完备Q矩阵 算法 

分 类 号：B841[哲学宗教—基础心理学]