Research On Parameter Estimation And Application Of IRT Model Based On EM Algorithm

The development of Item Response Theory(IRT)provides new ideas for improving the analysis of evaluation data.The significant feature of IRT is that it expresses how the test taker's response is affected by the ability and the item parameters in the form of a probability model.When the difficulty of the item matches the ability of the test taker's,the efficiency of the test will be greatly improved.The key content of the effective application of the IRT to efficiently estimate the parameters in the IRT model,especially based on the big data,it is of great importance to make research on the efficient parameter estimation algorithms and effective data input types,which significantly impacts on improving the accuracy of parameter estimation.Also,it promotes the theoretical development and practical application of IRT in a way.As an iterative optimization strategy,the Expectation Maxization(EM)algorithm has become an effective method for dealing with problems with missing data for its simple ideas in recent years.Based on the EM algorithm,it is possible to use the response data of the test taker's to solve the parameter estimation problem of the IRT model effectively.In this study,the parameter estimation of the IRT model is studied based on the EM algorithm.The main research contents are follows:First,the estimation process of item parameters and latent ability distribution parameters were derived based on the principle of the EM algorithm in the form of discretization of continuous latent variables.The factors affecting the accuracy of the parameter estimation were analyzed and the effective parameter settings of the influencing factors were determined through simulation experiments.Also,the results are compared with the estimation results of the true value,the EM algorithm based on Gauss-Hermite integral and the MCMC algorithm,which illustrates the accuracy of parameter estimation of the EM algorithm has implemented in this paper.Next,an improved PE-PM algorithm based on parallelism is proposed in order to solve theproblem that the EM algorithm requires a long time to obtain the parameter estimation results for large data-intensive tasks.The algorithm realizes the parallel operation in the E step and the parallel operation in the M step of the EM algorithm by using the dask parallel computing library in Python.In this way,the algorithm execution speed is improved effectively and the memory consumption is reduced.It also makes it possible for the EM algorithm to process large-scale evaluation data.Then,as for the impact of different data types on parameter estimation based on EM algorithm,here two parts are mainly studied.For the first part,the influence of regional data and overall data on the parameter estimation are studied.By means of simulation experiment analysis,the relationship between the mean and variance of the ability distribution in the data and the difficulty parameter and discrimination parameter estimation in the item parameters are obtained.For the second part,the impact of the abnormal data on the parameter estimation results are discussed when the correct answer rate was inconsistent with the difficulty of the item.The influence relationship of abnormal data on parameter estimation is clearly obtained through simulation experiment analysis,and the stability of item response model parameter estimation is proved by the abnormal data detection statistics in the case of a small amount of abnormal data.Finally,the response data of test takers in mathematics in a certain area are collected and organized in this paper,which applying IRT model based on EM algorithm to the analysis and evaluation of test data.After preprocessing the raw data,with the help of the EM algorithm,the item parameters and the ability parameters of IRT were estimated,and the rationality of the item parameter settings and the consistency between the test taker's ability levels and the difficulty parameters were analyzed.Reasonable suggestions are proposed for better measurement of the test taker's ability level.The innovations of this study are: Firstly,The influencing factors in the process of parameter estimation of the EM algorithm are analyzed by means of simulation experiments,and the optimal parameter settings are given.Secondly,An improved PE-PM algorithm based on parallelism is proposed,which realized the parallel operation in the E step and the parallel operation in the M step of the EM algorithm,and the algorithm execution speed is effectivelyimproved.Thirdly,the influence of the data with different characteristics on the parameter estimation results is studied based on the EM algorithm,which provides a reference for the data processing process to obtain accurate parameter estimation results.