Embretson Susan E, Yang Xiangdong
School of Psychology, Georgia Institute of Psychology, 654 Cherry St., Atlanta, GA, 30332, USA,
Psychometrika. 2013 Jan;78(1):14-36. doi: 10.1007/s11336-012-9296-y. Epub 2012 Dec 6.
This paper presents a noncompensatory latent trait model, the multicomponent latent trait model for diagnosis (MLTM-D), for cognitive diagnosis. In MLTM-D, a hierarchical relationship between components and attributes is specified to be applicable to permit diagnosis at two levels. MLTM-D is a generalization of the multicomponent latent trait model (MLTM; Whitely in Psychometrika, 45:479-494, 1980; Embretson in Psychometrika, 49:175-186, 1984) to be applicable to measures of broad traits, such as achievement tests, in which component structure varies between items. Conditions for model identification are described and marginal maximum likelihood estimators are presented, along with simulation data to demonstrate parameter recovery. To illustrate how MLTM-D can be used for diagnosis, an application to a large-scale test of mathematics achievement is presented. An advantage of MLTM-D for diagnosis is that it may be more applicable to large-scale assessments with more heterogeneous items than are latent class models.
本文提出了一种用于认知诊断的非补偿性潜在特质模型，即诊断多成分潜在特质模型（MLTM-D）。在MLTM-D中，指定了成分与属性之间的层次关系，以适用于两个层面的诊断。MLTM-D是多成分潜在特质模型（MLTM；怀特利，《心理测量学》，45:479 - 494，1980；恩布雷森，《心理测量学》，49:175 - 186，1984）的推广，适用于广泛特质的测量，如成就测验，其中项目间的成分结构有所不同。描述了模型识别的条件，并给出了边际极大似然估计量，以及用于证明参数恢复的模拟数据。为说明MLTM-D如何用于诊断，文中给出了其在大规模数学成就测验中的应用。MLTM-D用于诊断的一个优点是，与潜在类别模型相比，它可能更适用于项目更具异质性的大规模评估。
