Unlocking nonlinear dynamics and multistability from intensive longitudinal data

What is it about?

In the current work, we propose to use a nonparametric kernel method to estimate a vector field from data. This allows a very flexible description of the changing rate of the system at any starting point. After having the vector field of the system, we can also construct the potential landscape, which clearly shows the multistability of the system and the relative stability of phases. We developed a package, fitlandr, as an implementation of all the things above.

Featured Image

Photo by Pietro De Grandi on Unsplash

Photo by Pietro De Grandi on Unsplash

Why is it important?

Intensive longitudinal data collected with ESM provides important information about the dynamics of psychological systems. It's very often that we see multimodality/skewness in data, yet, we don't have a very suitable method to directly describe those features. Most previous methods are based on linear models, which we believe are very helpful in analyzing the relationships between variables. Nonetheless, to describe nonlinear dynamics and multistability, we need a more flexible method, as described in this article.