An Unscented Kalman Filter Approach to the Estimation of Nonlinear Dynamical Systems Models

Multivariate Behavioral Research
Sy-Miin ChowJohn R Nesselroade

Abstract

In the past several decades, methodologies used to estimate nonlinear relationships among latent variables have been developed almost exclusively to fit cross-sectional models. We present a relatively new estimation approach, the unscented Kalman filter (UKF), and illustrate its potential as a tool for fitting nonlinear dynamic models in two ways: (1) as a building block for approximating the log-likelihood of nonlinear state-space models and (2) to fit time-varying dynamic models wherein parameters are represented and estimated online as other latent variables. Furthermore, the substantive utility of the UKF is demonstrated using simulated examples of (1) the classical predator-prey model with time series and multiple-subject data, (2) the chaotic Lorenz system and (3) an empirical example of dyadic interaction.

References

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Citations

Jul 31, 2009·Multivariate Behavioral Research·Sy-Miin ChowJason C Allaire
Sep 27, 2008·Annual Review of Psychology·John J McArdle
Oct 31, 2012·International Journal of Psychophysiology : Official Journal of the International Organization of Psychophysiology·Emilio Ferrer, Jonathan L Helm
Sep 23, 2014·Journal of Computational Biology : a Journal of Computational Molecular Cell Biology·Takanori HasegawaTatsuya Akutsu
Dec 1, 2011·Journal of Dr. NTR University of Health Sciences·John J McArdle
Feb 18, 2016·Multivariate Behavioral Research·Zita OraveczJoachim Vandekerckhove
Oct 28, 2014·International Journal for Numerical Methods in Biomedical Engineering·S PantI E Vignon-Clementel
Apr 17, 2016·Assessment·Kathleen M Gates, Siwei Liu
Nov 6, 2018·Multivariate Behavioral Research·Philippe Rast, Emilio Ferrer
Jan 1, 2014·Multivariate Behavioral Research·Hairong Song, Zhiyong Zhang
Sep 29, 2020·Structural Equation Modeling : a Multidisciplinary Journal·Steven M BokerGustav R Sjobeck
May 24, 2017·Multivariate Behavioral Research·Janne K AdolfFlorian Schmiedek
Oct 8, 2020·Multivariate Behavioral Research·Zachary F FisherKathleen M Gates
Jun 1, 2017·Current Opinion in Behavioral Sciences·Emilio Ferrer, Philippe Rast
Jun 23, 2021·Multivariate Behavioral Research·Jonas M B Haslbeck, Oisín Ryan

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Software Mentioned

LISREL
fminsearch
Matlab

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