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), the recommendation of which model to use is not clear (Boker et al. 2020). Based on a data set, which consists of T=56 observations of daily stress for 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.
Highlights
Differential equations (e.g., Boker and Nesselroade 2002; Oud and Singer 2008; Hecht et al 2019) are of great interest in the study of psychological processes as self-regulating systems
Results generally indicate an advantage of applying fourth-order Latent differential equation (LDE) (FOLDE) when it comes to determining the optimal embedding dimension according to Hu et al (2014)
The absolute value of ζ is different with the second-order latent differential equation (SOLDE) model, indicating stronger damping in the self-regulation process
Summary
Differential equations (e.g., Boker and Nesselroade 2002; Oud and Singer 2008; Hecht et al 2019) are of great interest in the study of psychological processes as self-regulating systems. Constrained fourth-order LDE (FOLDE) models are an alternative to approximating secondorder systems. This is possible because FOLDE builds upon three mathematically equivalent sets. Before both models can be fit to ones data, the data from a time series need to be time delay embedded in a preprocessing step. This article showcases that combining these recent developments can add value to the data analysis using LDE. This research note demonstrates that carefully setting D is important, as substantive conclusions may differ depending on D
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