First Advisor

Daniel Taylor-Rodriguez

Date of Award

Spring 2021

Document Type



Mathematics and Statistics


Aphasia -- Statistical methods -- Evaluation, Psychometrics


For persons with aphasia, naming tests are useful for assessing the severity of the disease and observing progress toward recovery. The Philadelphia Naming Test (PNT) is a leading naming test composed of 175 items. The items are common nouns which are one to four syllables in length and with low, medium, and high frequency. Since the target word is known to the administrator, the response from the patient can be classified as correct or an error. If the patient commits an error, the PNT provides procedures for classifying the type of error in the response. Item response theory can be applied to PNT data to provide estimates of item difficulty and subject naming ability.

Walker et al. (2018) developed a multinomial processing tree (MPT) model to draw more insight from the types of errors patients commit in responding to an item. The MPT model expands on existing models by considering items to be heterogeneous and estimating multiple latent parameters for patients to more precisely determine at which step of word production a patient's ability is affected. These latent parameters represent the theoretical cognitive steps taken in responding to an item, shown in Figure 1.

The purpose of this paper is to provide an assessment of the goodness-of-fit of the MPT model through posterior predictive checking. Background information for the MPT model is provided, followed by details of the statistical methods applied and results. The paper concludes with a discussion of areas for improvement for the MPT model and implications of use with the current design.


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An undergraduate honors project submitted in partial fulfillment of the requirements for the Fariborz Maseeh Department of Mathematics and Statistics Honors Track.

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