Coupled latent differential equation with moderators: Simulation and application.

Abstract

Latent differential equations (LDE) use differential equations to analyze time series data. Because of the recent development of this technique, some issues critical to running an LDE model remain. In this article, the authors provide solutions to some of these issues and recommend a step-by-step procedure demonstrated on a set of empirical data, which models the interaction between ovarian hormone cycles and emotional eating. Results indicated that emotional eating is self-regulated. For instance, when people do more emotional eating than normal, they will subsequently tend to decrease their emotional eating behavior. In addition, a sudden increase will produce a stronger tendency to decrease than will a slow increase. We also found that emotional eating is coupled with the cycle of the ovarian hormone estradiol, and the peak of emotional eating occurs after the peak of estradiol. The self-reported average level of negative affect moderates the frequency of eating regulation and the coupling strength between eating and estradiol. Thus, people with a higher average level of negative affect tend to fluctuate faster in emotional eating, and their eating behavior is more strongly coupled with the hormone estradiol. Permutation tests on these empirical data supported the reliability of using LDE models to detect self-regulation and a coupling effect between two regulatory behaviors.

Adaptive Equilibrium Regulation: Modeling Individual Dynamics on Multiple Timescales

“…If more timescales are nested, the data resolution requirements and expectations of measurement error become stricter proportional to each additional timescale. This model may also be expanded to the multivariate case outlined by Hu et al (2014) by cross-regressing derivatives between observed series on one or both timescales. This would allow variables, whether within or between persons, to exhibit influence on each other specific to timescale.…”

“…Dynamical Systems Analysis (DSA) has been advocated to provide parameterizations of change that better represent feedback control as it is found in living systems (Barton, 1994; Boker, 2002). DSA has seen a growing variety of applications to time series data in the life sciences and medical research where they have been used, for example, to model cognitive response patterns (Smith, 2000), postural control (Oie, Kiemel, & Jeka, 2002), regulation of emotions in nonclinical populations (Chow, Ram, Boker, Fujita, & Clore, 2005; Oravecz, Tuerlinckx, & Vandekerckhove, 2011) as well as in borderline personality disorder (Ebner-Priemer et al, 2015), patterns of nicotine and alcohol use (Boker & Graham, 1998), ovarian hormone cycles (Boker, Neale, & Klump, 2014), and to link hormone cycles to negative affect and eating behavior (Hu, Boker, Neale, & Klump, 2014). …”

A Comparison of Two-Stage Approaches for Fitting Nonlinear Ordinary Differential Equation Models with Mixed Effects

“…Like the models above, Equation 8 has analytic solutions; the mathematical form of the solution depends on the values of η and ζ (Hu, Boker, Neale, & Klump, 2014), but all solutions can be readily found in most standard textbooks on ODEs (e.g., Zill, 1993), or in discrete-time form for the SDE variation of Equation 8 (Oud, 2007; Voelkle et al, 2012). 3 …”

“…In earlier implementations of the GLLA, the selection of τ was informed by fitting the hypothesized ODE model multiple times to GLLA-based derivative estimates obtained across a range of τ values, and identifying the optimal τ as the τ that provides the best model fit (e.g., in terms of R 2 , or information criterion measures), or the τ at which the estimate of particular model parameter (e.g., the frequency parameter in a damped linear oscillator model) has begun to stabilize (Hu et al, 2014). More recently, there has been a shift toward setting τ to 1 and selecting d such that the embedding dimension is spans further than notable autocorrelations in the time series (Boker et al, 2014).…”

“…The corresponding derivatives are also computed based on raw observed data without additional smoothing. With d > 3, a larger window of neighboring observations is used to compute the local level and derivative estimates (Hu et al, 2014). The greater overlap between successive windows “smooths” the level and derivative estimates, much like a weighted moving average process.…”