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SEM State Space Modeling of Panel Data in Discrete and Continuous Time and its Relationship to Traditional State Space Modeling

  • Chapter
Recent Developments on Structural Equation Models

Part of the book series: Mathematical Modelling: Theory and Applications ((MMTA,volume 19))

Abstract

The state space approach, introduced by Kalman (1960) and Zadeh and Desoer (1963), distinguishes modern systems and control theory (Cames, 1988; Hannan & Deistler, 1988; Polderman & Willems, 1998) from the classical theory. Its application field, starting from space technology in the 1960s, has extended considerably since (Shumway & Stoffer, 2000). The state space model covers an extremely general class of dynamic models. In fact, all nonanticipative models (models with no causal arrows heading backward in time) can be represented in state space form. For example, both the Box-Jenkins ARMA model and the extended ARMAX model, which adds exogenous or input variables to the ARMA model, are easily formulated as special cases of the state space model (Cames, 1988; Deistler, 1985; Ljung, 1985). The state space model covers also longitudinal latent factor and path analysis models and allows the optimal estimation of the latent states or factor scores (Oud, van den Bercken & Essers, 1990; Oud, Jansen, van Leeuwe, Aarnoutse, & Voeten, 1999). Latent state estimation is performed by two important results of the state space approach: the Kalman filter and smoother (Kalman, 1960; Rauch, Tung, & Striebel, 1965).

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Author information

Authors and Affiliations

  1. Institute of Family and Child Care Studies, University of Nijmegen, Nijmegen, The Netherlands

    Johan Oud

  2. Monitoring Systems Consult, Nijmegen, The Netherlands

    Johan Oud

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  1. Johan Oud
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Editors and Affiliations

  1. Free University Amsterdam, Amsterdam, The Netherlands

    Kees van Montfort

  2. University of Nijmegen, Nijmegen, The Netherlands

    Johan Oud

  3. Universitat Pompeu Fabra, Barcelona, Spain

    Albert Satorra

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Oud, J. (2004). SEM State Space Modeling of Panel Data in Discrete and Continuous Time and its Relationship to Traditional State Space Modeling. In: van Montfort, K., Oud, J., Satorra, A. (eds) Recent Developments on Structural Equation Models. Mathematical Modelling: Theory and Applications, vol 19. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-1958-6_2

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  • DOI: https://doi.org/10.1007/978-1-4020-1958-6_2

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-6549-0

  • Online ISBN: 978-1-4020-1958-6

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