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Time Delay Embedding Increases Estimation Precision of Models of Intraindividual Variability

Published online by Cambridge University Press:  01 January 2025

Timo von Oertzen  and
Steven M. Boker
Timo von Oertzen*
Affiliation:
Max Planck Institute for Human Development
Steven M. Boker
Affiliation:
University of Virginia
*
Requests for reprints should be sent to Timo von Oertzen, Center for Lifespan Psychology, Max Planck Institute for Human Development, Berlin, Germany. E-mail: vonoertzen@mpib-berlin.mpg.de
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Abstract

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This paper investigates the precision of parameters estimated from local samples of time dependent functions. We find that time delay embedding, i.e., structuring data prior to analysis by constructing a data matrix of overlapping samples, increases the precision of parameter estimates and in turn statistical power compared to standard independent rows of panel data. We show that the reason for this effect is that the sign of estimation bias depends on the position of a misplaced data point if there is no a priori knowledge about initial conditions of the time dependent function. Hence, we reason that the advantage of time delayed embedding is likely to hold true for a wide variety of functions. We support these conclusions both by mathematical analysis and two simulations.

Keywords

time delay embeddingdynamical systems modelsintraindividual variabilityoscillatory data
Type
Theory and Methods
Information
Psychometrika , Volume 75 , Issue 1 , March 2010 , pp. 158 - 175
Creative Commons
Creative Common License - CCCreative Common License - BYCreative Common License - NC
This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
Copyright
Copyright © 2009 The Psychometric Society

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