Statistical Inference Methods Based On Item Response Theory And Cognitive Diagnosis

Item response theory (IRT), also known as latent trait theory, is a modern psychological measurement theory, which can guide the item selection and test preparation. IRT assumes that a subject has a "latent trait" which is presented based on a statistical conception. In a test, the latent trait generally refers to a potential ability, and is frequently used as an estimation of a potential test score. The responses of a subject in a test are relationship with his latent trait in IRT, and an item response function is used to show their relationship. IRT is through item response curves to analysis data, so we can analysis features of the item difficulty and item discrimination directly to guide the item selection and test preparation.Ability estimation method is one of the important components of IRT. Most previous studies mainly focused on the dichotomous and polytomous models, however, mixed models composed of both dichotomous and polytomous models are applied widely in large scale tests. For mixed-type tests composed of both dichotomous and polytomous items, polytomous items often yield more information than dichotomous items. To reflect the difference between the two types of items and to improve the precision of ability estimation methods, this paper presents an ability estimation method based on mixed type tests-weighted maximum a posterior (WMAP) estimation method. This method is a Bayesian estimation method and uses the characteristics of mixed type tests.To evaluate the performance of WMAP estimation method, a Monte Carlo simulation comparison and real data analysis are presented with usual ability estimation method such as maximum likelihood estimation (MLE) and Bayesian estimation method. Simulation results showed that the proposed method was much less biased than any of the other estimators, with relatively smaller standard errors and smaller root-mean-square errors. Real data analysis showed that the difference between WMAP and the other three methods was quite apparent even though there was only one polytomous item among the51items. The importance of the WMAP estimation method is that it can provide a nearly unbiased ability estimation method with smaller standard deviation and smaller root mean square error to make people get subjects’real ability levels more accurately.Since people are paying more and more attention to cognitive bugs behavior in study, cognitive diagnostic theory based on item response theory has been springing up increasingly, which combines both cognitive psychology and psychometrics to form a new science and utilizes modern statistical methods and computer technology to discuss subjects’cognitive structures and processes. A variety of cognitive diagnosis models have been developed. However, almost all of the current cognitive diagnosis models are single-strategy models that assume all examinees use the same strategies to solve the same items in a test, and this neglects the diversity of strategies. In this paper the dichotomous DINA model is extended to a multiple-strategy cognitive diagnosis model. The model is proposed for investigating individual difference in the selection of response categories in multiple-strategy items, called MMS-DINA model, and MCMC algorithm is employed to estimate its parameters. Simulation results showed the MCMC algorithm held fairly robustness, and the precision of item and person parameters was preferably great. It indicated that the MMS-DINA model was reasonable and feasible.It is the core content of both IRT and cognitive diagnosis that establishing proper models and improving the precision of parameter estimation methods. Weighted maximum a posterior estimation method is a successful attempt of ability estimation methods in IRT. With the development of both the information science and computer technology, the method has application prospect and potential advantage, which can be applied to cognition diagnosis.