Damped Linear Oscillators estimated by 2nd-order Latent Differential Equation have assumed a constant equilibrium and one oscillatory component. Lower-frequency oscillations may come from seasonal background processes, which non-randomly contribute to deviation from equilibrium at each occasion and confound estimation of dynamics over shorter timescales. Boker (2015) proposed a model of individual change on multiple timescales, but implementation, simulation, and applications to data have not been demonstrated. This study implemented a generalization of the proposed model; examined robustness to varied timescale ratios, measurement error, and occasions-per-person in simulated data; and tested for dynamics at multiple timescales in experience sampling affect data. Results show small standard errors and low bias to dynamic estimates at timescale ratios greater than 3:1. Below 3:1, estimate error was sensitive to noise and total occasions; rates of non-convergence increased. For affect data, model comparisons showed statistically significant dynamics at both timescales for both participants.

中文翻译：

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自适应均衡调节：在多个时间尺度上对个体动态进行建模

由二阶潜在微分方程估计的阻尼线性振荡器假设了一个恒定的平衡和一个振荡分量。低频振荡可能来自季节性背景过程，它非随机地导致每次偏离平衡，并混淆较短时间尺度上的动态估计。Boker (2015) 提出了一个在多个时间尺度上个体变化的模型，但实施、模拟和数据应用尚未得到证实。本研究对所提出的模型进行了推广；在模拟数据中检查了对不同时间尺度比率、测量误差和人均事件的稳健性；并在经验抽样影响数据中测试了多个时间尺度的动态。结果显示，在时间尺度比率大于 3:1 时，对动态估计的标准误差较小，偏差较小。低于 3:1，估计误差对噪声和总场合敏感；不收敛率增加。对于影响数据，模型比较显示两个参与者在两个时间尺度上的统计显着动态。