From Modeling Long-Term Growth to Short-Term Fluctuations: Differential Equation Modeling Is the Language of Change

Modeling dynamic processes with panel data: An application of continuous time models to prevention research

Many interventions are characterized by repeated observations on the same individuals (e.g., baseline, mid-intervention, two to three post-intervention observations), which offer the opportunity to consider differences in how individuals vary over time. Effective interventions may not be limited to changing means, but instead may also include changes to how variables affect each other over time. Continuous time models offer the opportunity to specify differing underlying processes for how individuals change from one time to the next, such as whether it is the level or change in a variable that is related to changes in an outcome of interest. After introducing continuous time models, we show how different processes can produce different expected covariance matrices. Thus, models representing differing underlying processes can be compared, even with a relatively small number of repeated observations. A substantive example comparing models that imply different underlying continuous time processes will be fit using panel data, with parameters reflecting differences in dynamics between control and intervention groups.

Continuous-time causal mediation analysis

While causal mediation analysis has seen considerable recent development for a single measured mediator (M) and final outcome (Y), less attention has been given to repeatedly measured M and Y. Previous methods have typically involved discrete-time models that limit inference to the particular measurement times used and do not recognize the continuous nature of the mediation process over time. To overcome such limitations, we present a new continuous-time approach to causal mediation analysis that uses a differential equations model in a potential outcomes framework to describe the causal relationships among model variables over time. A connection between the differential equation models and standard repeated measures models is made to provide convenient model formulation and fitting. A continuous-time extension of the sequential ignorability assumption allows for identifiable natural direct and indirect effects as functions of time, with estimation based on a two-step approach to model fitting in conjunction with a continuous-time mediation formula. Novel features include a measure of an overall mediation effect based on the "area between the curves," and an approach for predicting the effects of new interventions. Simulation studies show good properties of estimators and the new methodology is applied to data from a cohort study to investigate sugary drink consumption as a mediator of the effect of socioeconomic status on dental caries in children.

On Measuring and Modeling Physiological Synchrony in Dyads

Physiological synchrony within a dyad, or the degree of temporal correspondence between two individuals' physiological systems, has become a focal area of psychological research. Multiple methods have been used for measuring and modeling physiological synchrony. Each method extracts and analyzes different types of physiological synchrony, where 'type' refers to a specific manner through which two different physiological signals may correlate. Yet, to our knowledge, there is no documentation of the different methods, how each method corresponds to a specific type of synchrony, and the statistical assumptions embedded within each method. Hence, this article outlines several approaches for measuring and modeling physiological synchrony, connects each type of synchrony to a specific method, and identifies the assumptions that need to be satisfied for each method to appropriately extract each type of synchrony. Furthermore, this article demonstrates how to test for between-dyad differences of synchrony via inclusion of dyad-level (i.e., time-invariant) covariates. Finally, we complement each method with an empirical demonstration, as well as online supplemental material that contains Mplus code.

Advances in mediation analysis: a survey and synthesis of new developments

Mediation processes are fundamental to many classic and emerging theoretical paradigms within psychology. Innovative methods continue to be developed to address the diverse needs of researchers studying such indirect effects. This review provides a survey and synthesis of four areas of active methodological research: (a) mediation analysis for longitudinal data, (b) causal inference for indirect effects, (c) mediation analysis for discrete and nonnormal variables, and (d) mediation assessment in multilevel designs. The aim of this review is to aid in the dissemination of developments in these four areas and suggest directions for future research.

Trait Stress Resistance and Dynamic Stress Dissipation on Health and Well-Being: The Reservoir Model

Daily data from the NDHWB (n = 783; age range 37-90) were analyzed to produce 'dynamic characteristic' estimates of stress input and dissipation. These were used in multi-level modeling (with age and trait stress resistance) to predict depression and health trajectories. Main effects suggest that dissipation and stress resistance predict lower depression and better health, but lower stress input was only related to lower depression. Interactions revealed that subjects with above average stress resistance had lower depression irrespective of their ability to dissipate stress, but for individuals low in trait resistance those with better stress dissipation show lower depression and better health.