A hierarchical Bayesian model for measuring individual-level and group-level numerical representations

TL;DR

This paper introduces a hierarchical Bayesian model to improve the measurement of individual and group numerical representations, specifically for effects like SNARC and numerical distance, offering better accuracy especially with small samples.

Contribution

The paper develops a hierarchical Bayesian framework for joint estimation of individual and group slopes in numerical cognition studies, enhancing measurement accuracy over classical methods.

Findings

Bayesian model provides more reliable estimates with small samples.

The framework effectively assesses SNARC and numerical distance effects.

Bayesian approach improves measurement fidelity.

Abstract

A popular method for indexing numerical representations is to compute an individual estimate of a response time effect, such as the SNARC effect or the numerical distance effect. Classically, this is done by estimating individual linear regression slopes and then either pooling the slopes to obtain a group-level slope estimate, or using the individual slopes as predictors of other phenomena. In this paper, I develop a hierarchical Bayesian model for simultaneously estimating group-level and individual-level slope parameters. I show examples of using this modeling framework to assess two common effects in numerical cognition: the SNARC effect and the numerical distance effect. Finally, I demonstrate that the Bayesian approach can result in better measurement fidelity than the classical approach, especially with small samples.