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Modeling Noisy Data with Differential Equations Using Observed and Expected Matrices

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.

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Correspondence to Pascal R. Deboeck.

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Deboeck, P.R., Boker, S.M. Modeling Noisy Data with Differential Equations Using Observed and Expected Matrices. Psychometrika 75, 420–437 (2010). https://doi.org/10.1007/s11336-010-9168-2

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Keywords

  • intraindividual variability
  • differential equation model(s)(ing)
  • time series
  • damped linear oscillator
  • analytic solution(s)