Loop impact explains a model's behavior one stock at a time. For each stock, it asks which feedback loops are making that stock speed up or slow down, and by how much. The method was introduced by Hayward and Boswell (2014) and extended by Hayward and Roach (2017, 2022), who showed that it can be read using the language of Newton's laws of motion: forces, work and energy.
To turn it on, check Loop impact and energy in the Simulation Control dialog, or, in a Vensim DSS command script, SIMULATE>LINEARIZE|1. It is much faster than eigenvalue analysis, and is also included whenever eigenvalue analysis is on. See Structural intelligence (loop dominance) for all the options.
The idea
Think of each stock as an object moving through time. Its net rate of change is its velocity. Whenever its rate of change itself changes - the stock's growth speeds up or slows down - something must be pushing on it. In a system dynamics model, what pushes on a stock is the feedback from other stocks (and from itself).
•The force from one stock on another is how much the first stock's movement is changing the second stock's rate.
•The impact is that force divided by the second stock's own rate. It is unit-free, so impacts on stocks with very different units can be compared directly. It tells you how much of the bending (curvature) in the stock's behavior comes from that source.
•The loop impact of a loop on a stock is the impact delivered along that loop (Hayward and Boswell 2014).
A positive impact makes the stock's movement steeper - growth accelerates, or decline accelerates. A negative impact makes its movement flatter, pulling it toward a turning point.
Note that the sign of a loop's impact is not the same as the loop's polarity. A balancing loop can have a positive impact on a stock for part of an oscillation, for example.
Which loop dominates
At each analysis point Vensim follows Hayward and Boswell's rule for each stock: take the impacts that have the same sign as the overall effect, and add them up from largest to smallest until they outweigh everything else. The loop, or group of loops, needed to do that is dominant for that stock at that time.
Sometimes no loop dominates. This happens when the stock is close to equilibrium, at a turning point, or when all the forces on it are very small and it is simply continuing at its current rate.
Power, work and energy
Impact describes what is happening at one moment. To see which loops matter over a whole run, Hayward and Roach (2022) extended the idea to energy:
•Power is the rate at which a loop is adding energy to, or taking it from, a stock's movement.
•Work (or energy) is the total of that power from the start of the run.
A loop can do the most work on a stock over a run without ever being the dominant loop at any one moment. When the instantaneous picture (impact) and the cumulative picture (energy) disagree, that is often an important finding about the model.
Energy classes
Hayward and Roach (2022) also showed that loops play different roles depending on their polarity and length. Vensim labels each loop at each analysis time:
Class |
Loops |
Role |
|---|---|---|
Sink |
First-order balancing loops (a stock acting on itself) |
The only structure that removes energy. It is what allows a model to settle down. |
Exchange |
Second-order balancing loops |
Moves energy back and forth between stocks - the typical source of oscillation. |
Source |
Reinforcing loops, and all loops of third order or more |
Adds energy to the system. |
None |
Loop gain is zero at this time |
The loop is switched off, for example by a saturated lookup. |
A useful rule of thumb follows from this: a model with no first-order balancing loop cannot settle down. A loop whose class changes during the run is one whose polarity flips, and these are often the loops behind the most interesting behavior.
What else affects a stock
As well as the feedback loops, Vensim measures the other things that make a stock's rate change, so that every stock's behavior is fully accounted for:
•Exogenous effects - changes caused directly by time, such as STEP, RAMP or PULSE functions and data.
•Upstream effects - pushes from stocks outside the stock's own feedback block.
•Residual - whatever the linear picture cannot explain. A large residual marks a moment where the model is switching regime (for example, a lookup reaching its limit or a MAX function switching), and the loop results should be read with care there.
Relation to eigenvalue analysis
Loop impact and eigenvalue analysis are two ways of looking at the same linearized model, and they share the same eigenvalues. Eigenvalue analysis asks which loops control the system's growth, decay and oscillation; loop impact asks which loops are moving each stock. Hayward and Roach (2024) compare the two methods in detail. In practice:
•use loop impact when you want to explain the behavior of a particular stock, or need a fast answer for a large model;
•use eigenvalue analysis when you want to understand the character of the system as a whole;
•where both are available, check whether they identify the same loops at the same times.
Limitations
•At a turning point a stock's rate is zero, so its impacts are undefined. These points are skipped when deciding dominance. Power and work stay well-behaved there.
•Vensim works with stocks rather than every individual causal link. If two loops share the same link between two stocks, their impact on that link cannot be separated, and the results show the combined value with a flag.
•As with eigenvalue analysis, the results are based on a local linear picture at each analysis point.
See also
•Structural intelligence (loop dominance) overview
