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Continuous Time State Space Modeling of Panel Data by Means of Sem

Published online by Cambridge University Press:  01 January 2025

Johan H. L. Oud  and
Robert A. R. G. Jansen
Johan H. L. Oud*
Affiliation:
University of Nijmegen, The Netherlands
Robert A. R. G. Jansen
Affiliation:
University of Nijmegen, The Netherlands
*
Requests for reprints, for the Mx input files, and for other software used in the analysis of the example should be sent to Johan H.L. Oud, University of Nijmegen, Institute of Special education, PO Box 9104, 6500 HE Nijmegen, THE NETHERLANDS. E-Mail: J. [email protected]
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Abstract

Maximum likelihood parameter estimation of the continuous time linear stochastic state space model is considered on the basis of large N discrete time data using a structural equation modeling (SEM) program. Random subject effects are allowed to be part of the model. The exact discrete model (EDM) is employed which links the discrete time model parameters to the underlying continuous time model parameters by means of nonlinear restrictions. The EDM is generalized to cover not only time-invariant parameters but also the cases of stepwise time-varying (piecewise time-invariant) parameters and parameters varying continuously over time according to a general polynomial scheme. The identification of the continuous time parameters is discussed and an educational example is presented.

Keywords

continuous time state space modelingexact discrete modellinear stochastic differential equationslongitudinal structural equation modelingpanel analysis
Type
Original Paper
Information
Psychometrika , Volume 65 , Issue 2 , June 2000 , pp. 199 - 215
Copyright
Copyright © 2000 The Psychometric Society

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Footnotes

Research supported by the University of Nijmegen, Ph.D. project: “Constructing monitoring systems in the behavioral sciences: The SEM state space approach,” under supervision of E.E.J. De Bruyn, J.H.L. Oud and J.F.J. van Leeuwe. The authors thank Martijn P.F. Berger of the University of Maastricht, The Netherlands, for his help in the preparation of the manuscript.

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