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Parameter correlations in the predictive performance equation: Implications and solutions

Michael Collins
Cognitive Models and Agents Branch ~ Cognitive Models and Agents Branch
Florian Sense
InfiniteTactics, LLC
Michael Krusmark
Joshua Fiechter
Tiffany (Jastrzembski) Myers
Air Force Research Laboratory

Research of mathematical models of learning and retention have focused on accounting for an individual’s performance across a variety of learning schedules (i.e., spaced and massed). The attempted goal of such research is to develop a model which can adequately predict human performance across a range of learning scenarios. However, little attention of this model development has focused on the interpretation of a model’s best fitting parameters given the structure of a model’s equations and its predicted performance values. The effect of this can lead to the development of models where the parameter values are correlated hindering a theoretical interpretation of performance. Here we examine the structure of the Predictive Performance Equation (PPE) and highlight portions of PPE’s equations that lead to correlations across its free parameters. We propose a fix for these issues (Modified PPE) and conduct a formal model comparison showing the Modified PPE is simpler, has less parameter correlation and its best fitting parameters map on to identifiable aspects of an individual’s performance.



spacing effect
mathematical modeling
model comparison
model identifiability

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Cite this as:

Collins, M., Sense, F., Krusmark, M., Fiechter, J., & Myers, T. (2021, July). Parameter correlations in the predictive performance equation: Implications and solutions. Paper presented at Virtual MathPsych/ICCM 2021. Via