Item Parameter Estimation For A Continuous Bounded Response Model Using A MMLE/EM Algorithm

A continuous response model which was proposed by Samejima in 1973 was obtained as a limiting case of the graded response model and also in which a response was on a continuous scale.Yvonnick Noel and Bruno Dauvier proposed a new continuous response model in 2007:a beta item response model for continuous bounded responses.The two natural parameters of the beta distribution are extensive form as monotonic functions of person and item distance by this model,and also its logistic expected response function is a very interesting property.This paper will propose a Three-parameter beta response model based on this.The properties of the model arc studied here,including the response density function,the expected and variance function,and information function and the practical meaning of the item parameters,etc.As the marginal likelihoods function and equation of this model are derived,integral calculus is explored by the Gauss quadrature formula,and estimate the item parameters of the Two-parameter model used by MMLE/EM algorithm which was considered as a more strong method by many experts of statistics calculate. and has been used in many statistical computations.The data of parameter estimate is simulated by Monte Carlo Method.The simulation studies indicate that:MMLE/EM Algorithm can be used to estimate item parameters of this model,and has a very high precision of estimation.