Abstract: The core issue in IRT is how to estimate the item and person parameters. The common methods used often were N—R algorithm、E—M algorithm and so on. Because of their special characteristics in themselves, there were always certain shortcomings to hinder their development. With more and more complex models appearing, it is also difficult to estimate the parameters using those methods. Then the method called Markov Chain Monte Carlo (MCMC) was appearing. The emergence of MCMC algorithm provides the new solution. MCMC algorithm has been used in statistical physics for more than 50 years. In recent 20 years, it was also widely used in Bayesian estimation, test of significance and maximum likelihood estimation. Albert,J.H.（1992）is the first statistician to apply the algorithm in IRT parameter estimations. Many experts including Albert,J.H.（1992）、Patz &Junker（1999a,1999b）、Kim,Jee.Seon.& Daniel,M.Bolt.（2007）provide the information about MCMC algorithm and how to use it in detail. The character of MCMC algorithm is that it gives full play to the advantages of computer simulation technology, collects a sufficiently large sample of state by simulating, uses the elementary method to estimate the model parameters, in this way it bypasses the complex calculation of the EM algorithm to improve the success rate of estimation. There is not any algorithm that is perfect. Although the traditional MCMC algorithm has been widely used, the shortcomings of it , for example, the serious dependence on the prior distribution of the parameters and the extremely long time spent in performing the procedure, are still always existed. It is the main purpose of this paper to solve the problems. In the paper, the idea of the MCMC algorithm is firstly and briefly introduced. Following is two important suggestions to improve the algorithm and resolve the problems existed. The first suggestion is about the stationary distribution, which of the traditional MCMC algorithm is largely dependent on the prior distribution of the model parameters, however, in practice ,it is often that the researcher do not know the prior distribution, so this influences the accuracy of the estimation results. In this paper, the author provide another method to avoid the above situation. The second suggestion is about the acceptance probability. In this paper, the view the authors is following. In order to reduce the run time of the procedure, only when the stationary distribution value of the new iteration value is greater than that of the original iteration value, does the new iteration value replace the old one to be the value of the iterative chain. Then, the traditional and improved versions of MCMC algorithm are used to simulate and analyze data. Through the comparison of the results from the two methods, it shows that the new method performs better. Finally, the advantage the new algorithm has is pointed out and the future research direction is suggested.

Key words: item response theory, MCMC algorithm, parameter estimation, stationary distribution

摘要： 本文首先简要的阐述了MCMC算法的思想及在IRT参数估计中的操作过程；其次，针对该算法存在的一些问题，提出相应的改进建议；然后，分别运用传统的和改进型的MCMC算法进行模拟数据分析和比较，结果显示新的方法表现更好；最后总结新方法的优点所在，并指出下一步的研究方向。

关键词: 项目反应理论, MCMC算法, 参数估计, 平稳分布