1. Dynamical Correlation: A New Method to Quantify Synchrony Siwei Liu 1, Yang Zhou 1, Richard Palumbo 2, & Jane-Ling Wang 1 1 UC Davis; 2 University of Rhode Island

2. Motivating Study  Physiological synchrony between romantic partners during nonverbal conditions 30 Minutes Total 15 Minutes Face to Face 15 Minutes Back to Back N=16

3. Electrodermal Activity (EDA) from Two Couples

5. Multilevel Modeling?  Assumes a universal model  Random effects are normally distributed  Violations lead to biased estimates  Difficult to converge with small sample size - (Bell et al., 2008, 2010; Maas & Hox, 2004, 2005) Within Dyad Between Dyad

7. Time Series Analysis?  Vector Autoregressive Model (VAR)  Cointegration Relation y 1 ~ I(1) y 2 ~ I(1) y 1 -2*y 2 ~ I(0) Stationarity

8. Dynamical Correlation  Functional data analysis (Ramsay & Silverman, 2005)  Longitudinal data: Observations taken from a set of smooth curves or functions, which are realizations of an underlying stochastic process  Functional Regression  Functional principle component analysis  Functional clustering  Dynamical correlation  Similarity in the shape of two curves, range = [-1,1]  Nonparametric – no functional form needed  No assumption on distribution of subject-level estimates  Population-level inferences

9. Dynamical Correlation between X(t) and Y(t)  Define the standardized curve where  Dynamical correlation is defined as:  Compare to Pearson correlation: (1)(1) (2)(2)

10. Simulation Example I

11. Simulation Example II

12. Synchrony in EDA  Back-to-Back Condition  Face-to-Face Condition  Random pairs in face-to-face condition Romantic partners synchronized their EDA during nonverbal interactions, but only when they were able to see each other. Synchrony was not due to shared experience.

13. Extensions  Other variables  Parent-child interactions  Positive affect and negative affect  Derivatives and lags  Links to DFM  Links to Granger causality  Matrix of dynamical correlation  Principal component analysis  Limitations  Require intensive data  No true subject-level estimates  Functional multilevel model (Li, Root, & Shiffman, 2006)