Fabian A. Soto¹, Emily R. Martin¹; ¹Florida International University

Many perceptual tasks result in behavioral gradients depicting a continuous response as a function of stimulus value. Examples are gradients of confidence in perceptual decisions or response times. In many cases, researchers are interested in linking the mechanisms underlying continuous behavioral measures and perceptual choices. For example, while the other-race effect (ORE) in face recognition is usually measured using proportion of correct responses, the other-race categorization advantage (ORCA) is usually measured using response times. Understanding the mechanisms behind these two other-race effects could benefit from a way of measuring both of them in the same scale, such as sensitivity measures and thresholds obtained from detection theory. Here, we propose a generalization of the signal detection model for the psychometric curve that deals with continuous responses such as response times. As in the traditional model, we assume normally-distributed decision variables with means and variances that change depending on the presented stimulus. We also assume that a monotonic link function transforms such variables into the measured responses, which are perturbed by random normal noise. The model is a generalization of traditional signal detection models, which are obtained by assuming a staircase link function. We propose an algorithm that uses a combination of quantile functions and monotone spline regression to estimate the parameters of this model from data, and show that the inclusion of a flexible link function allows the model to fit continuous data better than ROC analyses previously proposed for continuous data. We show through simulations that our estimation procedure produces accurate parameter recovery. One can directly compare parameters estimated from the generalized SDT model across tasks that share the same stimulus space or behavioral response. We show an example of this by analyzing choice data obtained from an ORE task and response time data obtained from an ORCA task.

Acknowledgements: This research was funded by NSF grant 2319234 awarded to Fabian Soto