Cross-Impact Matrix Analysis for Feedback Loops

Extract

[...] To do this, we perform a matrix operation and obtain the following matrix: Cross-Impact Matrix: E1 E2 E3 E4 E5 E6 E7 E8 E1 3 4 3 2 3 3 2 4 E2 3 5 5 1 1 4 2 3 E3 2 3 3 2 2 1 2 2 E4 3 5 4 2 3 4 3 5 E5 1 1 1 2 1 1 2 E6 3 3 2 2 3 3 1 3 E7 2 4 3 2 3 3 3 4 E8 2 5 4 1 2 3 4 5 3. Find the 2nd order feedback loops. [...]

[...] Let's find the indirect influences of length 3 that caregivers can exert on other actors. To do this, it is enough to determine all the paths starting from node passing through 2 intermediaries and arriving at another node. From a matrix point of view, we are interested in row 2 of the MIC at the cube, each coefficient indicates the number of paths. B. Considering the 2x2 matrix of cross-impacts 1. From the MIC, we can draw the graph of direct cross-impacts below. [...]

[...] From a matrix point of view, we are interested in line each coefficient indicates the number of paths. Healthcare professionals exert indirect influences of length 2 on all actors: [...]

[...] For node there are no paths, for node E5, there is 1 path passing through E2. For node E6, there is 1 path passing through E3. For node E7, there are no paths and for E8, there are 2 paths passing through E1 and E2. 4. Let's find the indirect influences of length 2 that caregivers can exert on other actors. To do this, it is enough to determine all the paths starting from node passing through an intermediary and arriving at another node. [...]

[...] Find the 3rd order feedback loops. We say there is 3rd order feedback when for a node, there is a path with two intermediates that allows to return to the starting node. On the MIC at the cube, this translates to a non-zero value on the diagonal. On our 3x3 matrix, we notice that there is no 0 on the diagonal so each node admits at least one feedback loop, each actor exercises an indirect influence of length 3 on itself. [...]