Modeling Psychophysical Data in R: A Comparative Study of Four Model Frameworks

Inferential models in psychophysics are essential for quantifying the relation between physical properties of the stimulus and their perceptual representations. The psychometric function is typically used to model the responses of individual participants in forced-choice experiments. The accuracy and the noise of the response can be estimated from the Point of Subjective Equality (PSE) and the Just Noticeable Difference (JND) of the function, respectively. Traditionally, a two-level approach is used to model the behavior of a group of participants, where psychometric functions are first fitted to individual participant data, followed by hypothesis testing across participants on parameters of interest. Recent studies have introduced alternative approaches based on hierarchical models, such as Generalized Linear Mixed Models (GLMM) and Models within the Bayesian Hierarchical Framework (BHF), to analyze in a single framework the responses from multiple participants. These two approaches can be effectively implemented in R, thanks to its flexibility and robust statistical capabilities. Here, we provide a tutorial on how to model and analyze data from psychophysical experiments in R, using both two-level and hierarchical frameworks. Our goal is to provide researchers with a practical guide for building a complete and reproducible analysis pipeline, using core R functionalities together with custom packages, and facilitate rigorous and efficient data analysis in psychophysics. Competing Interest Statement The authors have declared no competing interest. Footnotes p.balestrucci{at}hsantalucia.it maura.mezzetti{at}uniroma2.it b.lascaleia{at}hsantalucia.it

section clarified, added supplemental information and moved all supplemental materials in separate document https://github.com/moskante/hierarchical-models-psychophysics