Comparison And Application Of G-DINA Model Parameter Estimation: HMC And EM Algorithm

Diagnostic classification models(DCMs),also known as cognitive diagnosis models,are multidimensional discrete latent variable models,which have received increasing attention within the field of social,behavioral,educational measurement and others.According to whether the latent attribute mode is parameterized or not,two types model,the parametric DCMs and the nonparametric DCMs have been proposed in literature.The G-DINA(Generalized Deterministic Inputs,Noisy “and”Gate)model is a typical parametric DCMs model.Model parameter estimation plays an important role in DCMs parameter estimation.At present,the widely used model parameter estimation algorithms in DCMs are the EM algorithm and Bayesian analysis method.The MCMC(Markov chain Monte Carlo)algorithm is one of the representatives of Bayesian method.Some Bayesian studies have demonstrated that the Hamiltonian Monte Carlo(HMC)algorithm is powerful and efficient for statistical model estimation,as a variant of MCMC algorithm,especially for complicated models.Stan which is a software program built upon HMC has been introduced as a means of psychometric modeling estimation.In this dissertation,new Stan code was developed to estimate the model parameters of G-DINA model under the identity-link function.The performance of the EM and HMC algorithms for computing the model parameter were further compared.Specifically,the R software packages CDM,GDINA,and Stan program were used to explore the performance of the EM and HMC algorithms in estimating the model parameters of G-DINA model via simulation and empirical studies.Meanwhile,the dissertation developed a cognitive diagnostic assessment of decimal division in primary school,and the practical applications of the EM and HMC algorithms for this cognitive diagnostic test were explored,by taking the Stan code,CDM and GDINA packages as examples.In the first study,the stability and accuracy of EM and HMC algorithms in estimating the model parameters was investigated via simulation study by adopting the G-DINA model under identity-link function as data generation model.Simulation study showed that:(1)Under the two sample sizes condition(1,000 and 2,000),the intercept and main effect parameters obtained EM algorithm via CDM and GDINA packages performed more precise than those estimated with HMC algorithm by Stan program,but when the sample size was 2,000,the accuracy of HMC algorithm in estimating interaction effect parameters was better than EM algorithm;(2)When the sample size was 2,000,the HMC algorithm performed better than the EM algorithm in term of the stability of model parameter estimation;(3)Under two sample sizes conditions considered in this study,the intercept parameters performed best in terms of accuracy,followed by the main effect parameters.The purpose of the second study was to development a cognitive diagnostic test of decimal division for primary school students.And a preliminary study based on classic test theory(CTT)was conducted.Cognitive diagnostic questionnaire was constructed by taking the chapter of “Decimal division in Grade 5 of primary school”as an example.The formal test with 30 items was administrated in several primary schools in Jining City,Shandong Province.The four attributes included in this test are:(A1)Multiplication table inverse operation(A2)Trial quotient rule;(A3)Quotient invariant rule and(A4)Decimal division operation rules.The results showed that the cognitive diagnostic questionnaire had good reliability and content validity,and all indicators satisfy the psychometric criteria.The third study presented an empirical study based on cognitive diagnosis theory,so as to obtain more fine-grained latent attribute profiles about decimal division for each student.The results shown that:(1)The interaction parameters estimated with HMC algorithm by Stan program were negative,but some of those estimated with EM algorithm by CDM and GDINA packages were positive;(2)Some items which had high intercept parameters were highly consistent with the findings that some items had higher difficulty in Study 2;(3)Some of the structural parameter estimates obtained by the Stan,CDM or GDINA packages were small and even close to 0,which demonstrated that attribute hierarchy might exist in the cognitive attributes of decimal division;(4)Most of the latent attribute profiles of the students in this test were the complete mastery of the attributes(1111)and the non-mastery of the attributes(0000),which imply that the knowledge of decimal division are closely associated.To sum up,(1)the new Stan code developed in this dissertation would serve as a reliable tool to estimate the model parameters of G-DINA model under the identity-link function.(2)The cognitive diagnostic test developed in this study are useful tool for the cognitive diagnosis of the decimal division knowledge for primary school students.