Development Of Continuous Attribute Profile Cognitive Diagnostic Model And Its Fisher Information Function

Cognitive diagnostic assessment(CDA)is the product of the combination of cognitive psychology and modern metrology.Compared with other theories,one of the main advantages of CDA is that it can evaluate and analyze the micro-knowledge level of subjects,provide them with more in-depth and detailed diagnostic information,and then personalized remedial teaching and help them achieve greater progress and eventually achieve the aim of whole person development.The core structure of CDA is the cognitive diagnosis model(CDM),which combines cognitive theory and psychometric model to achieve the diagnosis of subjects’ cognitive strengths and weaknesses.The nature of the CDM directly determines the accuracy and effectiveness of cognitive diagnosis assessment.Most CDMs in current research generally assume that subjects’ latent attributes are deterministically dichotomous-mastery or non-mastery.From a statistical point of view,the dichotomy hypothesis of attribute mastery is so deterministic that it would lead to a decrease in the refinement of the subject’s diagnosis and affect the remedial teaching of the subject.In addition,the CDMs may not explain well the heterogeneity of their responses when students have partial mastery.Therefore,it calls for the introduction of continuous variables in CDMs to describe the subjects’ attribute mastery.In fact,the MIRT is often considered as a prototype of this kind of model.However,the latent traits in MIRT have no boundaries,resulting in the inability of MIRT to provide participants with a direct and accurate diagnosis with good explanation.The estimation error of the subjects’ latent traits is a key topic of concern in psychometric theory.In one hand,reliability is a well-known index for the level of random error of a measurement,and there are many methods for estimating reliability in psychometrics.In another,the Fisher information,which is equal to the reciprocal of the square of the sampling standard error(i.e.,variance),is often used to indices the estimation error of the subjects’ latent traits in the item response theory.However,the Fisher information can only be calculated for non-discrete variables.At present,the subjects’ latent traits in most cognitive diagnostic models are discrete,and it is impossible to calculate the Fisher information,Therefore,it is not feasible to accurately assess the estimation error of the participants’ attribute profiles.Taking on the problems above,this study will mainly discuss the following two issues: first,the construction of the model based on continuous attribute profile;Second,the construction of Fisher information function based on the new model.Specific research contents and results include the following four aspects:In the first study,following the idea of mixed membership model,a DINA based model for continuous attribute profile(CAP-DINA)was developed,and the properties of the model and its relationship with related models were analyzed in detail.The analysis results show that the model is mathematically equivalent to the PM-DINA model,but its philosophy of construction is different and the formulation obtained are much simpler and easier for understanding and use.At the same time,since the model includes the DINA model,the CAP-DINA model is suitable for both discrete and continuous attribute mastery profile.It can not only classify the subjects,but also make a more detailed and accurate estimation of the subjects’ attribute mastery.In the second study,the parameter estimation algorithm of the CAP-DINA model was developed and the estimation effect was verified.Firstly,the estimation process of CAP-DINA model was constructed based on MCMC algorithm.Then,the new model and DINA model were studied for cross-comparison simulation under the condition of model misspecification.That is,when the real model was DINA,both DINA and CAP-DINA models were used to estimate parameters and compare their results.When the true model is CAP-DINA,we also used both DINA and CAP-DINA to estimate the parameters and compared the results of the two.The results show that:(1)the parameter estimation process is relatively simple due to the simplicity of the model form and the directness of the data generating method;(2)The CAP-DINA model has good convergence and regression in parameter estimation.Study 3 proved the existence of the Fisher information matrix based on the CAPDINA model,deduced it and demonstrated the two preliminary applications.The first application is item quality analysis.The second application developed the item selection strategy CAT based on Fisher information matrix: FI-D and FI-A and made preliminary applications in the computerized adaptive testing.The results of the first part show that the Fisher information matrix based on the new model can be constructed and used to guide the analysis of item quality and the estimation error of subjects’ attribute profile in the future.The second part of the research results show that the item selection strategy based on the Fisher information matrix of the new model has a good performance in the computerized adaptive testing.Study Four investigated the fit of the CAP-DINA model to actual test data.The CAP-DINA model was applied to the English test data in the Examination for the Certificate of Proficiency in English(ECPE).The parameter estimation results of the model were analyzed in detail,and the fitting of CAP-DINA model and DINA model was compared by AIC,BIC and DIC.The results show that the CAP-DINA model has smaller AIC,BIC and DIC,and the CAP-DINA model has better model fitting.