Bayesian Cluster Of Ability Parameters Of A Joint Model Based On Response And Response Time

In some exams(such as college course exams),AB papers will be adopted to prevent cheating,and the difficulty level of AB papers should be consistent in the two sets of papers.In both sets of papers,different questions of the same difficulty made up roughly the same proportion of columns.This paper mainly draws on the ideas of Van der Linden(2007)and Ma et al.(2020).The layered modeling method proposed by Van der Linden(2007)is one of the most important developments in the analysis of the relationship between speed and accuracy.Ma et al.(2020)proposed a Bayesian clustering regression method for spatially correlated data.Based on this idea,in the first part of this study,a Bayesian clustering method based on the joint model of response and reaction time is proposed to classify the difficulty parameters of the questions.For response and reaction time data,the joint modeling idea of Van der Linden(2007)and the clustering method idea of Ma et al.(2020)are adopted to classify the topic difficulty parameters in the joint model.This method is based on Dirichlet process(DP for short),which provides a framework for clustering numbers.In the combined model of response and response time,the parameters are estimated by Bayesian inference,and the classification results are obtained by Markov Chain Monte Carlo(MCMC).In 500 simulation studies,cluster evaluation index Rand index(RI)shows that the simulation effect is good(RI=0.780),coefficient of variation =0.034,indicating that the simulation results are reliable.In the empirical study,the above clustering method was applied to PISA data,and16 test questions were divided into 8 categories.In the second part,a Bayesian clustering method based on the joint model of response and response time is proposed,which classifies the parameters of discrimination degree and difficulty.In 500 simulation studies,RI=0.807,coefficient of variation =0.069,indicating that the simulation results are reliable.In the empirical study,the above clustering method was applied to PISA data,and 16 questions were divided into 9 categories.In order to better analyze the potential ability of the subjects,the third part proposes the clustering of Bayes method based on the joint model of reaction and reaction time,and classifies the ability parameters.In 200 simulation studies,RI=0.832,coefficient of variation=0.030,indicating that the simulation results are reliable.In the empirical study,the above clustering method was applied to PISA data.The 548 items were divided into 17 categories.