The Asymmetric Laplace Gaussian (ALG) Distribution as the Descriptive Model for the Internal Proactive Inhibition in the Standard Stop Signal Task

Abstract

Measurements of response inhibition components of reactive inhibition and proactive inhibition within the stop-signal paradigm have been of particular interest to researchers since the 1980s. While frequentist nonparametric and Bayesian parametric methods have been proposed to precisely estimate the entire distribution of reactive inhibition, quantified by stop signal reaction times (SSRT), there is no method yet in the stop signal task literature to precisely estimate the entire distribution of proactive inhibition. We identify the proactive inhibition as the difference of go reaction times for go trials following stop trials versus those following go trials and introduce an Asymmetric Laplace Gaussian (ALG) model to describe its distribution. The proposed method is based on two assumptions of independent trial type (go/stop) reaction times and Ex-Gaussian (ExG) models. Results indicated that the four parametric ALG model uniquely describes the proactive inhibition distribution and its key shape features, and its hazard function is monotonically increasing, as are its three parametric ExG components. In conclusion, the four parametric ALG model can be used for both response inhibition components and its parameters and descriptive and shape statistics can be used to classify both components in a spectrum of clinical conditions.