Painfree and accurate Bayesian estimation of psychometric functions for (potentially) overdispersed data

Abstract

The psychometric function describes how an experimental variable, such as stimulus strength, influences the behaviour of an observer. Estimation of psychometric functions from experimental data plays a central role in fields such as psychophysics, experimental psychology and in the behavioural neurosciences. Experimental data may exhibit substantial overdispersion, which may result from non-stationarity in the behaviour of observers. Here we extend the standard binomial model which is typically used for psychometric function estimation to a beta-binomial model. We show that the use of the beta-binomial model makes it possible to determine accurate credible intervals even in data which exhibit substantial overdispersion. This goes beyond classical measures for overdispersion-goodness-of-fit-which can detect overdispersion but provide no method to do correct inference for overdispersed data. We use Bayesian inference methods for estimating the posterior distribution of the parameters of the psychometric function. Unlike previous Bayesian psychometric inference methods our software implementation-psignifit 4-performs numerical integration of the posterior within automatically determined bounds. This avoids the use of Markov chain Monte Carlo (MCMC) methods typically requiring expert knowledge. Extensive numerical tests show the validity of the approach and we discuss implications of overdispersion for experimental design. A comprehensive MATLAB toolbox implementing the method is freely available; a python implementation providing the basic capabilities is also available.

Symbol Discrimination Speed in Children With Visual Impairments

“…2 for illustration). 31 The guess rate was fixed to the 50% chance level performance for a 2AFC task and the lapse rate was allowed to vary between 0% and 10%. The reaction times were analyzed in relation to the chronometric response functions obtained in children with NV.…”

Adaptation to Skew Distortions of Natural Scenes and Retinal Specificity of Its Aftereffects

“…The percentage of leftward skew responses as a function of skew amplitude of test stimuli was then fitted with a cumulative Gaussian using Psignifit 4.0 software (asymptotes set free but assumed to be equal) (Schutt et al, 2016). The point of subjective equality (PSE), i.e., the skew amplitude at 50 percent of leftward responses indicated the skew amplitude that was perceived as undistorted.…”

Contrast invariant tuning in human perception of image content

“…We then fit the data for each psychometric function separately using a Weibull function in July 22, 2019 the radius increment detection experiment and a logistic function in the rotation discrimination experiment (both parametrized as in [50]). Psychometric functions were determined using Bayesian inference, which tends to give slightly better confidence intervals [51], by directly integrating the posterior [52]. Thresholds were defined as the point at which the psychometric function reached 75% correct performance.…”