Application Of Copula Method In IRT Based On Bayesian Estimation

Item Response Theory(IRT),as a kind of modern education and psychological measurement method,is more and more widely applied actually.When using Item Response Theory model to deal with problems,in order to facilitate,we always assume that a person under the condition of the same subjects,and the reaction between items is independent and unrelated.However,this background does not conform to the actual test,and influence the accuracy.Dealing with local residual problem is the prerequisite for the application of IRT.With the development of modern statistics and mathematics,the method of dealing with local dependencies has also been developed.Common treatment is the addition of random effects factors,such as some scholars put forward the project response model.However,there are some problems in the joint distribution function,such as the non-reproducibility of the marginal distribution and the problem of parameter description,even lose significance.This paper mainly introduce Copula connect function to solve local residual dependency problem in the IRT.Copula connect function as a new connection function,is widely used in the financial sector.The model is established for multiple marginal reaction distributions,and their joint distributions also will be obtained.The correlation of each marginal distribution is considered,and problems of the irreversibility of the marginal distribution and parameter interpretation are solved.Copulas connect function is the joint distribution function of marginal distribution.On this basis,the MCMC estimation method is used to give the Bayesian estimation of the parameters and the correlation coefficient of the Copula.This paper mainly uses statistical software R to simulate and analyze the data.The R2 WinBUGS software can be called from R to get a posteriori estimation results.Related program code can be seen in Appendix.By selecting the Frank copula function and Clayton copula function,we analyze the actual dependent data and conclude that,when ignoring the dependency of data,namely the use of local independent modeling of item response theory,the error is relatively large,and would have greatly influenced the selected test and ability estimation.