Development of a Cognitive Diagnostic Model with Ability Covariate and Its Applications
The item response theory(IRT)is an important model to estimate the ability parameters,and the cognitive diagnosis model(CDM)is a vital model to diagnose the cognitive structure of the examinees.Because test item responses contain the information about the ability parameters and the knowledge states and their relationship,how to fully utilize the information to further enhance the accuracy of the knowledge states,becomes very important for helping to decrease the number of tests and test lengths.Considering the strong relationship between higher-order DINA(HO-DINA)model and two-parameter logistic model(2PLM),this new statistical measurement model was proposed by regarding the general ability as higher-order ability and estimated by Markov Chain Monte Carlo.In the estimation of ability,the knowledge states are considered as response patterns in establishing the relationship between the ability and knowledge states.Five attributes were considered in the study.Test consists of two parts of items,one is fitted by 2PLM and the other is fitted by the DINA model.The simulation study examined the performance of the new model with four model parameter distributions and five different test lengths,and compared it with the DINA model and 2PLM respectively.In the analysis of Examination for the Certificate of Proficiency in English(ECPE)test data,the absolute fit indices,-2LL,AIC,BIC and DIC were provided as an example to evaluate the model-data fit.The results show that:(a)The new proposed model in this study can obtain the ability parameters and cognitive structure parameters of the examinees in one test,and it has a good recovery for the estimation of attribute patterns,item parameters,and ability parameters.In particular,the accuracy of ability parameters has been greatly improved,and the MCMC algorithm is feasible;(b)The longer the CDM-based test length is,the higher the correct classification rate of knowledge state is,and the same is true for the ability estimation based on 2PLM;(c)Compared with lognormal distribution,the error of ability estimation is slightly smaller when the item discriminations followed from uniform distribution.When the slip parameters and the guessing parameters are small,the correct classification rate for attributes or attribute patterns are higher.In addition,the analysis of the ECPE data shows that the estimation accuracy of the new model is reasonable and has practical implications.Because there is always a relationship between the levels of ability and the mastery of knowledge,the ability of estimation enriched in test items fitting by an item response theory model can provide information for the classification of knowledge state,and item only fitting the CDM can also indirectly provide the information to improve the precision of ability estimation.In addition,it does not need calibrate the attribute vector for all test items and not require all items fitted two models at the same time.The new model uses a general or high-order ability as bridge between item response theory and cognitive diagnostic models,utilizing information from different test items to improve the accuracy of abilities and knowledge,tates estimation.
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