# Near-Infrared Spectroscopy Applied to Complex Systems and Human Hyperscanning Networking
## 6 Optical Imaging and Methods for fNIRS Hyperscanning Applications
### Methodological Remarks on Integrated Data Analysis: Primary Indices and Statistical Issues  
As underlined by [PERSON] and [PERSON] [21], the availability of a complex set of data constituted by the recording of brain activity from multiple co-acting or interacting individuals allows for the investigation of not only the association or dependence between brain activity and behavior within each agent (first-level analyses), but also the investigation of associations and dependencies between brain activity of various inter-agents (second-level integrated analyses, see Figure 2). Such an opportunity, however, opens new questions on proper analysis tools and approaches to quantify and qualify those potential associations. Answers to those questions have been found, to date, by looking at procedures and algorithms used to explore functional connectivity. The term functional connectivity defines statistical associations between physiological responses or activation patterns of distributed neural structures, without any stringent assumption or constraint concerning the actual existence of a structural connection between them (an assumption that could never be met when analysing the consistency of data series from different people). As a consequence, a key feature of functional connectivity is that it is strongly time-dependent. In other words, even if the pattern of statistical associations can arise in multiple time scales and may present only for short time windows, a consistency in the time course of different series of data needs to be present. However, as within-individual statistical associations are typically estimated via correlation, spectral coherence, or phase-locking analyses, novel methods had to be defined to focus on inter-individual analysis, since traditional methods assume that data concerns different facets of the activity of the same system. Depending on the nature of collected hyperscanning data, on the defining features of the recorded biosignals, and on the interest in associations vs. dependencies in analyzed data, different methods can be selected for second-level integrated data analyses. Nevertheless, the most diffused and tested analysis tools when working with hemodynamic data are correlation and coherence analyses [4; 49]. In particular, the first are mainly used when exploring data in the time-domain, while the latter are used when exploring data in the frequency-domain. Furthermore, correlation indices mirror time consistency between different neural responses (as represented by waveforms), whereas coherence indices mirror phase consistency for different frequency components between oscillating signals. Both the kinds of analyses are based on bivariate tests and can then only offer information on pairs of signals one at a time. An alternative is offered by the application of methods based on Granger causality [52; 53]. Granger causality is a definition of causality and dependency between series of data based on prediction and on the theoretical premise that if a time-varying signal causes another time-varying signal, then past values of the first should contribute more than past values of the latter in explaining its present values and predicting its future values. The spreading application of this concept to intra-individual and inter-individual coupling analyses is due to the fact that the Granger-based modeling approach is data-driven and does not necessarily require setting an a priori model of potential underlying data structure. While this feature seems peculiarly relevant in hyperscanning research, where an a priori model of inter-brain associations can hardly be defined, some methodological points need to be taken into consideration. Potential interpretation biases have been reported in case of spurious findings from Granger causality models [52] and depending on inter-individual variability in hemodynamic responses [54].