概率分布等值法及其应用

Methodology of Equating Based on Probability Distribution and Its Applications

在项目反应理论框架下，根据已有文献提出了开发新的测验等值准则的方法，即许多准则都可以看成是通过对锚题上作答反应概率分布进行变换而导出。据此揭示了两个著名的等值准则——Haebara方法和Stocking-Lord方法之间的联系，并且导出了一个新的等值准则——余弦等值准则。为了讨论余弦准则的行为表现，开展了一系列Monte-Carlo模拟研究。模拟结果表明，余弦准则在多级评分模型GPCM上表现比Haebara方法和 Stocking--Lord方法都好，而对GRM和2PLM，其表现不如Haebara，但可以和Stocking-Lord方法相提并论。这一发现提醒我们等值准则的选用是否恰当，不仅与等值系数所落的范围有关，而且还与项目反应函数（IRF）有更密切的关系。

This paper， divided into two parts， discusses the following two issues: (1) the methodology of developing a new test equating criterion and (2) the behavior of a new test equating method， referred to as cosine criterion.Under the item response theory (IRT) and in light of the probability distribution of an examinee’s response to some item， the first part of this paper proposes the methodology derived from the published literature on some test equating criteria. Moreover， some test equating criteria could be regarded as certain functions of probability distributions. Based on this， a series of test equating approaches， such as the Haebara item characteristic curve equating method (Hcrit)， Stocking-Lord test characteristic curve equating method (SLcrit)， logcontract equating method， SQRT method， and weighted Haebara method， could be clearly illustrated. Further， the relationship between Hcrit and SLcrit was identified: if the mutual compensation of the responses to the anchor items is evident， then SLcrit is suitable， and if not， then Hcrit is more appropriate.In the second part of the paper， a new test equating criterion， known as cosine criterion (COScrit) was discussed as an example of the application of this methodology of the equating criteria. The results of the Monte Carlo study show that the behavior of the new criterion is better than that of Hcrit and SLcrit; this is evident when the data is fit to the generalized partial credit model (GPCM) in the sense that the root mean squared deviations (RMSDs) corresponding to the three criteria are compared. Further， the RMSD to COScrit is smaller and statistically significant. When the data is fit to the 2-parameter logistic model 2PLM， or the graded response model (GRM)， COScrit is comparable to SLcrit; in fact， it is considerably better than SLcrit， provided that the equating coefficient A is not smaller than 1.2. If， however， coefficient A is smaller than 1.2， an inverse result is observed. Nevertheless， COScrit is inferior to Hcrit in both the cases. The findings suggest that the behavior of a test equating criterion is related to the domain of coefficient A， particularly to the item response function (IRF) .