Nominal cross recurrence as a generalized lag sequential analysis for behavioral streams. (English) Zbl 1247.91168

Dale, Rick; Warlaumont, Anne S.; Richardson, Daniel C.

Int. J. Bifurcation Chaos Appl. Sci. Eng. 21, No. 4, 1153-1161 (2011).

Summary: We briefly present lag sequential analysis for behavioral streams, a commonly used method in psychology for quantifying the relationships between two nominal time series. Cross recurrence quantification analysis (CRQA) is shown as an extension of this technique, and we exemplify this nominal application of CRQA to eye-movement data in human interaction. In addition, we demonstrate nominal CRQA in a simple coupled logistic map simulation used in previous communication research, permitting the investigation of properties of nonlinear systems such as bifurcation and onset to chaos, even in the streams obtained by coarse-graining a coupled nonlinear model. We end with a summary of the importance of CRQA for exploring the relationship between two behavioral streams, and review a recent theoretical trend in the cognitive sciences that would be usefully informed by this and similar nonlinear methods. We hope this work will encourage scientists interested in general properties of complex, nonlinear dynamical systems to apply emerging methods to coarse-grained, nominal units of measure, as there is an immediate need for their application in the psychological domain.

MSC:

91E99	Mathematical psychology
37N99	Applications of dynamical systems
37M10	Time series analysis of dynamical systems

Keywords:

recurrence; cross recurrence; psychology; coupling; language

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