Analysis And Application Of Multidimensional Project Response Theory In Examination

This paper studies the comprehensive evaluation problem of examinees’ multi-dimensional abilities, and how to measure the multidimensional abilities based on the examination.In this paper, we consider the following three-parameter-multidimensional-model. In addition, the Q-matrix is considered in the model above. It can build the relationship between the unobservable ability indicator and the observable correct answer response, so the examinees’ abilities will estimate conveniently.The current study developed a parameter estimation method of 3 PL-MIRT with MCMC and MMLE/EM algorithm, and designed a simulation experiment on three different samples under the two levels (3 & 5 dimensions). Experimental results show that the parameter estimation algorithm has a higher estimation accuracy, which demonstrated the validity of the algorithm. The mean relative error of item parameters is less than 5%, the mean relative error of ability parameters is between 5%～10% by MCMC algorithm, and the estimation accuracy and robustness are better than MMLE/EM method.According to the analysis above, we can discuss the application of MIRT models on high school math tests. Firstly, based on the discrimination under each dimension parameter estimate, we choose multidimensional discrimination MDSIC to evaluate the quality of the test paper. Secondly, in the cognitive diagnostic analysis of the examinees’ abilities, we can gain correlation among different test-internal ability dimensions and examinees’ ability parameters of different dimensions. Compared with the UIRT model, it provides more abundant and valuable information.