Cognitive Diagnosis Models (CDMs) provide a powerful statistical and psychometric tool for researchers and practitioners to learn fine-grained diagnostic information about respondents' latent attributes. There has been a growing interest in the use of CDMs for polytomous response data, as more and more items with multiple response options become widely used. Similar to many latent variable models, the identifiability of CDMs is critical for accurate parameter estimation and valid statistical inference. However, the existing identifiability results are primarily focused on binary response models and have not adequately addressed the identifiability of CDMs with polytomous responses. This paper addresses this gap by presenting sufficient and necessary conditions for the identifiability of the widely used DINA model with polytomous responses, with the aim to provide a comprehensive understanding of the identifiability of CDMs with polytomous responses and to inform future research in this field.

翻译：认知诊断模型（CDMs）为研究人员和实践者提供了强大的统计与心理测量工具，以获取关于被试潜在属性的精细诊断信息。随着包含多个反应选项的题目日益普及，对基于多项式反应数据的CDMs应用需求正持续增长。与许多潜变量模型类似，CDMs的可辨识性对于参数精准估计和有效统计推断至关重要。然而，现有可辨识性研究主要集中于二分反应模型，尚未充分解决多项式反应CDMs的可辨识性问题。本文通过提出广泛应用的DINA模型在多项式反应情境下的可辨识性充分必要条件来填补这一空白，旨在为多项式反应CDMs的可辨识性提供全面理解，并为该领域的未来研究提供指导。