TY - JOUR
T1 - An unscented kalman filter approach to the estimation of nonlinear dynamical systems models
AU - Chow, Sy Miin
AU - Ferrer, Emilio
AU - Nesselroade, John R.
N1 - Funding Information:
We thank Jack McArdle, Ellen Bass, Howard Epstein, Fumiaki Hamagami and a few anonymous reviewers for their valuable comments on earlier versions of this article. This study was supported by a National Institute on Aging grant 5 R01 AG18330 awarded to John R. Nesselroade while the first author was completing her Ph.D. at the University of Virginia. Support from the Humboldt Foundation and the Max Planck Institute for Human Development is also gratefully acknowledged. Matlab codes used for model fitting can be downloaded from Sy-Miin Chow’s website at http://www.nd.edu/ schow. Correspondence concerning this article should be addressed to Sy-Miin Chow, Department of Psychology, 108 Haggar Hall, University of Notre Dame, Notre Dame, IN 46556. Electronic mail may be sent to [email protected].
PY - 2007
Y1 - 2007
N2 - 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.
AB - 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.
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U2 - 10.1080/00273170701360423
DO - 10.1080/00273170701360423
M3 - Article
AN - SCOPUS:34547444901
SN - 0027-3171
VL - 42
SP - 283
EP - 321
JO - Multivariate Behavioral Research
JF - Multivariate Behavioral Research
IS - 2
ER -