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）是研究者和实践者用于学习受访者潜在属性精细诊断信息的一种强大的统计和心理测量工具。随着具有多级响应选项的题目日益普及，人们对将CDMs用于多级响应数据的兴趣不断增加。与许多潜在变量模型类似，CDMs的可识别性对于准确的参数估计和有效的统计推断至关重要。然而，现有的可识别性结果主要集中于二元响应模型，未能充分解决具有多级响应的CDMs的可识别性问题。本文通过提出充分必要条件，论证了广泛使用的具有多级响应的DINA模型的可识别性，旨在全面理解具有多级响应的CDMs的可识别性，并为该领域的未来研究提供指导。