Cognitive Diagnosis Models (CDMs) are 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）是研究人员和实践者用以获取关于被试潜在属性细粒度诊断信息的一种强大的统计与心理测量工具。随着具有多种反应选项的项目日益普及，将CDMs应用于多级反应数据的研究兴趣持续增长。与许多潜变量模型相似，CDMs的可识别性对于精确的参数估计和有效的统计推断至关重要。然而，现有的可识别性结论主要集中于二元反应模型，未能充分解决多级反应CDMs的可识别性问题。本文通过提出广泛使用的多级反应DINA模型可识别性的充分必要条件来填补这一空白，旨在为多级反应CDMs的可识别性提供全面理解，并为该领域的未来研究提供参考依据。