Adaptive Equilibrium Regulation: Modeling Individual Dynamics on Multiple Timescales

Abstract

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.

Keywords:

• Dynamical systems
• feedback control
• intra-individual
• multi-timescale

ACKNOWLEDGMENTS

The authors thank Drs. Joshua Pritikin, Steven Aggen, and Robert Kirkpatrick of Virginia Commonwealth University’s Virginia Institute of Psychiatric and Behavioral Genetics for feedback on model development and OpenMx technical support. Collection of the affect data was supported by Social Sciences and Humanities Research Council of Canada and Fonds Pour la Formation de Chercheurs et lAide a’ la Recherche du Quebec.

Notes

¹ In all occurrences, we use the term ‘noise’ to refer to superposed, i.i.d., random variation such as measurement error, as distinct from stochastic variation in the signal, otherwise known as dynamic error.

² For the simulations in this study, values of were sufficiently small, and timescale ratios were approximate and randomly varied, such that both terms were excluded from calculations.

³ Compatible techniques for data with irregular intervals have been developed (see Tiberio, 2008).

⁴ Innovational outliers often go by other names including events, dynamic error outliers, jump discontinuities, or disturbances.

Additional information

Funding

This work was supported by the National Institute on Drug Abuse [DA 018673 (PI Neale)].