SMABS 2004 Jena University
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European Association of Methodology

Department of methodology and evaluation research

Jena University

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Contributions: Abstract

A comparison of different procedures to estimate the damped linear ocillator for panel data

Johan Oud
University of Nijmegen
The Netherlands

There is a growing interest in the application of the damped linear oscillator in panel research (Boker, 2002; Oud, 2002; Singer, 1993) of partially observed systems. Examples in psychological research are discussed by Boker. The damped linear oscillator is a special case of differential equation modeling (Oud, 2000), which since Newton is the standard approach of dynamic phenomena in natural science.

Different procedures, exact and approximate, have been used to estimate the damped linear oscillator. In his software package LSDE (Linear Stochastic Differential Equations), Singer used the exact discrete model (EDM) and the expectation-maximization (EM) algorithm. Oud used also the exact discrete model but in combination with structural equation modeling (EDM/SEM procedure). In addition to this procedure, which requires highly nonlinearly oriented SEM software, Oud also proposed the less demanding approximate ADM/SEM procedure. A final approximate procedure was proposed by Boker: the multivariate linear differential equation (MLDE) procedure. The four procedures will be compared in a simulation study and their advantages and drawbacks expounded.


Boker, S.M. (2002). Consequences of continuity: the hunt for intrinsic properties within parameters of dynamics in psychological processes. Multivariate Behavioral Research, 37, 405-422.

Oud, J.H.L., & Jansen, R.A.R.G. (2000). Continuous time state space modeling of panel data by means of SEM. Psychometrika, 65, 199-215.

Oud, J.H.L. (2002). Continuous time modeling of the cross-lagged panel design. Kwantitatieve Methoden, 23 (69), 1-26.

Singer, H. (1993). Continuous-time dynamic systems with sampled data, errors of measurement and unobserved components. Journal of Time Series Analysis, 5, 527-545.