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Chromatic and Anisotropic Cross-Recurrence Quantification Analysis of Interpersonal Behavior

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Book cover Recurrence Plots and Their Quantifications: Expanding Horizons

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 180))

Abstract

Cross-recurrence quantification analysis (CRQA) is a powerful nonlinear time-series method to study coordination and cooperation between people. This chapter concentrates on two methodological issues related to CRQA on categorical data streams, which are commonly encountered in the behavioral sciences . Firstly, we introduce a more general definition of recurrence as ‘behavioral matching ’, which can be applied to several kinds of matches simultaneously, visualized by a color coding. We will refer to this as cross -matching, and to the resulting quantification procedure as Chromatic CRQA . Secondly, cross-recurrence plots of categorical data often prominently consists of rectangular structures. This calls for a differential analysis of vertical and horizontal lines, rather than of diagonal lines. We introduce a simple procedure for this, referred to as Anisotropic CRQA . Both procedures are demonstrated with empirical studies on children’s problem-solving behavior and by means of a model simulation. The authors hope that the ideas presented here increase the power and applicability of CRQA in the behavioral sciences, and that this chapter serves as a stepping stone for their mathematical and methodological development.

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Notes

  1. 1.

    Note that recoding the data oftentimes will also do the trick. However, complex cases with multiple matches and non-matches require a more general and powerful approach. Interestingly, this also gives rise to a set of additional measures, as will become clear further on.

  2. 2.

    These tests can readily be applied to small sample sizes or unequal groups of data, in this case to determine the statistical significance (p-value) of the differences between the line structures. The test repeatedly (e.g., 1000 times) compares the observed difference to the difference found within a range of simulated data drawn from the original sample. The p-value is computed by dividing the number of times the observed or a bigger difference occurs in these random samples by the number of drawn samples.

  3. 3.

    This basically constructs a symbolic dynamics by introducing a static encoding of the time series (see e.g. [26, 27]).

  4. 4.

    In fact written in this way the system models a system of three asymmetrically coupled Kuramoto oscillators under a specific set of parameter settings, among which, in particular equal intrinsic frequency.

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Acknowledgment

The first author wishes to express his appreciation to Fred Hasselman, for the many fruitful discussions arising from shared encounters with the methodological issues regarding recurrence analysis on categorical behavioral time series.

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Authors and Affiliations

  1. Department of Psychology, Faculty of Behavioural and Social Sciences, University of Groningen, Groningen, The Netherlands

    Ralf F. A. Cox, Lisette de Jonge-Hoekstra & Marijn van Dijk

  2. Department of Special Needs Education and Youth Care, Faculty of Behavioural and Social Sciences, University of Groningen, Groningen, The Netherlands

    Steffie van der Steen

  3. Institute of Psychology, Universidad del Valle, Cali, Colombia

    Marlenny Guevara

Authors
  1. Ralf F. A. Cox
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  2. Steffie van der Steen
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  3. Marlenny Guevara
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Corresponding author

Correspondence to Ralf F. A. Cox .

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Editors and Affiliations

  1. Dept. of Cell and Molecular Physiology, Loyola University Chicago, Maywood, Illinois, USA

    Charles L. Webber, Jr.

  2. GIPSA-Lab, University Grenoble Alpes, Grenoble, France

    Cornel Ioana

  3. Potsdam Ins. for Climate Impact Research, Potsdam, Germany

    Norbert Marwan

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Cox, R.F.A., van der Steen, S., Guevara, M., de Jonge-Hoekstra, L., van Dijk, M. (2016). Chromatic and Anisotropic Cross-Recurrence Quantification Analysis of Interpersonal Behavior. In: Webber, Jr., C., Ioana, C., Marwan, N. (eds) Recurrence Plots and Their Quantifications: Expanding Horizons. Springer Proceedings in Physics, vol 180. Springer, Cham. https://doi.org/10.1007/978-3-319-29922-8_11

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