Bayesian Estimation Of Parameters Of The Multidimensional Four-Parameter Normal Ogive Item Response Model

In recent years,Item Response Theory(IRT)has played an important role in psychological measurement and educational evaluation.In the IRT framework,the unidimensional ability is one of the basic assumptions,However,the response results of examinees are generally affected by the multidimensional ability in large-scale educational tests,so multidimensional item response theory(MIRT)has been widely concerned.MIRT models the relationship between the multidimensional ability of the items and the response results to obtain more accurate parameter information,Therefore,the parameter estimation of MIRT model is an important problem.In this paper,Gibbs sampling method based on data augmentation strategy is introduced for the multidimensional four-parameter Normal Ogive(4PNO)model,which effectively realizes bayesian estimation of the model.In the simulation study,the traceplot,ergodic mean graph and potential scale reduction factor were used to verify the convergence of Gibbs sampling method for two-dimensional and three-dimensional 4PNO model.In addition,the influence of the sample size and the covariance matrix of ability on the accuracy of model parameter estimation was considered.The results show that along with the sample size increased,the accuracy of parameter estimation improved significantly,but along with the correlation coefficient between abilities increased,the accuracy of parameter estimation reduced.In the empirical study,the method proposed in this paper is applied to data from the Programme for International Student Assessment(PISA)2018 Reading and Mathematics Tests,and the expected a posterior estimation of relevant parameters are calculated.The effectiveness and practicability of the method are further verified.