多维项目反应理论等级反应模型

Multidimensional Grade Response Model

基于因子分析和单维项目反应理论的多维项目反应理论是测量理论的新发展方向之一。但是,多维项目反应理论仍处于不成熟的发展阶段,多数研究也只是以二级评分为主。本文首先介绍了逻辑斯蒂形式的多维等级反应模型,并以二维等级反应模型为例,分析了模型的数学函数图像及其性质。然后,推导出了多维等级反应模型的项目信息函数,并结合实例进行了讨论。进一步地,本文阐述了使用联合极大似然估计和马尔科夫链蒙特卡洛方法估计多维等级反应模型参数的思想。最后,指出了一些有待研究的问题。

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.