Abstract
Cognitive models provide a principled alternative for hypothesis testing and measuring individual differences. However, many cognitive models are computationally intensive to simulate, making their use difficult. Using approximations can make the application of cognitive models more tractable. We compare the standard and hybrid approximations of the base-level activation equation for the ACT-R cognitive architecture with respect to four criteria: (1) preservation of core properties, (2) computational efficiency, (3) robustness to violations of assumptions, and (4) mathematical tractability. Contrary to a core property of the theory, activation for the standard approximation was non-monotonic with respect to the decay parameter, rendering it unidentifiable. Consequentially, the standard approximation is not valid for investigating individual differences in decay or experiments designed to manipulate decay. However, monotonicity is largely preserved with the hybrid approximation. Additionally, we show that both approximations are equally more computationally efficient than the exact equation. Furthermore, the hybrid approximation can achieve the same level of computational efficiency as the standard approximation while achieving greater accuracy. Our robustness analysis reveals that the hybrid approximation is more robust to violations of the assumption of equally spaced retrievals compared to the standard approximation. However, the hybrid approximation sacrifices some mathematical tractability in order to achieve improvements along the other criteria. Based on these findings, we encourage the use of the hybrid approximation for parameter estimation.
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Notes
We explicitly exclude the possibility that d = 1 because neither of the approximations discussed below are defined at that value.
This reflects a more fundamental issue with the formulation of base-level activation that we do not address here, as our focus is on comparing the approximations.
As mentioned by a reviewer, taking the log or non-integer power of a dimension, such as time, is problematic because the dimension will become scale dependent, causing the values of various parameters to change.
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The views expressed in this paper are those of the authors and do not reflect the official policy or position of the Department of Defense or the US Government. Approved for public release; distribution unlimited. Cleared 06/06/2018;88ABW-2018-3530. CF’s contributions to this work were supported by a postdoctoral research associateship, administered by the Oak Ridge Institute for Science and Education (ORISE).
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This work was supported by the Air Force Research Laboratory’s Warfighter Readiness Research Division and the Air Force Office of Scientific Research (grant 18RHCOR068).
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Fisher, C.R., Houpt, J. & Gunzelmann, G. A Comparison of Approximations for Base-Level Activation in ACT-R. Comput Brain Behav 1, 228–236 (2018). https://doi.org/10.1007/s42113-018-0015-3
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DOI: https://doi.org/10.1007/s42113-018-0015-3