A Stochastic EM Algorithm For The Marginal Maximum Likelihood Estimation Of The Multidimensional Three-Parameter Normal-Ogive Model

In the actual measurement of education,psychology and medicine,,multidimensional structured tests have been increasingly prevalent,which directly promotes the development of multidimensional item response theory(MIRT)and its model.In recent years,the statistical calculation of the parameter estimation of the MIRT model has become the focus and difficulty of the research.Monte Carlo Expectation Maximization Algorithm(MCEM)and Metropolis-Hastings Robbins Monro Algorithm(MH-RM)etc.are proposed,but they all have disadvantages.Thus,the improved Stochastic Expectation Maximization Algorithm is adopted in this paper,which does not require manual adjustment of parameter.In the implementation process,two parameters of the algorithm: the pre-sampling period T and the final iteration number m are automatically selected based on data drive.This research focuses for the multidimensional three-parameter Normal-Ogive(3PNO)model,introducing improved St EM algorithm,which provides a part of method support and technical guarantee for the application of multidimensional normal-ogive model.The simulation results show that:(1)The automatic selection of T and m provides a guarantee for the calculation accuracy and efficiency of St EM algorithm.(2)The estimation results of the improved St EM algorithm are not very sensitive to the selection of initial values,which means a good stability.(3)When the dimension is low,the computational speed of the improved St EM algorithm is comparable to that of the MH-RM algorithm;When the dimension becomes higher,the St EM algorithm often outperforms the MH-RM algorithm in terms of computational efficiency.