The Normal Fitting Test For Item Response Model

Item response theory,which was developed in 1970 s,is widely used in the field of psychology and educational measurement.It is under certain assumptions,use mathematical model to describe the relationship between the performance of the subjects on the project and the level of their characteristics,Therefore,it can be said that the basis of item response theory is hypothesis,the core is the model.Thus it can be seen,The key to the effective use of IRT lies in the fitting degree of the IRT model and the actual data.Only when the IRT model fits well with the actual data sets,can the advantages of the item response theory be fully developed.So how to judge whether the selected model is appropriate,we need to test the model.In item response theory,there are a lot of fitting test statistics,It mainly includes the chi-square statistics,the posterior predictive model statistics and the statistics based on the information matrix test,The chi-square statistic is a relatively common statistic,The Bock's chi-square statistic and likelihood ratio statistic are the most commonly used in Chi-square statistics.However,the problem of the degree of freedom for the chi-square statistics has always been controversial,the commonly used degrees of freedom is usually mJ-,but some scholars believe that the degree of freedom may be between mJ-to J.In addition,the chi-square statistic can be classified according to the ability of the subjects,and the error caused by the ability estimation may lead to inaccurate observation frequency in each group,In addition,the chi-square test results are related to sample size,According to the calculation formula of chi-square statistics,if the sample size increases,the chi-square value will increase,The degree of freedom of the chi-square distribution is related to item parameters and number of groups,independent of sample size,so as to increase the sample size,the chi-square value increases,and the critical values of chi-square unchanged,there will be significant results of chi-square test.That is to say,the fitting test of a project is only in the case of small sample size,the BCHI method and the likelihood ratio test method can give full play to its effectiveness,when sample size is larger,even if the actual data set and thelogistic model fit very well,this method still is rejected the logistic model hypothesis.The likelihood ratio test method can also be used to test the overall fitting test,However,it is still based on the idea of chi-square,so there are some disadvantages of the chi-square statistics,but there is no research on the application of BCHI method in the whole test.In view of the defects of these methods,this paper presents a new test method which can be used for both the project and the whole test.In this study,the first chapter introduces the item response theory,and the commonly used model of single parameter and two parameter and three parameter logistic model;In the second chapter,we briefly introduce the model fitting test statistic,Bock's chi-square statistic and likelihood ratio statistic;In the third chapter,the test steps of BCHI and likelihood ratio test are introduced,and puts forward the Normal fitting test method,under the assumption of single parameters,two parameters,three parameters logistic model,The effectiveness of the three methods is compared through simulation experiments and practical applications.The practice study found that Normal fitting test method in the hypothesis test of single parameter and two parameter logistic model,have certain universality,In the hypothesis test of three parameter logistic model,suitable for large sample test.In the fourth chapter,the Normal fitting test is extended to the whole test,and under the assumption of the three models,it is proved that this method can be applied to the whole test.The fifth chapter,summary and prospect,summarizes the advantages and disadvantages of the Normal fitting test method and points out the future research direction.