Identifying individual difference correlations when the data are noisy: A case study of proactive and reactive control

The Dual Mechanisms of Control (DMC) framework postulates two distinct and semi-independent modes of cognitive control. Proactive control is hypothesized to be anticipatory, engaged prior to stimulus onset, whereas reactive control is triggered by stimulus or response features. In the current study, we test a key prediction of this framework: that individual differences in proactive control and reactive control should be weakly correlated, if at all. There is a key challenge faced by correlational analyses: measurement error will systematically lower correlation values; so much so that observing a small (or non-existent) correlation is difficult to interpret. To address this challenge, we develop a hierarchical model that appropriately estimates measurement error and individual covariation simultaneously. Drawing on a recent large-sample dataset that experimentally dissociates proactive and reactive control during the Stroop color word task (Ileri-Tayar et al, 2025), we demonstrate that hierarchical-model-based analyses not only disattenuate correlations from the impact of measurement error noise, but also provide trustworthy credible intervals that are better suited for statistical inference. With measurement error properly estimated and removed, we find evidence that proactive and reactive control indices are only weakly related, consistent with the DMC framework. This work showcases the advantages of hierarchical models for individual differences research, by providing a blueprint for how researchers can accurately estimate correlations as well as measurement-related uncertainty in low-reliability task contexts.