Measurement and Statistics, College of Education, University of Washington, 312E Miller Hall, 2012 Skagit Ln, Seattle, WA 98105, USA.
Psychometrika. 2021 Mar;86(1):167-189. doi: 10.1007/s11336-020-09742-1. Epub 2021 Jan 15.
Cognitive diagnostic models (CDMs) have arisen as advanced psychometric models in the past few decades for assessments that intend to measure students' mastery of a set of attributes. Recently, quite a few studies attempted to extend CDMs to longitudinal versions, and they all tended to model transition probabilities from non-mastery to mastery or vice versa for each attribute separately, with an exception of a few studies (e.g., Chen et al. 2018; Madison & Bradshaw 2018). However, these pioneering works have not taken into consideration the attribute relationships and the ever-changing attributes in a learning period. In this paper, we consider a profile-level latent transition CDM (TCDM hereafter), which can not only identify transition probabilities across the same attributes over time, but also the transition pathways across different attributes. Two versions of the penalized expectation-maximization (PEM) algorithms are proposed to shrink the probabilities associated with impermissible transition pathways to 0 and, thereby, help explore attribute relationships in a longitudinal setting. Simulation results reveal that PEM with group penalty holds great promise for identifying learning trajectories.
认知诊断模型 (CDMs) 在过去几十年中作为先进的心理测量模型出现，旨在衡量学生对一组属性的掌握程度。最近，相当多的研究试图将 CDMs 扩展到纵向版本，它们都倾向于分别为每个属性建模从非掌握到掌握或反之的转变概率，只有少数研究例外（例如，Chen 等人，2018 年；Madison 和 Bradshaw，2018 年）。然而，这些开创性的工作没有考虑属性关系和学习期间不断变化的属性。在本文中，我们考虑了一种基于剖面的潜在转变 CDM（以下简称 TCDM），它不仅可以识别随时间在同一属性上的转变概率，还可以识别不同属性之间的转变途径。提出了两种惩罚期望最大化 (PEM) 算法版本，将与不允许的转变途径相关的概率收缩到 0，从而有助于在纵向设置中探索属性关系。模拟结果表明，具有组惩罚的 PEM 有望识别学习轨迹。
