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

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.

A tutorial on ordinary differential equations in behavioral science: What does physics teach us?

“…A similar approach based on the structural equation model (SEM) paradigm has been developed by Boker and coworkers (Boker et al, 2004; Boker & Nesselroade, 2002), improved over time (Boker, Moulder, et al, 2019; Hu et al, 2014; Hu & Boker, 2016; McKee et al, 2020), and used in numerous studies (Chow et al, 2005; Deboeck & Boulton, 2016; Hardt et al, 2020; Pettersson et al, 2013; Steele & Ferrer, 2011). It is called the latent differential equation (LDE) method.…”