Adaptive Equilibrium Regulation: Modeling Individual Dynamics on Multiple Timescales

• Published in: Structural equation modeling Vol. 25; no. 6; pp. 888 - 905
• Main Authors: McKee, Kevin L., Rappaport, Lance M., Boker, Steven M., Moskowitz, Debbie S., Neale, Michael C.
• Format: Journal Article
• Language: English
• Published: United States Routledge 01-01-2018; Psychology Press
• Subjects: Dynamical systems; Equilibrium; feedback control; intra-individual; multi-timescale; intra-individual; Dynamical systems; feedback control; multi-timescale
• ISSN: 1070-5511; 1532-8007
• DOI: 10.1080/10705511.2018.1442224

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.