Conditional GLMMs for reaction times in choice tasks

This study connects two methods for modeling reaction times (RTs) in choice tasks: (1) the first-hitting time of a simple diffusion model with a single barrier, representing the cognitive process leading to a response, and (2) Generalized Linear Mixed Models (GLMMs). We achieve this by analyzing the RT distributions conditioned on each response alternative. Because certain diffusion model variants yield Inverse Gaussian (IG) and Gamma distributions for first-hitting times, we can justify using these distributions in RT models. Conversely, employing IG and Gamma distributions within GLMMs allows us to infer the underlying cognitive processes, reconstructed under a moment-based approximation, being this reconstruction exact when random-effect conditionals are set at C = 0. We demonstrate this concept through simulations and apply it to previously published real-world data. Finally, we discuss the scope and potential extensions of our approach.