Department of Statistics, University of Illinois at Urbana-Champaign, 605 E Springfield Ave, Champaign, IL61820, USA.
Psychometrika. 2023 Mar;88(1):158-174. doi: 10.1007/s11336-022-09875-5. Epub 2022 Jul 27.
Restricted latent class models (RLCMs) are an important class of methods that provide researchers and practitioners in the educational, psychological, and behavioral sciences with fine-grained diagnostic information to guide interventions. Recent research established sufficient conditions for identifying RLCM parameters. A current challenge that limits widespread application of RLCMs is that existing identifiability conditions may be too restrictive for some practical settings. In this paper we establish a weaker condition for identifying RLCM parameters for multivariate binary data. Although the new results weaken identifiability conditions for general RLCMs, the new results do not relax existing necessary and sufficient conditions for the simpler DINA/DINO models. Theoretically, we introduce a new form of latent structure completeness, referred to as dyad-completeness, and prove identification by applying Kruskal's Theorem for the uniqueness of three-way arrays. The new condition is more likely satisfied in applied research, and the results provide researchers and test-developers with guidance for designing diagnostic instruments.
受限潜在类别模型 (RLCMs) 是一类重要的方法，为教育、心理和行为科学领域的研究人员和从业者提供了精细的诊断信息，以指导干预措施。最近的研究确定了识别 RLCM 参数的充分条件。目前限制 RLCM 广泛应用的一个挑战是，对于某些实际情况，现有的可识别性条件可能过于严格。本文为多元二项数据的 RLCM 参数识别确立了一个较弱的条件。尽管新的结果放宽了一般 RLCM 的可识别性条件，但新的结果并没有放宽更简单的 DINA/DINO 模型的现有必要和充分条件。从理论上讲，我们引入了一种新的潜在结构完整性形式，称为对偶完整性，并通过应用 Kruskal 的三向数组唯一性定理来证明识别。新的条件在应用研究中更有可能得到满足，研究结果为研究人员和测试开发者设计诊断工具提供了指导。
