Estimating Appropriate Lag Length for Synchronized Physiological Time Series: The Electrodermal Response

Stephen J. Guastello, Marquette University, Milwaukee, WI

Katherine Reiter, Marquette University, Milwaukee, WI

Matthew Malon, Mount Mary University, Milwaukee, WI

**Abstract: **Physiological synchronization of autonomic arousal between people is
thought to be an important component of work team dynamics, therapist-client relationships,
and other interpersonal dynamics. This article examines concepts and
mathematical models of synchronization that could be relevant to work teams.
Before it is possible to deploy nonlinear modeling, however, it is
necessary to develop a strategy for determining appropriate lag lengths.
If a measurement at time 2 is a function of itself at time 1 and
a coupling effect from another source, what is the appropriate amount of real time
that should be allowed to elapse between the two measurements in
order to observe the coupling effect? This study examined four strategies
for doing so. In the experiment, 78 undergraduates worked in pairs to perform
a vigilance dual task for 90 min while galvanic skin responses (GSR) were recorded.
Lags based on mutual entropy and the natural rate criteria produced corroborating results,
whereas strategies based on a critical decline in the linear autocorrelation (max r/e)
and Theiler”s W did not produce usable results for this situation. Some connections
were uncovered between linear autocorrelation strength and lag based on mutual entropy
with performance on the tasks and subjective ratings of workload.

*Keywords: *nonlinear time series, lag lengths, Theiler window, synchronization, mutual entropy