## Data_Sheet_1_Studying Complex Adaptive Systems With Internal States: A Recurrence Network Approach to the Analysis of Multivariate Time-Series Data Representing Self-Reports of Human Experience.pdf

We discuss formal, theoretical, and practical issues with the statistical analysis of multivariate time-series data that represent self-reports of human experience, often referred to as Ecological Momentary Assessment (EMA) data or Experience Sampling Method (ESM) data. We argue that such time series likely violate the assumptions required for valid statistical inference, such as the memoryless-ness property (due to the presence of long-range temporal correlations) and ergodicity (due to non-stationarity and non-homogeneity of central moments). Moreover, we consider the common practice of interpreting outcomes of self-reports as if they were outcomes of classical physical measurements as extremely problematic and suggest to consider them as records of the temporal evolution of observables of a complex adaptive system with internal state dynamics. We propose to address some of these issues by analyzing the change profile instead of the observed time series, using recurrence-based analyses, specifically (multiplex) recurrence networks. We analyze a publicly available dataset in which four participants rated six questions about their self-esteem and physical self, twice a day over a period of 512 days and introduce the concept of recurrence networks weighted by recurrence time. The edge weights represent either recurrence times or recurrence time frequencies and results show that the scaling relation between vertex degree and vertex strength (the weighted variant of vertex degree) is associated to the scaling relation between frequency and spectral power based on the “raw” time series. We present a new spiral layout for recurrence networks that might be more appropriate when the detection of critical periods, regime shifts, and tipping points requires insight into the temporal order in which those events occur. We conclude that a complex systems approach to analyzing multivariate time series of self-reports of human experience is preferred over and above fitting statistical models like the Gaussian Graphical Model or its derivatives.

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- Statistics
- Mathematical Physics not elsewhere classified
- Ordinary Differential Equations, Difference Equations and Dynamical Systems
- Computation Theory and Mathematics
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- Optimisation
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- Applied Statistics
- Numerical Computation
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