The Comparison Of Three Parameter Estimation Methods For3PNO Multidimensional IRT Model

Multidimensional Item Response Theory (MIRT) is the result of the developmentof factor analysis and unidimensional IRT, It is the extensions of unidimensionalplane to the Multidimensional space. The application of MIRT is based on therealization of parameters estimations, which is an challenging and important issues.The models contain parameters for both persons and test items, meanwhile, It isimpossible to estimate the two sets of parameters independent of each other, there aretoo many parameters to be estimated. During the estimation procedure, someindeterminacies in the models to be considered, such as the location of the origin ofspace, the units of measurement for each coordinate axies, and the orientation of thecoordinate axes relative to the locations of the persons.This research introduced three item parameter estimation methods ofcompensatory Multidimensional IRT model such like3PNO multidimensional IRTmodel. they are the Marginal maximum likelihood estimation(MMLE) Methodrepresent by TESTFACT, the Least Square estimation (LS) Method represent byNoharm and the Monte Carlo Markov Chain（MCMC）method represent by BMIRT,and compared their performance in different conditions by controlling of three factors:the number of dimension, the relation of coordinate and the estimation methods.The results of this research are listed below:i. a-Parameter, The discrimination index1) Noharm is the best, BMIRT is the second and the worst is TESTFACT.With the increase of numbers of dimension, the accuracy of parameters isdecreasing.2) The performance is better when the coordinates of axes is unrelated.TESTFACT is not applicable when the coordinates of axes is related.3) Noharm and BMIRT performance are unaffected by the numbers ofdimension and the relation of dimensions.ii. b-Parameter, The difficulty index1) the main effects have no significant counts.2) BMIRT is the best, TESTFACT is the worst when the coordinates of axesis related.3) TESTFACT is the best, Noharm is the worst when the coordinates of axesis unrelatediii. c-Parameter, The guessing indexthe estimation of c-parameter doesn’t effected by the numbers of dimensionand the relation of coordinates, the accuracy are better than a-parameters andb-parameters.