四参数Logistic模型潜在特质参数的Warm加权极大似然估计  

Warm'sweighted maximum likelihood estimation of latent trait in the four-parameter logistic model

作　　者：孟祥斌[1,2] 陶剑[2,3] 陈莎莉[2] 

机构地区：[1]东北师范大学教育学部 [2]东北师范大学数学与统计学院,应用统计教育部重点实验室 [3]中国基础教育质量监测协同创新中心东北师范大学分中心,长春130024

出　　处：《心理学报》2016年第8期1047-1056,共10页Acta Psychologica Sinica

基　　金：国家自然科学基金项目(11501094;11571069);中国基础教育质量监测协同创新中心自主课题项目;应用统计教育部重点实验室开放课题(230026510);东北师范大学哲学社会科学校内青年基金项目(中央高校基本科研业务费专项资金资助;1409124)

摘　　要：本文以四参数Logistic(4-parameter Logistic,4PL)模型为研究对象,根据Warm的加权极大似然估计技巧,提出了4PL模型潜在特质参数的加权极大似然估计方法,并借助模拟研究对加权极大似然估计的性质进行验证。研究结果表明,与通常的极大似然估计和后验期望估计相比,加权极大似然估计的偏差(bias)明显减小,并且具有良好的返真性能。此外,在测试的长度较短和项目的区分度较小的情况下,加权极大似然估计依然保持了良好的统计性质,表现出更加显著的优势。There are two types of aberrant responses, the correct responses resulting from lucky guesses, and the false responses resulting fromcarelessness. Because the two aberrant responses do not reflect the examinee’s actual knowledge, they may cause an erroneous estimation of the latent trait of examinee.Compared with guesses, careless errors might cause more serious estimation biases, especially if these errors occur at the beginning of a test. To account for the effect of careless errors, Barton and Lord （1981） developed a four-parameter logistic （4PL） model by adding an upper asymptote parameter in the three-parameter logistic （3PL） model. Recently, the 4PLmodel received more attentions, and some literatures highlighted its potential and usefulness both from a methodological point of view and for practical purposes. It can be expected that the 4PL model will be promoted as a competing item response model in psychological and educational measurement. This paper focuses on one important aspect of the 4PL model, that is, the estimation of latent trait levels. In general, unbiased parameter estimation is desirable. Reducing bias in the latent trait estimator is very important for the application of IRT model. Warm （1989） proposed a weighted maximum likelihood （WML） method for estimating the latent trait parameter in the 3PL model, which was found to be less bias than the maximum likelihood （ML） and expected a posteriori （EAP） estimates. The WML estimate has also been extended to the generalized partial credit model （GPCM）. In light of the superior performance of the WML method in previous studies, this studyapplies a WML latent trait estimator to the 4PL model. The main works of this article are to present the derivations of the WML estimator under the 4PL model, and to construct a simulation study to compare the properties of the WML estimator to that of the ML and EAP estimators. The results of the simulation study suggested that, the bias of the WML estimator was consistently smalle

关 键 词：项目反应理论 四参数Logistic模型 加权极大似然估计 

分 类 号：B841[哲学宗教—基础心理学]