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., [Formula: see text]), the recommendation of which model to use is not clear (Boker et al. 2020). Based on a data set, which consists of [Formula: see text] observations of daily stress for [Formula: see text] 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.

中文翻译：

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关于约束四阶潜微分方程模型在小 T 情况下的有用性的注记

已经提出了约束四阶潜在微分方程 (FOLDE) 模型（例如，Boker 等人，2020 年）作为二阶潜在微分方程 (SOLDE) 模型的替代方法来估计二阶线性微分方程系统，例如阻尼线性振荡器模型。然而，当只有相对少量的测量场合 T 可用时（即[公式：见正文]），使用哪种模型的推荐并不明确（Boker 等人，2020 年）。基于一个数据集，其中包含 [公式：见正文] 对 [公式：见正文] 个人日常压力的观察，我们说明 FOLDE 可以帮助选择嵌入维度，即使在 T 很小的情况下。这非常重要，因为参数估计取决于嵌入维度以及潜在微分方程模型。因此，波长作为潜在的实质性利益的数量可能会有很大差异。我们扩展了过去研究中使用的建模方法，包括多个主题，考虑到均衡中的个体差异，以及包括多个而不是一个观察到的指标。