The Parameter Estimation Problem Of Two Kinds Of Special IRT Model

In the last few years,more and more attention has been attracted in educational and psychological measurement.With the development of the item response theory, for the guidance of psychological and educational measurement,it has provided the strong theory and technical support,It has the incomparable advantage over classical measurement theory.This theory is combined with the use of computer technology,providing a broad and bright prospect for the development of test.With the development of IRT,There are many mathematical models of Item Response Theory,such as Rasch Model,Nomal Ogive Model,Logistic Model,GPCM Model.Firstly the paper is about two parameter logistic model and discussed the superiority of the item characteristic curve fitting when ability parameter respectively obey equidistant group of uniform distribution,normal distribution and equiprobability group of normal distribution.the paper also introduces order constraint into IRT,for Rasc h model,Considering the maximum likelihood estimation of item difficulty parameter s under simple order.when the subjects were at the same level,the maximun likelihood estimation under order constraint can be estimated by PAVA algorithm.In general,wecan prove the existence of maximum likelihood estimation under order constraint.Onthe other hand,we consider how to determine the structure of the parameters when the difficulty parameters satisfy a simple order and through the simulation to illustrate the applicability of ORIC criterion.