Abstract
Maximum likelihood parameter estimation of the continuous time linear stochastic state space model is considered on the basis of largeN 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.
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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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Oud, J.H.L., Jansen, R.A.R.G. Continuous time state space modeling of panel data by means of sem. Psychometrika 65, 199–215 (2000). https://doi.org/10.1007/BF02294374
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DOI: https://doi.org/10.1007/BF02294374