Item response theory(IRT) is to overcome the limitations of the classical test theory(CTT), developing in the latent trait theory basis and mainly discussing the subjects in the test item response and the latent trait relationships between participants, so the problem of parameter estimation is the core problem of item response theory. The process of parameter estimation often requires data integrity. Therefore, the parameter of the missing data draws much attention of the scholars at home and abroad.Due to the widespread existence of nonignorable missing, the way of dealing with the missing data is a research hotspot of item response theory. This paper studies modeling and estimation for nonignorable missing data in the educational and psychological measurement. Model the observed and missing data simultaneously. We use the item response model to fit the missing indicator. A Bayesian approach is developed for analyzing item response models with nonignorable missing data.The first chapter briefly introduces the development of item response theory, foreign research present situation and the main work of this thesis; the second chapter introduces the advantage of the item response theory compared with classical test theory, the model of item response theory which will be used in the paper, the estimation method of MCMC and some basic concepts, basic theory; the third chapter studies the Bayesian estimation of the non-ignoreable missing data under the two scoring model. We use the two scoring model to fit the observed data and Rasch model to fit the missing data. Then model them simultaneously. Finally use the Gibbs sampling method to give the posterior estimation of the model; the fourth chapter studies the Bayesian estimation of the non-ignoreable missing data under the graded item response model. We use the graded item response model to fit the observed data and Rasch model to fit the missing data. Then model them simultaneously. Finally use the Gibbs sampling method to give the posterior estimation of the model.Each chapter uses a simulation study to test the effectiveness of the method which can reduce the deviation owing to ignore the missing data during parameter estimation. At last, make a summary and propose the future research direction and work ideas. |