, Volume 74, Issue 4, pp 603-618,
Open Access This content is freely available online to anyone, anywhere at any time.
Date: 09 Apr 2009

A Truncated-Probit Item Response Model for Estimating Psychophysical Thresholds


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.

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.