Dynamical systems analysis applied to working memory data.
Fidan Gasimova, Alexander Robitzsch, Oliver Wilhelm, Steven M Boker, Yueqin Hu, Gizem Hülür
Author Information
Fidan Gasimova: Department of Psychology, Ulm University Ulm, Germany.
Alexander Robitzsch: Federal Institute for Education Research, Innovation and Development of the Austrian Schooling System (BIFIE Salzburg) Salzburg, Austria.
Oliver Wilhelm: Department of Psychology, Ulm University Ulm, Germany.
Steven M Boker: Department of Psychology, University of Virginia Charlottesville, VA, USA.
Yueqin Hu: Department of Psychology, Texas State University San Marcos, TX, USA.
Gizem Hülür: Department of Psychology, Humboldt University Berlin, Germany.
In the present paper we investigate weekly fluctuations in the working memory capacity (WMC) assessed over a period of 2 years. We use dynamical system analysis, specifically a second order linear differential equation, to model weekly variability in WMC in a sample of 112 9th graders. In our longitudinal data we use a B-spline imputation method to deal with missing data. The results show a significant negative frequency parameter in the data, indicating a cyclical pattern in weekly memory updating performance across time. We use a multilevel modeling approach to capture individual differences in model parameters and find that a higher initial performance level and a slower improvement at the MU task is associated with a slower frequency of oscillation. Additionally, we conduct a simulation study examining the analysis procedure's performance using different numbers of B-spline knots and values of time delay embedding dimensions. Results show that the number of knots in the B-spline imputation influence accuracy more than the number of embedding dimensions.
