Ramsay James O, Li Juan, Wallmark Joakim, Wiberg Marie
McGill University, Montreal, Canada.
Ottawa Hospital Research Institute, Ottawa, Canada.
Appl Psychol Meas. 2024 Dec 20:01466216241310600. doi: 10.1177/01466216241310600.
Modifications of current psychometric models for analyzing test data are proposed that produce an additive scale measure of information. This information measure is a one-dimensional space curve or curved surface manifold that is invariant across varying manifold indexing systems. The arc length along a curve manifold is used as it is an additive metric having a defined zero and a version of the bit as a unit. This property, referred to here as the scope of the test or an item, facilitates the evaluation of graphs and numerical summaries. The measurement power of the test is defined by the length of the manifold, and the performance or experiential level of a person by a position along the curve. In this study, we also use all information from the items including the information from the distractors. Test data from a large-scale college admissions test are used to illustrate the test information manifold perspective and to compare it with the well-known item response theory nominal model. It is illustrated that the use of information theory opens a vista of new ways of assessing item performance and inter-item dependency, as well as test takers' knowledge.
本文提出了对当前用于分析测试数据的心理测量模型的修改方法，这些方法可生成信息的累加量表度量。这种信息度量是一种一维空间曲线或曲面流形，在不同的流形索引系统中具有不变性。沿曲线流形的弧长被用作累加度量，它有定义明确的零点，并以比特的一种形式作为单位。这里将此属性称为测试或项目的范围，这有助于对图表和数值摘要进行评估。测试的测量能力由流形的长度定义，而人的表现或经验水平则由沿曲线的位置定义。在本研究中，我们还使用了来自各个项目的所有信息，包括来自干扰项的信息。来自大规模大学入学考试的测试数据用于说明测试信息流形的观点，并将其与著名的项目反应理论名义模型进行比较。结果表明，信息理论的使用为评估项目表现、项目间依赖性以及考生知识开辟了新的途径。
