The interpretation of behavior-model correlations in unidentified cognitive models

van Maanen, Leendert; Miletić, Steven · 2021 · Crossref

DOI: 10.3758/s13423-020-01783-y

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Summary

This theoretical review addresses a critical methodological issue in computational cognitive modeling: the interpretation of behavior-model correlations when models are unidentified. The authors argue that many widely used models, including Signal Detection Theory (SDT), Reinforcement Learning (RL), and the Linear Ballistic Accumulator (LBA), are only identifiable up to a scaling constraint. This means that parameter estimates are relative to one another, requiring one parameter to be fixed to a constant value to estimate the others. The paper warns that this scaling constraint imposes strong, often implicit assumptions about cognitive processes, leading to potential overinterpretation of individual differences in neurophysiological or psychological factors. To demonstrate these issues, the authors analyze three modeling frameworks. In SDT, they show that fixing the standard deviation of the noise distribution to 1 (standard practice) yields different correlation patterns with an underlying factor than fixing the discriminability ($d'$) or criterion ($c$). Similarly, in RL models, the inverse temperature ($\beta$) and reward weighting ($\gamma$) parameters are unidentified relative to each other; correlations with $\beta$ under the assumption $\gamma=1$ are mathematically equivalent to correlations with $\gamma$ under the assumption $\beta=1$. The authors illustrate that the observed correlation is actually with the ratio of these parameters, not the individual parameters themselves. The paper further provides a reanalysis of empirical data using the LBA model, originally published by Miletić and van Maanen (2019), which correlated LBA parameters with temporal reproduction precision. The original analysis assumed the standard deviation of the winning accumulator was constant, finding that better timers had higher decision thresholds. However, the authors show that changing the scaling constraint—such as fixing the sum of drift rates or the threshold value—alters the statistical outcomes. For instance, under a different constraint, the correlation between drift rate and temporal precision flipped sign, suggesting that precise timers might suppress irrelevant information rather than accumulate evidence faster. These contradictory conclusions arise because parameter values are defined relative to the fixed scaling parameter. The significance of this work lies in its call for clearer interpretation of modeling results. The authors conclude that researchers must explicitly state scaling constraints and interpret parameters as ratios or relative quantities rather than absolute values. By acknowledging that parameters are often expressed relative to each other, similar to how fuel efficiency is measured as a ratio of distance to volume, researchers can avoid ambiguous or contradictory inferences. This approach ensures that associations between model parameters and external variables are interpreted correctly, preventing the misattribution of cognitive mechanisms due to arbitrary mathematical constraints.

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• individual differences