Using derivative estimates to describe intraindividual variability at multiple time scales

Modeling Latent Topics in Social Media using Dynamic Exploratory Graph Analysis: The Case of the Right-wing and Left-wing Trolls in the 2016 US Elections

The past few years were marked by increased online offensive strategies perpetrated by state and non-state actors to promote their political agenda, sow discord, and question the legitimacy of democratic institutions in the US and Western Europe. In 2016, the US congress identified a list of Russian state-sponsored Twitter accounts that were used to try to divide voters on a wide range of issues. Previous research used latent Dirichlet allocation (LDA) to estimate latent topics in data extracted from these accounts. However, LDA has characteristics that may limit the effectiveness of its use on data from social media: The number of latent topics must be specified by the user, interpretability of the topics can be difficult to achieve, and it does not model short-term temporal dynamics. In the current paper, we propose a new method to estimate latent topics in texts from social media termed Dynamic Exploratory Graph Analysis (DynEGA). In a Monte Carlo simulation, we compared the ability of DynEGA and LDA to estimate the number of simulated latent topics. The results show that DynEGA is substantially more accurate than several different LDA algorithms when estimating the number of simulated topics. In an applied example, we performed DynEGA on a large dataset with Twitter posts from state-sponsored right- and left-wing trolls during the 2016 US presidential election. DynEGA revealed topics that were pertinent to several consequential events in the election cycle, demonstrating the coordinated effort of trolls capitalizing on current events in the USA. This example demonstrates the potential power of our approach for revealing temporally relevant information from qualitative text data.

Affect dynamics and well-being: explanatory power of the model of intraindividual variability in affect (MIVA)

Affective experience is inherently dynamic and short-term changes in affect are supposed to offer important insights into well-being. Past years have shown a tremendous rise in investigations into the relation between affect dynamics and well-being. The indicators that have been introduced to capture unique dynamical aspects of affect, however, have been criticised for being purely statistical measures without theoretical foundation and were shown to have little added value for explaining well-being over and above mean levels of affect. To address these concerns, we applied our newly developed theory-based MIVA model to data on daily affective experience. The MIVA model allows estimating parameters for anchoring, reactivity, and regulation based on affective states in combination with daily events. Everyday affective experience was measured with a high temporal resolution, multiple indicators of well-being (e.g. life satisfaction, depression) were assessed, and the incremental value of the MIVA model parameters in predicting well-being was determined. The MIVA model parameters reflect essential processes that accounted for observed fluctuations in affective experience. Incremental validity for predicting well-being over and above mean levels of affect, however, was low. Together, our results suggest that research on affect dynamics needs to identify how affect dynamics can be assessed more validly.

Dynamical System Modeling of Self-Regulated Systems Undergoing Multiple Excitations: First Order Differential Equation Approach

This article proposes a dynamical system modeling approach for the analysis of longitudinal data of self-regulated homeostatic systems experiencing multiple excitations. It focuses on the evolution of a signal (e.g., heart rate) before, during, and after excitations taking the system out of its equilibrium (e.g., physical effort during cardiac stress testing). Such approach can be applied to a broad range of outcomes such as physiological processes in medicine and psychosocial processes in social sciences, and it allows to extract simple characteristics of the signal studied. The model is based on a first order linear differential equation with constant coefficients defined by three main parameters corresponding to the initial equilibrium value, the dynamic characteristic time, and the reaction to the excitation. Assuming the presence of interindividual variability (random effects) on these three parameters, we propose a two-step procedure to estimate them. We then compare the results of this analysis to several other estimation procedures in a simulation study that clarifies under which conditions parameters are accurately estimated. Finally, applications of this model are illustrated using cardiology data recorded during effort tests.

Gα/GSA-1 works upstream of PKA/KIN-1 to regulate calcium signaling and contractility in the Caenorhabditis elegans spermatheca

Correct regulation of cell contractility is critical for the function of many biological systems. The reproductive system of the hermaphroditic nematode C. elegans contains a contractile tube of myoepithelial cells known as the spermatheca, which stores sperm and is the site of oocyte fertilization. Regulated contraction of the spermatheca pushes the embryo into the uterus. Cell contractility in the spermatheca is dependent on actin and myosin and is regulated, in part, by Ca2+ signaling through the phospholipase PLC-1, which mediates Ca2+ release from the endoplasmic reticulum. Here, we describe a novel role for GSA-1/Gαs, and protein kinase A, composed of the catalytic subunit KIN-1/PKA-C and the regulatory subunit KIN-2/PKA-R, in the regulation of Ca2+ release and contractility in the C. elegans spermatheca. Without GSA-1/Gαs or KIN-1/PKA-C, Ca2+ is not released, and oocytes become trapped in the spermatheca. Conversely, when PKA is activated through either a gain of function allele in GSA-1 (GSA-1(GF)) or by depletion of KIN-2/PKA-R, the transit times and total numbers, although not frequencies, of Ca2+ pulses are increased, and Ca2+ propagates across the spermatheca even in the absence of oocyte entry. In the spermathecal-uterine valve, loss of GSA-1/Gαs or KIN-1/PKA-C results in sustained, high levels of Ca2+ and a loss of coordination between the spermathecal bag and sp-ut valve. Additionally, we show that depleting phosphodiesterase PDE-6 levels alters contractility and Ca2+ dynamics in the spermatheca, and that the GPB-1 and GPB-2 Gβ subunits play a central role in regulating spermathecal contractility and Ca2+ signaling. This work identifies a signaling network in which Ca2+ and cAMP pathways work together to coordinate spermathecal contractions for successful ovulations.

Experience of Stress Assessed by Text Messages and Its Association with Objective Workload-A Longitudinal Study

Exploring stress trajectories in detail and over a long time may give valuable information in terms of both understanding and practice. We followed a group of primary health care employees in a randomized controlled trial. The objective was to describe their experience of stress, explore the intra-individual variability and examine the association between the experience of stress and the objective workload. Weekly text messages with a single item stress question were distributed in two time series: 12 weeks at the beginning of the trial and 26 weeks after the 6-month follow up. Aggregated objective data about workload were collected from their administration office and related to stress levels. There was a seasonal variation, with higher stress during the fall than in spring and summer. The analysis comparing high and low stress subgroups showed that the stress trajectory of a high-stress subgroup was different from that of a low-stress subgroup. Individuals with high exhaustion scores had higher odds of belonging to a subgroup of individuals with high intra-individual variability in stress experience. The objective workload was measured in two ways and was strongly associated with the stress experience. We found that the lower the productivity, the higher the feeling of stress.

Constrained Fourth Order Latent Differential Equation Reduces Parameter Estimation Bias for Damped Linear Oscillator Models

Second order linear differential equations can be used as models for regulation since under a range of parameter values they can account for return to equilibrium as well as potential oscillations in regulated variables. One method that can estimate parameters of these equations from intensive time series data is the method of Latent Differential Equations (LDE). However, the LDE method can exhibit bias in its parameters if the dimension of the time delay embedding and thus the width of the convolution kernel is not chosen wisely. This article presents a simulation study showing that a constrained fourth order Latent Differential Equation (FOLDE) model for the second order system almost completely eliminates bias as long as the width of the convolution kernel is less than two thirds the period of oscillations in the data. The FOLDE model adds two degrees of freedom over the standard LDE model but significantly improves model fit.

Practical Tools and Guidelines for Exploring and Fitting Linear and Nonlinear Dynamical Systems Models

A dynamical system is a system of variables that show some regularity in how they evolve over time. Change concepts described in most dynamical systems models are by no means novel to social and behavioral scientists, but most applications of dynamic modeling techniques in these disciplines are grounded on a narrow subset of-typically linear-theories of change. I provide practical guidelines, recommendations, and software code for exploring and fitting dynamical systems models with linear and nonlinear change functions in the context of four illustrative examples. Cautionary notes, challenges, and unresolved issues in utilizing these techniques are discussed.

VIII. THE PAST, PRESENT, AND FUTURE OF DEVELOPMENTAL METHODOLOGY

This chapter selectively reviews the evolution of quantitative practices in the field of developmental methodology. The chapter begins with an overview of the past in developmental methodology, discussing the implementation and dissemination of latent variable modeling and, in particular, longitudinal structural equation modeling. It then turns to the present state of developmental methodology, highlighting current methodological advances in the field. Additionally, this section summarizes ample quantitative resources, ranging from key quantitative methods journal articles to the various quantitative methods training programs and institutes. The chapter concludes with the future of developmental methodology and puts forth seven future innovations in the field. The innovations discussed span the topics of measurement, modeling, temporal design, and planned missing data designs. Lastly, the chapter closes with a brief overview of advanced modeling techniques such as continuous time models, state space models, and the application of Bayesian estimation in the field of developmental methodology.

Within-person changes in salivary testosterone and physical characteristics of puberty predict boys' daily affect

Recent investigations highlighted the role of within-person pubertal changes for adolescents' behavior. Yet, little is known about effects on adolescents' daily affect, particularly regarding the hormonal changes underlying physical changes during puberty. In a study with 148 boys aged 10 to 20years, we tested whether within-person physical and hormonal changes over eight months predicted everyday affect fluctuations, measured with experience sampling. As expected, greater within-person changes in testosterone (but not in dehydroepiandrosterone) were associated with higher affect fluctuations in daily life. Additionally, greater physical changes predicted higher affect fluctuations for individuals in the beginning of puberty. The findings demonstrate the relevance of physical and hormonal changes in boys' affective (in)stability.

Integrating developmental theory and methodology: Using derivatives to articulate change theories, models, and inferences

Matching theories about growth, development, and change to appropriate statistical models can present a challenge, which can result in misuse, misinterpretation, and underutilization of different analytical approaches. We discuss the use of derivatives --- the change of a construct with respect to changes in another construct. Derivatives provide a common language linking developmental theory and statistical methods. Conceptualizing change in terms of derivatives allows precise translation of theory into method and highlights commonly overlooked models of change. A wide variety of models can be understood in terms of the level, velocity and acceleration of constructs: the 0th, 1st, and 2nd derivatives, respectively. We introduce the language of derivatives, and highlight the conceptually differing questions that can be addressed in developmental studies. A substantive example is presented to demonstrate how common and unfamiliar statistical methodology can be understood as addressing relations between differing pairs of derivatives.

Dynamics of Change and Change in Dynamics

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 a selected models' feasibility within a chosen experimental design.

Trait enactments as density distributions: The role of actors, situations, and observers in explaining stability and variability

The purposes of this article were to determine (a) whether the high consistency of individual differences in average aggregated behavior is because of actors' personalities or because of the consistency in the situations those actors encounter; and (b) whether the surprisingly high within-person variability in trait enactment is a real phenomenon corroborated by observers, or merely in individuals' heads. Although traits are supposed to describe what individuals are like in everyday life, little evidence exists about the enactment of trait content in everyday life. Past experience-sampling studies have found both highly variable and highly consistent trait enactment, but were restricted to self-report data and to naturally occurring situations. The current study used experience-sampling in controlled lab environments with 97 targets and 183 observers to address these shortcomings. Targets attended hour-long lab sessions 20× each and observers rated targets' behavior. Parameters of distributions were highly consistent (rs ∼ .80), revealing that actors were responsible for consistency, not situations. Nonetheless, observer ratings revealed that most variability in trait enactment was within-person, confirming that even when people put it on the line in ways that affected others, they still varied rapidly in the traits they enacted. In the face of 2 historically vexing objections to traits, this article supports the density distributions model of traits and argues that trait conceptualizations must accommodate large within-person variability.

Dynamical systems analysis applied to working memory data

In the present paper we investigate weekly fluctuations in the working memory capacity (WMC) assessed over a period of 2 years. We use dynamical system analysis, specifically a second order linear differential equation, to model weekly variability in WMC in a sample of 112 9th graders. In our longitudinal data we use a B-spline imputation method to deal with missing data. The results show a significant negative frequency parameter in the data, indicating a cyclical pattern in weekly memory updating performance across time. We use a multilevel modeling approach to capture individual differences in model parameters and find that a higher initial performance level and a slower improvement at the MU task is associated with a slower frequency of oscillation. Additionally, we conduct a simulation study examining the analysis procedure's performance using different numbers of B-spline knots and values of time delay embedding dimensions. Results show that the number of knots in the B-spline imputation influence accuracy more than the number of embedding dimensions.

Ups and downs of daily life: age effects on the impact of daily appraisal variability on depressive symptoms

OBJECTIVES

Day-to-day variability in appraisals has emerged as an index of emotion regulation and overall well-being; there is also evidence that such emotion regulation processes change with age. We investigate the impact of day-to-day variability in positive and negative event appraisals on depressive symptoms, focusing on (a) how variability and mean appraisal characteristics interact to impact well-being and (b) whether these effects differ by age.

METHODS

Participants from the Notre Dame Study of Health & Well-Being (aged 40-75 years, N = 654) completed daily diaries for up to 56 days, along with a global survey. Measures included daily data on life events and appraisals and global assessments of depressive symptoms (Center for Epidemiologic Studies Depression scale) and neuroticism.

RESULTS

Both mean and variability components of daily positive and negative event appraisals predict global depressive symptoms; mean and variability interactions were also significant. The negative appraisal effects became less pronounced with age.

DISCUSSION

Findings suggest that those in later life are better able to manage the impact that their cognitive and emotional responses to daily stressors have on depressive symptoms. The results also highlight the importance of examining daily variability-in addition to mean levels-in understanding the impact of daily events and appraisals on well-being.

Coupled latent differential equation with moderators: simulation and application

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.

Unfolding Potential as Dynamic Emergence: A View From the Theory of Complex, Nonlinear Dynamic Systems

The process of unfolding learning and developmental potential is discussed from the viewpoint of complex dynamic systems. After a brief overview of the notions of unfolding and potential in the context of development and education, a definition of complex dynamic systems is given, emphasizing the aspects of self-organization and emergence. The concept of nonergodicity is introduced, which implies that statistical relationships between variables applying to samples of independent individuals (the classical methodological setup of educational and developmental research) do not necessarily apply to statistical relationships found in individual time series. The consequences of complexity and nonergodicity for empirical research in education and development are presented in the form of four methodological design steps, with illustrations of usable methods and empirical research focusing on individual educational and developmental trajectories.

The reservoir model: a differential equation model of psychological regulation

Differential equation models can be used to describe the relationships between the current state of a system of constructs (e.g., stress) and how those constructs are changing (e.g., based on variable-like experiences). The following article describes a differential equation model based on the concept of a reservoir. With a physical reservoir, such as one for water, the level of the liquid in the reservoir at any time depends on the contributions to the reservoir (inputs) and the amount of liquid removed from the reservoir (outputs). This reservoir model might be useful for constructs such as stress, where events might "add up" over time (e.g., life stressors, inputs), but individuals simultaneously take action to "blow off steam" (e.g., engage coping resources, outputs). The reservoir model can provide descriptive statistics of the inputs that contribute to the "height" (level) of a construct and a parameter that describes a person's ability to dissipate the construct. After discussing the model, we describe a method of fitting the model as a structural equation model using latent differential equation modeling and latent distribution modeling. A simulation study is presented to examine recovery of the input distribution and output parameter. The model is then applied to the daily self-reports of negative affect and stress from a sample of older adults from the Notre Dame Longitudinal Study on Aging.

Intraindividual Variability and Stability of Affect and Well-Being

Whereas subjective well-being remains relatively stable across adulthood, emotional experiences show remarkable short-term variability, with younger and older adults differing in both amount and correlates. Repeatedly assessed affect data captures both the dynamics and stability as well as stabilization that may indicate emotion-regulatory processes. The article reviews (1) research approaches to intraindividual affect variability, (2) functional implications of affect variability, and (3) age differences in affect variability. Based on this review, we discuss how the broader literature on emotional aging can be better integrated with theories and concepts of intraindividual affect variability by using appropriate methodological approaches. Finally, we show how a better understanding of affect variability and its underlying processes could contribute to the long-term stabilization of well-being in old age.

Emotion control during later life: The relationship between global perceptions and daily experience

The extent to which individuals generally believe that they can successfully manage their emotions is related to healthy coping and well-being. Nevertheless, it is unclear how this general belief is related to daily affective experiences. In the current study, the relationship between global emotion control beliefs and daily affect reports across 56 days were assessed in a sample of 298 older adults. Results indicate that higher global emotion control beliefs were related to lower mean daily negative affect and higher mean daily positive affect. Additionally, variability analyses investigating multiple potential time scales revealed that global beliefs were related to lower variance in daily negative affect and less variable speeds of daily negative affect change across a range of time scales (from windows of 3 days to windows of approximately 2 weeks). Alternatively, global control beliefs were not significantly related to variance in daily positive affect or variance in speeds of daily positive affect change. Together, results suggest that global emotion control beliefs predict average experience of daily affect and variability in daily negative affect.

Estimating Dynamical Systems: Derivative Estimation Hints From Sir Ronald A. Fisher

The fitting of dynamical systems to psychological data offers the promise of addressing new and innovative questions about how people change over time. One method of fitting dynamical systems is to estimate the derivatives of a time series and then examine the relationships between derivatives using a differential equation model. One common approach for estimating derivatives, Local Linear Approximation (LLA), produces estimates with correlated errors. Depending on the specific differential equation model used, such correlated errors can lead to severely biased estimates of differential equation model parameters. This article shows that the fitting of dynamical systems can be improved by estimating derivatives in a manner similar to that used to fit orthogonal polynomials. Two applications using simulated data compare the proposed method and a generalized form of LLA when used to estimate derivatives and when used to estimate differential equation model parameters. A third application estimates the frequency of oscillation in observations of the monthly deaths from bronchitis, emphysema, and asthma in the United Kingdom. These data are publicly available in the statistical program R, and functions in R for the method presented are provided.