模型参数点估计的可靠性:以CDM为例  

On the reliability of point estimation of model parameters:Taking cognitive diagnostic models as an example

作　　者：刘彦楼[1,2] 陈启山 王一鸣 姜晓彤 LIU Yanlou;CHEN Qishan;WANG Yiming;JIANG Xiaotong(Academy of Big Data for Education,Jining 273165,China;School of Psychology,Qufu Normal University,Jining 273165,China;Philosophy and Social Science Laboratory of Reading and Development in Children and Adolescents(South China Normal University),Ministry of Education,Guangzhou 510631,China;School of Psychology,South China Normal University,Guangzhou 510631,China)

机构地区：[1]曲阜师范大学教育大数据研究院,山东济宁273165 [2]曲阜师范大学心理学院,山东济宁273165 [3]“儿童青少年阅读与发展”教育部哲学社会科学实验室(华南师范大学),广州510631 [4]华南师范大学心理学院,广州510631

出　　处：《心理学报》2023年第10期1712-1728,共17页Acta Psychologica Sinica

基　　金：国家自然科学基金青年项目(31900794);山东省教育科学规划课题(2020KZD009);广东省哲学社会科学规划项目(GD22CXL01);广东省教育科学规划课题(2022GXJK176);大学生创新创业训练计划(202110446231X)资助。

摘　　要：心理学研究中,不恰当的模型参数估计框架或收敛准则严重影响模型参数点估计的可靠性,进而影响到研究结论的可靠性。本研究提出了基于MLE-EM的CDM模型参数估计新框架,以及新收敛判断方法。通过模拟研究与实证数据分析的方式,探索了新参数估计框架和新收敛判断方法的表现,并与已有模型参数估计框架及收敛判断方法进行了比较。结果显示,新的模型参数估计框架及收敛准则的表现优于已有的模型参数估计框架及收敛准则,能有效提高模型参数点估计的可靠性。Cognitive diagnostic models(CDMs)are psychometric models that have received increasing attention within fields such as psychology,education,sociology,and biology.It has been argued that an inappropriate convergence criterion for a maximum likelihood estimation using the expectation maximization(MLE-EM)algorithm could result in unpredictable and inaccurate model parameter estimates.Thus,inappropriate convergence criteria may yield unstable and misleading conclusions from the fitted CDMs.Although several convergence criteria have been developed,it remains an unexplored question,how to specify the appropriate convergence criterion for fitted CDMs.A comprehensive method for assessing convergence is proposed in this study.To minimize the influence of the model parameter estimation framework,a new framework adopting the multiple starting values strategy(mCDM)is introduced.To examine the performance of the convergence criterion for MLE-EM in CDMs,a simulation study under various conditions was conducted.Five convergence assessment methods were examined:the maximum absolute change in model parameters,the maximum absolute change in item endorsement probabilities and structural parameters,the absolute change in log-likelihood,the relative log-likelihood,and the comprehensive method.The data generating models were the saturated CDM and the hierarchical CDM.The number of items was set to J=16 and 32.Three levels of sample sizes were considered:500,1000,and 4000.The three convergence tolerance value conditions were 10-4,10-6,and 10-8.The simulated response data were fitted by the saturated CDM using the mCDM and the R package GDINA.The maximum number of iterations was set to 50000.The simulation results suggest the following.(1)The saturated CDM converged under all conditions.However,the actual number of iterations exceeded 30000 under some conditions,implying that when the predefined maximum iteration number is less than 30000,the MLE-EM algorithm might inadvertently stop.(2)The model parameter estimation framework affected

关 键 词：参数估计 点估计 收敛准则 认知诊断模型 

分 类 号：B841[哲学宗教—基础心理学]