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A Nonrecursive Model
Stability Index
The existence of feedback loops in a nonrecursive model permits certain problems to
arise that cannot occur in recursive models. In the present model, attractiveness
depends on perceived academic ability, which in turn depends on attractiveness, which
depends on perceived academic ability, and so on. This appears to be an infinite
regress, and it is. One wonders whether this infinite sequence of linear dependencies
can actually result in well-defined relationships among attractiveness, academic
ability, and the other variables of the model. The answer is that they might, and then
again they might not. It all depends on the regression weights. For some values of the
regression weights, the infinite sequence of linear dependencies will converge to a set
of well-defined relationships. In this case, the system of linear dependencies is called
stable; otherwise, it is called unstable.
Note: You cannot tell whether a linear system is stable by looking at the path diagram.
You need to know the regression weights.
Amos cannot know what the regression weights are in the population, but it estimates
them and, from the estimates, it computes a stability index (Fox, 1980; Bentler and
Freeman, 1983).
If the stability index falls between –1 and +1, the system is stable; otherwise, it is
unstable. In the present example, the system is stable.
To view the stability index for a nonrecursive model:
E Click Notes for Group/Model in the tree diagram in the upper left pane of the Amos
Output window.
An unstable system (with a stability index equal to or greater than 1) is impossible, in
the same sense that, for example, a negative variance is impossible. If you do obtain a
stability index of 1 (or greater than 1), this implies that your model is wrong or that
your sample size is too small to provide accurate estimates of the regression weights.
If there are several loops in a path diagram, Amos computes a stability index for each
one. If any one of the stability indices equals or exceeds 1, the linear system is unstable.
Stability index for the following variables is 0.003:
attract
academic