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A Note on the Usefulness of Constrained Fourth-Order Latent Differential Equation Models in the Case of Small T

Author

Listed:
  • Katinka Hardt

    (Humboldt-Universität zu Berlin)

  • Steven M. Boker

    (University of Virginia)

  • Cindy S. Bergeman

    (University of Notre Dame)

Abstract

Constrained fourth-order latent differential equation (FOLDE) models have been proposed (e.g., Boker et al. 2020) as alternative to second-order latent differential equation (SOLDE) models to estimate second-order linear differential equation systems such as the damped linear oscillator model. When, however, only a relatively small number of measurement occasions T are available (i.e., $$T=50$$ T = 50 ), the recommendation of which model to use is not clear (Boker et al. 2020). Based on a data set, which consists of $$T=56$$ T = 56 observations of daily stress for $$N=44$$ N = 44 individuals, we illustrate that FOLDE can help to choose an embedding dimension, even in the case of a small T. This is of great importance, as parameter estimates depend on the embedding dimension as well as on the latent differential equations model. Consequently, the wavelength as quantity of potential substantive interest may vary considerably. We extend the modeling approaches used in past research by including multiple subjects, by accounting for individual differences in equilibrium, and by including multiple instead of one single observed indicator.

Suggested Citation

  • Katinka Hardt & Steven M. Boker & Cindy S. Bergeman, 2020. "A Note on the Usefulness of Constrained Fourth-Order Latent Differential Equation Models in the Case of Small T," Psychometrika, Springer;The Psychometric Society, vol. 85(4), pages 1016-1027, December.
    • Handle: RePEc:spr:psycho:v:85:y:2020:i:4:d:10.1007_s11336-020-09738-x
    DOI: 10.1007/s11336-020-09738-x
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    References listed on IDEAS

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    1. Timo Oertzen & Steven Boker, 2010. "Time Delay Embedding Increases Estimation Precision of Models of Intraindividual Variability," Psychometrika, Springer;The Psychometric Society, vol. 75(1), pages 158-175, March.
    2. Johan H. L. Oud & Hermann Singer, 2008. "Editorial introduction," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 62(1), pages 1-3, February.
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