A New Method Of Irt Parameter Estimation-Three Points

One modern measurement theory of psychology and education, Item Response Theory(IRT), is used most widely currently. It is a new measurement theory which is developed to overcome the shortcomings of classical test theory. It is widely used in various large-scale examinations. However,Item Response Theory has been faced with a core issue which is how to estimate the parameters fast and efficiently, including estimate ability parameters, estimate project parameters, and estimate ability parameters and project parameters at the same time.In item response theory, the methods commonly used to estimate parameters have Conditional maximum likelihood estimation and Bayesian estimation and so on. The algorithms used to estimate parameters in item response theory have N-R algorithm, EM algorithm, MCMC algorithm and DSY algorithm. However, there have some problems exist in these algorithms themselves. Such as N-R algorithm requires that the objective function must be convex function, it is difficult to meet in practice; EM algorithm is complex, difficult to understand, complicate to program, and it involves integrating the operations. When the item response model was extended from single to multidimensional, it is difficult to use; MCMC algorithm involves looking for Markov chain. And the times of iterations usually get to 5000 or even more because that we don’t known when it tend to converge, which result in more time to estimate parameters. These defect of the algorithms existence make it can not achieve the exception of the researchers in application. Then, it needs a new method to estimate parameters.In this study, the second chapter describes the item response theory; In the third chapter, it introduces the methods commonly used to estimates project parameters in item response theory,including Conditional maximum likelihood estimation and Bayesian estimation; The fourth chapter describes the algorithms used to estimates parameters commonly, including EM algorithm, MCMC algorithms and DSY algorithm. It mainly introduces the theory and the process to estimate parameters. And it introduces how to use these algorithm into practice through an example. Through the introduction, we can founded that they have a certain complexity more or less; The fifth chapter introduces a new algorithm proposed in this paper: three-point method. Since the three-point method is proposed on the basis of the dichotomy, so in the beginning of this chapter describes the dichotomy. And then introduced the principle and its proof; The sixth chapter compare the four algorithms by simulation experiments. It have three experiments. In the first experiment, it compares the influence of the retries on the estimation when the number of test items is fixed; In the second experiment, it compares the influence of the number of items on the estimation when the number ofretries is fixed; The third experiment is based on the three-parameter logistic model, it uses three-point method to estimate three parameters. The number of subjects have 1000,2000,3000,which is order to explain that the three-point method is useful to estimate a number of parameters in large sample case. The first and second experiment are based on the two-parameter logistic model.They estimate the item parameters when the ability parameters are known. In the first two experiments, the difference of the four algorithms for parameter estimation error is not large, which is available for a sophisticated algorithm. It can illustrate the usefulness of three-point method effectively. The results of the estimation also show the difference of the time to estimate parameters between the four algorithms.The simulation experiments show that it can get better estimated accuracy of the parameters using Three-points method than that using EM algorithm; The time consumed by the Three-points method is far less than that by the DSY or MCMC algorithm; The theory of Three-points method is simpler than that of the EM algorithm or MCMC algorithm, and it is easy to understand and program;The application in rang of the Three-points method is wider than that in EM algorithm of MCMC algorithm.