- The dynamical systems literature is rich data visualizations techniques, which have allowed for new insights into the processes of many systems. In psychology, the rich complexity of intraindividual variability may benefit from such visualization techniques. Vector field plots, for example, offer the potential for exploratory examination of the relations between constructs. By including derivatives in vector field plots --- the change in a construct with respect to another variable such as time --- relations between the levels (0th derivatives), velocity (1st derivative), and higher order derivatives (e.g., acceleration, jerk) can be explored. While readily accomplished on data with high sampling rates relative to the rates of change of the underlying constructs, such as physiological data, the application of vector field plots to psychological data (e.g., diary data, ecological momentary assessments) has been more challenging due to the number of observations, the sampling rate, the use of non-continuous scales (e.g., a small number of likert scale items), and the measurement error in these scales. The latter poses particular problem, as measurement error compounds as higher orders of derivatives are estimated, resulting in plots that are often too noisy for insights to be gained. This presentation will review the estimation of derivatives using time-delay embedding, and introduce a new method for estimating derivatives that is more efficient than other commonly used approaches. Applications to substantive data will be presented.
Time and Location:
12:30pm, Zoom
Date:
Thursday, October 22, 2020
Subtitle:
"Estimating Derivatives using Time-Delay Embedding." (Zoom link -- https://virginia.zoom.us/j/96496880314?pwd=RDRzRmVqd3ljUk1XU09jTkdVVUIwQT09#success, Meeting ID: 836 870 6265)