People are dynamic in different ways. Tools, such as smartphones, have allowed for an unprecedented opportunity to understand how individuals change across time in the social, behavioral, and medical sciences. This site consists of work integrating repeated observations on individuals and groups with statistics, dynamical system theory, methods for analyzing repeated observations. The potential is to move beyond stereotyped inferences — the “average” person — and towards being able to offer truly personalized social, behavioral, and medical information.

The following page provides links to papers, chapters, code, examples, supplementary materials, and presentations on which I have worked. Please don’t hesitate to let me know if you have suggestions, corrections, or questions.

### Time Delay Embedding/Derivative Estimation

These posts are on the use of time delay embedding. Time delay embedding can be used to estimate characteristics of a person at a given time, and how they are changing (e.g., level, velocity, acceleration — derivatives). These tools allow for opportunities to understand how change is related within and between variables.

### Substantive Work

These posts consist of substantive applications of dynamical systems, derivatives, or differential equation modeling to the social, behavioral, and medical sciences.

### Dynamic & Dynamical Systems

These posts consist of materials that introduce dynamic and dynamical systems topics, including topics like derivatives, differential equation model, and continuous time modeling.

### Exact Discrete Model

These post are on the exact discrete model, a method that uses integration of differential equations to fit a continuous time model.

### Other Work

These posts are a mix of other work related to intraindividual modeling.

### Some Recent Posts:

- An Application of Continuous Time Models to Prevention Research (2021)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. A substantive example compares models that imply different underlying continuous time processes using panel data.
- Empirical Bayes Derivative Estimates (2020)This article proposes a new method for estimating derivatives on calculating the Empirical Bayes estimates of derivatives from a mixed model. Two simulations compare four derivative estimation methods: Generalized Local Linear Approximation, Generalized Orthogonal Derivative Estimates, Functional Data Analysis, and the proposed Empirical Bayes Derivative Estimates.
- Differing Perspectives on Time Alter Mediation Inferences (2018)Time is unlike any other variable. This chapter considers the difference in perspectives offered by discrete-time and continuous-time approached to mediation. The differences in how one conceptualizes time have the potential to alter core mediation concepts as direct and indirect effect, complete and partial mediation, and even what constitutes a “mediation” model.
- Attachment Changes predicting Depression and Anxiety Changes (2017)Two studies examined the role short-term changes in adult attachment and mindfulness play in depression and general anxiety.
- Dynamical Systems Approaches (2016)This is an introduction to dynamical systems ideas. Dynamical systems are mathematical models of one or more constructs that change over time. Approaches to dynamical systems are concerned with describing the temporal evolution of constructs, with emphasis often placed on constructs that develop in a complex, nonlinear manner over time.