Bayesian hierarchical models and prior elicitation for fitting psychometric functions - Mezzetti, Maura; Ryan, Colleen P.; Balestrucci, Priscilla; Lacquaniti, Francesco; Moscatelli, Alessandro (Frontiers in Computational Neuroscience, 2023)
Our previous articles demonstrated how to analyze psychophysical data from a group of participants by means of Generalized Linear Mixed Models (GLMM) and two-level methods. The main goal of this article is to revisit hierarchical models into a Bayesian framework. Bayesian models have been previously discussed for the analysis of psychometric functions although this approach is still seldom applied. The main advantage of the using Bayesian models is that, if the prior is informative, the uncertainty of the parameters is reduced through the combination of prior knowledge and the experimental data. Here, we evaluate the uncertainties between and within participants through the posterior distributions. To demonstrate the Bayesian approach, we re-analyzed data from two of our previous studies on the tactile discrimination of speed. We considered different methods to include a priori knowledge in the prior distribution, not only from the literature but also from previous experiments. A special type of Bayesian model, the power prior distribution, allowed us to modulate the weight of the prior, constructed from a first set of data, and use it to fit a second one. Bayesian models estimated the probability distributions of the parameters of interest that convey information about the effects of the experimental variables, their uncertainty, and the reliability of individual participants. We implemented these models by means of the software Just Another Gibbs Sampler (JAGS) that we interfaced with R with the package rjags. Bayesian hierarchical model will provide a promising and powerful method for the analysis of psychometric functions in psychophysical experiments.