Posts Tagged ‘Dynamical Systems Analysis’

Dynamics of Change and Change in Dynamics

Friday, March 23rd, 2018

Boker, S. M., Staples, A., & Hu, Y. (2016) Dynamics of Change and Change in Dynamics. Journal for Person-Oriented Research, 2:1–2, 34–55.

A framework is presented for building and testing models of dynamic regulation by categorizing sources of differences between theories of dynamics. A distinction is made between the dynamics of change, i.e., how a system self–regulates on a short time scale, and change in dynamics, i.e., how those dynamics may themselves change over a longer time scale. In order to clarify the categories, models are first built to estimate individual differences in equilibrium value and equilibrium change. Next, models are presented in which there are individual differences in parameters of dynamics such as frequency of fluctuations, damping of fluctuations, and amplitude of fluctuations. Finally, models for within–person change in dynamics over time are proposed. Simulations demonstrating feasibility of these models are presented and OpenMx scripts for fitting these models have been made available in a downloadable archive along with scripts to simulate data so that a researcher may test selected models’ feasibility within a chosen experimental design.

The article accepted for publication can be downloaded as a PDF.

Adaptive Equilibrium Regulation: Modeling Individual Dynamics on Multiple Timescales

Friday, March 23rd, 2018

McKee, K. L., Neale, M. C., Rappaport, L. M., & Boker, S. M. (in press) Adaptive Equilibrium Regulation: Modeling Individual Dynamics on Multiple Timescales. Structural Equation Modeling

Damped Linear Oscillators estimated by 2nd-order Latent Differential Equation (LDE) 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.

The article accepted for publication can be downloaded as a PDF.

Selection, Optimization, Compensation, and Equilibrium Dynamics

Thursday, May 23rd, 2013

Boker, S. M. (2013) Selection, Optimization, Compensation, and Equilibrium Dynamics. The Journal of Gerontopsychology and Geriatric Psychiatry, 26:1, 61-73.

One of the major theoretic frameworks through which human development is studied is a process-oriented model involving selection, optimization, and compensation. These three processes each provide accounts for methods by which gains are maximized and losses minimized throughout the lifespan, and in particular during later life. These processes can be cast within the framework of dynamical systems theory and then modeled using differential equations. The current article will review basic tenets of selection, optimization, and compensation whilst introducing language and concepts from dynamical systems. Four categories of interindividual differences and intraindividual variability in dynamics are then described and discussed in the context of selection, optimization, and compensation.

The manuscript of this article accepted for publication can be downloaded as a PDF. This article may not exactly replicate the final version published in The Journal of Gerontopsychology and Geriatric Psychiatry. It is not the copy of record.

Latent Differential Equations with Moderators: Simulation and Application

Wednesday, January 16th, 2013

Hu, Y., Boker, S. M., Neale, M. C. & Klump, K. (in press) Latent Differential Equations with Moderators: Simulation and Application. Psychological Methods

Latent Differential Equations (LDE) is an approach using differential equations to analyze time series data. Due to its recent development, some technique issues critical to performing an LDE model remain. This article provides solutions to some of these issues, and recommends 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 have more emotional eating behavior 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 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. 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.

The full text of this article can be dowloaded from APA Psycnet as a PDF.

A Differential Equations Model for the Ovarian Hormone Cycle

Monday, December 17th, 2012

Boker, S. M., Neale, M. C. & Klump, K. L. (in press) A Differential Equations Model for the Ovarian Hormone Cycle. In Handbook of Relational Developmental Systems: Emerging Methods and Concepts, P. C. Molenaar, R. Lerner, & K. Newell (Eds). New York: John Wiley & Sons

Dynamical systems models of behavior and regulation have become increasingly popular due to the promise that within-person mechanisms can be modeled and explained. However, it can be difficult to construct differential equation models of regulatory dynamics which test specific theoretically interesting mechanisms. The current chapter uses the example of ovarian hormone regulation and develops a model step by step in order for the model to be able to capture features of observed hormone levels as well as to link parameters of the model to biological mechanisms. Ovarian hormones regulate the monthly female reproductive cycle and have been implicated as having effects on affective states and eating behavior. The three major hormones in this system are estrogen, progesterone, and lutenizing hormone. These hormones are coupled together as a regulatory system. Estrogen level is associated with the release of lutenizing hormone by the hypothalamus. Lutenizing hormone triggers ovulation and the transformation of the dominant follicle into the corpus luteus which in turn produces progesterone. A differential equations model is developed that is biologically plausible and produces nonlinear cycling similar to that seen in a large ongoing daily-measure study of ovarian hormones and eating behavior.

The manuscript of this article accepted for publication can be requested as a pdf file from the first author: Steve Boker.

On the Equilibrium Dynamics of Meaning

Monday, December 17th, 2012

Boker, S. M. & Martin, M. (in press) On the Equilibrium Dynamics of Meaning. In Current Issues in the Theory and Application of Latent Variable Models, M. Edwards & R. MacCallum, (Eds). New York: Taylor & Francis.

Meaning is at the heart of what we do in latent variable modeling. A latent construct is a way to aggregate and focus meaning into quantifiable constructs. Structural models, and in particular factor models, are a way to use the considerable power of product moment matrices to focus meaning in such a way that it aggregates across participants (or within participant across time) in the hope that the meaning that the psychologist had in mind is the meaning that emerges in the latent variable indicated by the participants’ responses. But, what is meaning? And how is it attached to words or utterances? Philosophers of language have written about this problem, and so we review some recent arguments in epistemology in order to build the central thesis of this paper: If one takes context into account, intraindividual meanings are likely to have intrinsic dynamics that tend towards stable equilibria. We then discuss the implications from a lifespan psychological perspective for the meaning of an example variable: quality of life. Finally, some we discuss some ideas about what might be necessary in order to specify a factor analysis of sufficiency rather than a factor analysis of aggregation.

The manuscript of this article accepted for publication can be requested as a pdf file from the first author: Steve Boker.

Dynamical Systems and Differential Equation Models of Change

Monday, December 17th, 2012

Boker, S. M. (2012) Dynamical Systems and Differential Equation Models of Change. In APA Handbook of Research Methods in Psychology, Volume 3, H. Cooper, A. Panter, P. Camic, R. Gonzalez, D. Long, & K. Sher, (Eds). Washington, DC: American Psychological Association, pp 323-333.

This chapter provides a brief introduction to dynamical systems modeling from the standpoint of latent differential equations.

The manuscript of this article accepted for publication can be requested as a pdf file from the author: Steve Boker.

Correlational Methods for Analysis of Dance Movements

Monday, December 17th, 2012

Brick, T. R. & Boker, S. M. (2011) Correlational Methods for Analysis of Dance Movements. Dance Research, Special Electronic Issue: Dance and Neuroscience: New Partnerships, 29:2, 283–304

We propose to present three methods for the exploration of symmetry and synchrony in motion-capture data as is it applied to dance and illustrate these with examples from a study of free-form dance. First, Generalized Local Linear Approximation (GLLA) provides a transformation from the positional data returned by such a system into a representation including approximations of velocity and acceleration. Using these newly transformed data, time-lagged autocorrelation can provide insight into the structure of temporal symmetry within a single person’s movements during the dance. Windowed cross-correlation can show other kinds of symmetry between individuals or between an individual and an outside stimuli, such as a rhythm or musical work. Combined, these techniques provide powerful tools for the examination of the structure of symmetry and synchrony in dance.

The manuscript of this article accepted for publication can be requested as a pdf file from the first author: Timothy Brick at the Max Planck Institute for Human Development.

Time Delay Embedding Increases Estimation Precision of Models of Intraindividual Variability

Monday, December 17th, 2012

Oertzen, T. v. & Boker, S. (2010) Time Delay Embedding Increases Estimation Precision of Models of Intraindividual Variability. Psychometrika, 75:1, 158-175. NIHMS ID: 427398

This paper investigates the precision of parameters estimated from local samples of time dependent functions. We find that time delay embedding, i.e., structuring data prior to analysis by constructing a data matrix of overlapping samples, increases the precision of parameter estimates and in turn statistical power compared to standard independent rows of panel data. We show that the reason for this effect is that the sign of estimation bias depends on the position of a misplaced data point if there is no a priori knowledge about initial conditions of the time dependent function. Hence, we reason that the advantage of time delayed embedding is likely to hold true for a wide variety of functions. We support these conclusions both by mathematical analysis and two simulations.

The manuscript of this article accepted for publication can be downloaded as a PDF. This article may not exactly replicate the final version published in Psychometrika. It is not the copy of record.

Resilience-As-Process: Negative Affect, Stress, and Coupled Dynamical Systems

Tuesday, March 23rd, 2010

Montpetit, M. A., Bergeman, C. S., Deboeck, P. R., Tiberio, S. S., & Boker, S. M. (2010) Resilience-As-Process: Negative Affect, Stress, and Coupled Dynamical Systems. Psychology and Aging 25:3, 631-640

This article describes a link between stress and negative affect as a system of coupled linear differential equations. The idea is basically that stress and negative affect are coupled, but that those individuals with higher trait resilience scores would experience stress as being less coupled to changes in negative affect. In addition it was found that higher levels of social support resulted in greater damping of the fluctuations in negative affect and decreased coupling between stress and negative affect.

The manuscript of this article accepted for publication can be requested as a pdf file from the first author: Mignon Montpetit at Illinois Wesleyan University.