Analyzing Sankey diagrams statistically? Sankey diagrams are helpful for visualizing multiple, interacting processes:

Are there any statistical tools available that can analyze the interactions of multiple processes? I'm aware of sequence analysis tools like TraMineR, but to my knowledge they cannot analyze interactions between multiple processes.
 A: In the sequence analysis literature and methodology, formally describing and analyzing interacting processes is approached through the concept of multi-channel sequence analysis.
The basic idea is that something can transition between states in multiple "channels", and that these (non-)transitions in different channels interact. For instance, to understand employment trajectories, it is likely that state-transitions in the channel of family formation (single - cohabiting - married), the channel of housing (parents - renting - buying) and the labor market channel (studying - unemployed - employed) are related.
To incorporate this into sequence analysis, the idea of clustering various pasterns of state-transitions within a single channel on the basis of optimal matching-distances is extended to the multivariate case. For details see cited papers below.
TraMineR supports multi-channel sequence analysis through e.g. the function seqdistmc() (docs).

Gauthier, J., Widmer, E. Bucher P. & Notredame, C. (2010). Multichannel Sequence Analysis Applied to Social Science Data. Sociological Methodology, Vol 40, Issue 1.
Pollock, Gary (2007). Holistic trajectories: a study of combined employment, housing and family careers by using multiple-sequence analysis. Journal of the Royal Statistical Society: Series A 170, Part 1, 167–183. 
