Multidimensional Grade Response Model

Abstract

Multidimensional Item Response Theory(MIRT),which is based on factor analysis and unidimensional Item Response Theory(IRT),is one of a new development trend of IRT.It's a fact that MIRT is in an early-developing stage and most studies are mainly concentrated on MIRT models for items with two score categories.With respect to polytomous MIRT models,it's until 1993 that Muraki and Carlson produced a generalization of unidimensional Grade Response Model(GRM) and it uses response functions that have the normal ogive form.Some other models such as multidimensional Generalized Partial Credit Model(MGPCM) and Continuous Response Model(MCRM) are even developed in recent years(Yao Schwarz,2006;Ferrando,2009).In the paper,a form of logistic Multidimensional Graded Response Model(MGRM) is firstly presented.The graphics,which are plotted by Matlab 2007,and properties for a special case of two-dimensional GRM are demonstrated.Then,base on the definition of item information for a dichotomous MIRT models,the item information function for MGRM is derived and item information for a case of two-dimensional GRM discussed.Moreover,the main ideas of Joint Maximum Likelihood Estimation(JML) and Markov Chain Monte Carlo(MCMC) methods to estimate MGRM parameters are stated.Finally,some significant further researches,which include research of item and test information,developing parameter estimate program for MGRM,are illustrated in the paper.