Lagged Multidimensional Recurrence Quantification Analysis for Determining Leader–Follower Relationships Within Multidimensional Time Series

Abstract

The current article introduces lagged multidimensional recurrence quantification analysis. The method is an extension of multidimensional recurrence quantification analysis and allows to quantify the joint dynamics of multivariate time series and to investigate leader–follower relationships in behavioral and physiological data. Moreover, the method enables the quantification of the joint dynamics of a group, when such leader–follower relationships are taken into account. We first provide a formal presentation of the method, and then apply it to synthetic data, as well as data sets from joint action research, investigating the shared dynamics of facial expression and beats-per-minute recordings within different groups. A wrapper function is included, for applying the method together with the “crqa” package in R.