Mean Field Dynamics of Graphs II: Assessing the Risk for the Development   of Phase Transitions in Empirical Data
  Psychological disorders like major depressive disorder can be seen as complex dynamical systems. By looking at symptom activation patterns, we can investigate the dynamic behaviour of individuals to see whether or not they are at risk for sudden changes (phase transitions). Here, we show how a mean field approximation is used to reduce a dynamic multidimensional system to one-dimensional system to analyse the dynamics. Using maximum likelihood estimation, we can estimate the parameter of interest which, in combination with a bifurcation diagram, reflects the risk that someone has for experiencing a transition. After validating the proposed method with simulated data, we apply this method to three empirical examples, where we validate our method using data that contains a transition, and where we show its use in a clinical and general sample. Results show an increased risk for a transition when the transition actually occurred, and that members of both the clinical and general sample were not susceptible to transitions from a healthy to a depressed mood, or vice versa. We conclude that the mean field approximation is valid to assess the risk for a transition, and could in the future aid clinical therapists in the treatment of depressed patient. 
Jolanda J Kossakowski, Marijke CM Gordijn, Harriette Riese, Lourens J   Waldorp
stat.AP