On The Parameter Estimation Of Cognitive Diagnosis Models And Its Application

With the development of cognitive psychology and psychometrics,more and more scholars have realized the importance of cognitive diagnosis.Cognitive diagnosis is the core of a new generation of test theory,and it relies on Cognitive diagnosis model.Therefore,parameter estimation of cognitive diagnosis model and its applications have gained extensive attention of researchers.Accurate estimation of model parameters is the basis of reasonable statistical in-ference.However,there is no analytic form for the posterior density function of the log-linear cognitive diagnostic model(LCDM),which leads to the low computational efficiency of its B ayesian estimation.In order to improve the computational efficiency of the algorithm,we proposed a new data-augmentation strategy to realize the Bayesian estimation of the LCDM model.This strategy provided an analytical form for the pos-terior distribution of LCDM model based on the Polya-Gamma family of distribution.The Polya-Gamma distribution was outlined within the framework of Logistic regres-sion.In addition,we also gave a detailed derivation for the conditional distribution of LCDM model parameters,and the Bayesian sampling was constructed by incorpo-rating the Polya-Gamma distribution into the conditional distribution,and was drawn randomly from the samplers to achieve faster convergence speed.The efficiency and utility of the proposed Bayesian method were demonstrated via the simulation studies and real data analysis.In cognitive diagnostic assessment(CDA),clustering analysis is an efficient ap-proach to classify examinees into attribute-homogeneous groups.Many researchers have proposed different methods,such as the nonparametric method with Hamming distance,K-means method,and hierarchical agglomerative cluster analysis,to achieve the classification goal.In this research,we introduced a spectral clustering algorithm(SCA)for clustering examinees according to their responses.The SCA was easy to operate,and often outperformed traditional clustering algorithms such as the K-means method.Simulation studies were used to compare the classification accuracy of S-CA,K-means algorithm,G-DINA model and its related reduced cognitive diagnostic models.A real data analysis was also conducted to evaluate the feasibility of SC A.Cognitive Diagnostic Computerized Adaptive Testing(CD-CAT)aims to obtain more useful diagnostic information by taking advantages of computerized adaptive testing(CAT).Cognitive diagnosis models(CDMs)have been developed to classify examinees into the correct proficiency classes so as to get more efficient remediation,whereas CAT tailors optimal items to the examinee s mastery profile.The item selec-tion method is the key factor of the CD-CAT procedure.In recent years,a large number of parametric/non-parametric item selection methods have been proposed.In this re-search,we proposed a series of stratified item selection methods in CD-CAT,which combined with posterior-weighted Kullback-Leibler(PWKL),non-parametric item s-election(NPS)and weighted NPS(WNPS)methods,named as S-PWKL,S-NPS,and S-WNPS,respectively.Two different types of stratification indices were used:orig-inal vs novel.The performances of proposed item selection methods were evaluated via simulation studies,and compared with the PWKL,NPS,WNPS methods without stratification.Manipulated conditions included calibration sample size,item quality,number of attribute,number of strata and data generation models.Results indicat-ed the S-WNPS and S-NPS methods performed similarly,and both outperformed the S-PWKL method.And item selection methods with novel stratification indices per-formed slightly better than ones with original stratification indices,and those without stratification performed the worst.