Murre and Dros (2015) used multiple studies to validate their findings in replicating the work on the "forgetting curve," originally pioneered by Ebbinghaus. These parameter values are based on Ebbinghaus's (1880) work.
Walsh et al. (2018) conducted an analysis of three models of the spacing effect in learning.
In this code, I reference the ACT-R model (Pavlik and Anderson, 2005), expanding upon its result, the activation level, by applying the work done by Murre and Dros.
- myu_1 is the initial strength of the memory traces in store 1,
- a_1 is the decay rate in store 1,
- myu_2 is the rate of consolidating the contents of store 1 to store 2, and
- a_2 is the decay rate in store 2
Under the conditions of this experiment, store 1 is the hippocampus, where memory exponentially declines in intensity and store 2 is the neocortex, where memory contents are steadily transferred for long-term retention and decline at a lower rate.
I applied Murre and Dros' equation to Walsh et al.'s (2018) work investigating ACT-R and two other models of spaced memory practice and, I think, expanded the accuracy of the activation likelihood predictions made by ACT-R's simplified implementation of Ebbinghaus' classic forgetting curve.
Further work could use ACT-R's models of spaced practice and retention; however, I strongly suggest investigating Walsh et al.'s claims that ACT-R is not the best means (of the three they investigated) to model accelerated relearning.
Murre JMJ, Dros J. (2015). Replication and Analysis of Ebbinghaus’ Forgetting Curve. PLoS ONE 10(7): e0120644. doi:10.1371/journal. pone.0120644
Ebbinghaus H. (1880). Urmanuskript "Ueber das Gedächtniß". Passau: Passavia Universitätsverlag.
Pavlik, PI & Anderson, JR. (2005). Practice and forgetting effects on vocabulary memory: An Activation-based model of the spacing effect. Cognitive Science, 29, 559-586.
Walsh, M.M., Gluck, K.A., Gunzelmann, G., Jastrzembski, T., Krusmark, M., Myung, J.I., Pitt, M.A., & Zhou, R. (2018). Mechanisms underlying the spacing effect in learning: A comparison of three computational models. Journal of Experimental Psychology: General, 147, (9):1325-1348.