标题： DINA模型与多项反应的可识别性的充分必要条件 显示英文标题

标题： Sufficient and Necessary Conditions for the Identifiability of DINA Models with Polytomous Responses

摘要： 认知诊断模型（CDMs）为研究者和实践者提供了一种强大的统计和心理测量工具，用于了解受试者的潜在属性的细致诊断信息。 越来越多的研究关注在多项选择响应数据中使用CDMs，因为越来越多的具有多个响应选项的题目被广泛使用。 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在二元响应模型上，并未充分解决具有多项选择响应的CDMs的可识别性问题。 本文通过提出广泛使用的DINA模型在多项选择响应下的可识别性的充分必要条件，填补了这一空白，旨在全面理解具有多项选择响应的CDMs的可识别性，并为该领域的未来研究提供指导。 显示英文摘要

摘要： 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.