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 - Hasselman, Fred; Bosman, Anna M. T. (Frontiers in Applied Mathematics and Statistics, 2020)
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 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-bases analyses, specifically, (multiplex) recurrence networks. We analyze a publicly available data set in which 4 participants rated 6 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 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. In addition, 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 in the temporal order in which those events occur. We conclude 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.