, 74:603 | Cite as

A Truncated-Probit Item Response Model for Estimating Psychophysical Thresholds

  • Richard D. Morey
  • Jeffrey N. Rouder
  • Paul L. Speckman
Open Access


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.


IRT item response theory threshold thresholds psychometrics psychophysics Bayesian hierarchical models MAC mass at chance 


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Copyright information

© The Psychometric Society 2009

Authors and Affiliations

  • Richard D. Morey
    • 1
  • Jeffrey N. Rouder
    • 2
  • Paul L. Speckman
    • 2
  1. 1.DPMGUniversity of GroningenGroningenThe Netherlands
  2. 2.University of MissouriColumbiaUSA

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