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A Truncated-Probit Item Response Model for Estimating Psychophysical Thresholds

Published online by Cambridge University Press:  01 January 2025

Richard D. Morey ,
Jeffrey N. Rouder  and
Paul L. Speckman
Richard D. Morey*
Affiliation:
University of Groningen
Jeffrey N. Rouder
Affiliation:
University of Missouri
Paul L. Speckman
Affiliation:
University of Missouri
*
Requests for reprints should be sent to Richard D. Morey, DPMG, University of Groningen, Grote Kruisstraat 2/1, 9712TS Groningen, The Netherlands. E-mail: r.d.morey@rug.nl
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Abstract

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Human abilities in perceptual domains have conventionally been described with reference to a threshold that may be defined as the maximum amount of stimulation which leads to baseline performance. Traditional psychometric links, such as the probit, logit, and t, are incompatible with a threshold as there are no true scores corresponding to baseline performance. We introduce a truncated probit link for modeling thresholds and develop a two-parameter IRT model based on this link. The model is Bayesian and analysis is performed with MCMC sampling. Through simulation, we show that the model provides for accurate measurement of performance with thresholds. The model is applied to a digit-classification experiment in which digits are briefly flashed and then subsequently masked. Using parameter estimates from the model, individuals’ thresholds for flashed-digit discrimination is estimated.

Keywords

IRTitem response theorythresholdthresholdspsychometricspsychophysicsBayesian hierarchical modelsMACmass at chance
Type
Original Paper
Information
Psychometrika , Volume 74 , Issue 4 , December 2009 , pp. 603 - 618
Creative Commons
Creative Common License - CCCreative Common License - BYCreative Common License - NC
This article distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
Copyright
Copyright © 2009 The Psychometric Society

Footnotes

This research is part of the first author’s Ph.D. thesis from the University of Missouri. We thank Mike Pratte and Andrew Kent for help in running the reported experiment. This research is supported by NSF grant SES-0351523 and NIMH grant R01-MH071418 and an Adeline Hoffman Fellowship from the University of Missouri.

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