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Modeling Noisy Data with Differential Equations Using Observed and Expected Matrices

Published online by Cambridge University Press:  01 January 2025

Pascal R. Deboeck  and
Steven M. Boker
Pascal R. Deboeck*
Affiliation:
University of Kansas
Steven M. Boker
Affiliation:
University of Virginia
*
Requests for reprints should be sent to Pascal R. Deboeck, Department of Psychology, University of Kansas, Lawrence, KS, USA. E-mail: [email protected]
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Abstract

Complex intraindividual variability observed in psychology may be well described using differential equations. It is difficult, however, to apply differential equation models in psychological contexts, as time series are frequently short, poorly sampled, and have large proportions of measurement and dynamic error. Furthermore, current methods for differential equation modeling usually consider data that are atypical of many psychological applications. Using embedded and observed data matrices, a statistical approach to differential equation modeling is presented. This approach appears robust to many characteristics common to psychological time series.

Keywords

intraindividual variabilitydifferential equation model(s)(ing)time seriesdamped linear oscillatoranalytic solution(s)
Type
Original Paper
Information
Psychometrika , Volume 75 , Issue 3 , September 2010 , pp. 420 - 437
Copyright
Copyright © 2010 The Psychometric Society

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