Identifiability of the Multinomial Processing Tree-IRT model for the Philadelphia Naming Test

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.