The authors present in this study a damped oscillator model that provides a direct mathematical basis for testing the notion of emotion as a self-regulatory thermostat. Parameters from this model reflect individual differences in emotional lability and the ability to regulate emotion. The authors discuss concepts such as intensity, rate of change, and acceleration in the context of emotion, and they illustrate the strengths of this approach in comparison with spectral analysis and growth curve models. The utility of this modeling approach is illustrated using daily emotion ratings from 179 college students over 52 consecutive days. Overall, the damped oscillator model provides a meaningful way of representing emotion regulation as a dynamic process and helps identify the dominant periodicities in individuals' emotions.

non-linear, multilevel, longitudinal, missing data, emotion,

Over the last few decades, researchers have become increasingly aware of the need to consider intraindividual variability in the form of cyclic processes. In this paper, we review two contemporary cyclic state-space models: Young and colleagues' dynamic harmonic regression model and Harvey and colleagues' stochastic cycle model. We further derive the analytic equivalence between the two models, discuss their unique strengths and propose multiple-subject extensions. Using data from a study on human postural dynamics and a daily affect study, we demonstrate the use of these models to represent within-person non-stationarities in cyclic dynamics and interindividual differences therein. The use of diagnostic tools for evaluating model fit is also illustrated.

Children should become more effective at regulating emotion as they age. Longitudinal evidence of such change, however, is scarce. This study uses a multiple-time scale approach to test the hypothesis that the self-regulation of emotion-the engagement of executive processes to influence the dynamics of prepotent emotional responses-becomes more effective as children move through early childhood. Second-by-second time-series data obtained from behavioral observation of 120 children (46% female) during an 8-min frustration-eliciting wait task completed at four ages (24 months, 36 months, 48 months, 5 years) were modeled using bivariate coupled differential equation models designed to capture age-related changes in the intrinsic dynamics and bidirectional coupling of prepotent and executive processes. Results revealed indirect influences of executive processes on the intrinsic dynamics of children's desire and frustration increased with age but also revealed complex and non-linear age-related changes in how specific aspects of the dynamic interplay between prepotent responses and executive processes influence the effectiveness of regulation at different ages. The findings illustrate the utility of using a dynamics system approach to articulate and study how specific aspects of emotion regulation change with age.

One of the promises of the experience sampling methodology (ESM) is that it could be used to identify relevant targets for treatment, based on a statistical analysis of an individual’s emotions, cognitions and behaviors in everyday-life. A requisite for clinical implementation is that outcomes of person-centered analyses are not wholly contingent on the researcher performing them. To evaluate how much researchers vary in their analytical approach and to what degree outcomes vary based on analytical choices, we crowdsourced the analysis of one individual patient’s ESM data to 12 prominent research teams, asking them what symptom(s) they would advise the treating clinician to target in subsequent treatment. The dataset was from a 25-year-old male with a primary diagnosis of major depressive disorder and comorbid generalized anxiety disorder, who completed momentary assessments related to depression and anxiety psychopathology prior to psychotherapy. Variation was evident at different stages of the analysis, from preprocessing steps (e.g., variable selection, clustering, handling of missing data) to the type of statistics. Most teams did include a type of vector autoregressive model, which examines relations between variables (e.g., symptoms) over time. Although most teams were confident their selected targets would provide useful information to the clinician, not one advice was similar: both the number (0-16) and nature of selected targets varied widely. This study makes transparent that the selection of treatment targets based on personalized models using ESM data is currently highly conditional on subjective analytical choices and highlights key methodological issues that need to be addressed in moving toward clinical implementation. Research proposal, data and materials: osf.io/h3djy/