von Davier Matthias
Research & Development, Educational Testing Service, Rosedale Road MS02-T, Princeton, NJ 08541, USA.
Br J Math Stat Psychol. 2008 Nov;61(Pt 2):287-307. doi: 10.1348/000711007X193957. Epub 2007 Mar 22.
Probabilistic models with one or more latent variables are designed to report on a corresponding number of skills or cognitive attributes. Multidimensional skill profiles offer additional information beyond what a single test score can provide, if the reported skills can be identified and distinguished reliably. Many recent approaches to skill profile models are limited to dichotomous data and have made use of computationally intensive estimation methods such as Markov chain Monte Carlo, since standard maximum likelihood (ML) estimation techniques were deemed infeasible. This paper presents a general diagnostic model (GDM) that can be estimated with standard ML techniques and applies to polytomous response variables as well as to skills with two or more proficiency levels. The paper uses one member of a larger class of diagnostic models, a compensatory diagnostic model for dichotomous and partial credit data. Many well-known models, such as univariate and multivariate versions of the Rasch model and the two-parameter logistic item response theory model, the generalized partial credit model, as well as a variety of skill profile models, are special cases of this GDM. In addition to an introduction to this model, the paper presents a parameter recovery study using simulated data and an application to real data from the field test for TOEFL Internet-based testing.
具有一个或多个潜在变量的概率模型旨在报告相应数量的技能或认知属性。如果所报告的技能能够被可靠地识别和区分，那么多维技能概况将提供单个测试分数之外的额外信息。由于标准的最大似然（ML）估计技术被认为不可行，最近许多技能概况模型的方法都局限于二分数据，并使用了计算密集型的估计方法，如马尔可夫链蒙特卡罗方法。本文提出了一种通用诊断模型（GDM），它可以用标准的ML技术进行估计，适用于多分类响应变量以及具有两个或更多熟练水平的技能。本文使用了一类更大的诊断模型中的一个成员，即用于二分和部分计分数据的补偿性诊断模型。许多著名的模型，如Rasch模型的单变量和多变量版本、两参数逻辑斯蒂项目反应理论模型、广义部分计分模型以及各种技能概况模型，都是这个GDM的特殊情况。除了对该模型的介绍，本文还使用模拟数据进行了参数恢复研究，并将其应用于托福网考现场测试的真实数据。
