Naming tests represent an essential tool in gauging the severity of aphasia and monitoring the trajectory of recovery for individuals afflicted with this debilitating condition. In these assessments, patients are presented with images corresponding to common nouns, and their responses are evaluated for accuracy. The Philadelphia Naming Test (PNT) stands as a paragon in this domain, offering nuanced insights into the type of errors made in responses. In a groundbreaking advancement, Walker et al. (2018) introduced a model rooted in Item Response Theory and multinomial processing trees (MPT-IRT). This innovative approach seeks to unravel the intricate mechanisms underlying the various errors patients make when responding to an item, aiming to pinpoint the specific stage of word production where a patient's capability falters. However, given the sophisticated nature of the IRT-MPT model proposed by Walker et al. (2018), it is imperative to scrutinize both its conceptual as well as its statistical validity. Our endeavor here is to closely examine the model's formulation to ensure its parameters are identifiable as a first step in evaluating its validity.

翻译：命名测试是评估失语症严重程度及监测患者康复轨迹的重要工具。在这类评估中，患者需观察对应常见名词的图片，其反应准确性将受到评判。费城命名测试（PNT）作为该领域的典范，能对患者反应中的错误类型提供细致入微的见解。在突破性进展中，Walker等人（2018）提出了一个基于项目反应理论与多项处理树（MPT-IRT）的模型。这一创新方法旨在揭示患者对项目做出反应时各类错误背后的复杂机制，力求锁定患者语言产出能力受损的具体阶段。然而，鉴于Walker等人（2018）提出的IRT-MPT模型结构精妙，有必要对其概念有效性与统计有效性进行审慎检验。本研究旨在首先通过严格审视模型的公式化表达，确保其参数具有可识别性，以此作为评估模型有效性的第一步。