Disentangling within- and between-subject correlations in cognitive models: The essential role of hierarchical estimation.

Cognitive models, such as evidence-accumulation models, are increasingly used in individual differences research in psychology and neuroscience. By computing correlations between cognitive model parameters across participants, researchers aim to understand how the psychological processes the parameters represent relate to one another and jointly determine performance. It is generally acknowledged that cognitive models can be challenging to estimate due to strong within-subject correlations among the parameters, which are embedded in the model's likelihood function. What is less often recognized, however, is that within-subject correlations can also distort correlations computed between parameters estimated with non-hierarchical methods, so they no longer reflect true individual differences, potentially leading to misleading conclusions. Here we illustrate this pitfall of non-hierarchical estimation and show how appropriately parameterized, descriptively adequate hierarchical models can mitigate the problem by effectively separating within- and between-subject sources of variation. We then offer recommendations for identifying and guarding against the inferential biases resulting from the strong within-subject correlations inherent in many cognitive models.