Analyzing Multivariate Dynamics Using Cross-Recurrence Quantification Analysis (CRQA), Diagonal-Cross-Recurrence Profiles (DCRP), and Multidimensional Recurrence Quantification Analysis (MdRQA) – A Tutorial in R - Wallot, Sebastian; Leonardi, Giuseppe (Frontiers in Psychology, 2018)
In recent years, increasing interest has emerged in the behavioral, cognitive and social sciences towards methods drawn from dynamic systems analysis. This might be because of the recognition that many behavioral and neurophysiological processes are intrinsically time dependent and reliant on environmental and social context. One of the methods that has enjoyed a particular gain in interest is Recurrence Quantification Analysis (RQA). Particularly, advances towards a multivariate analysis of behavioral dynamics have been made thanks to this method, which comes in various types of analyses addressing different questions. These analyses are useful for assessing the strength of coupling/correlation between two or more time-series, particularly if these time-series are nonstationary or have complicated dynamics, such as in longer recordings of continuous physiological or movement data, but also in the case of time-series of symbolic data. What has been limiting the use of recurrence-based analyses though, is that none of the techniques are implemented in standard commercial statistical software packages (such as STATA, JMP, SPSS etc.). As far as libraries are available (e.g. in Matlab or R) many of them require a certain expertise in programming. In this paper, we aim at filling this gap, explaining multivariate recurrence-based analyses conceptually and practically, drawing on a variety of R-functions than implement these methods. Particularly, we will introduce Cross-Recurrence Quantification Analysis (CRQA), Diagonal Cross Recurrence Profiles (DCRP) and Multidimensional Recurrence Quantification Analysis (MdRQA), showing in a step-by-step process how the analyses are performed and summarizing the current best practice of their application.