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A Nonrecursive Model
Perceived academic performance is modeled as a function of GPA and perceived
attractiveness (attract). Perceived attractiveness, in turn, is modeled as a function of
perceived academic performance, height, weight, and the rating of attractiveness by
children from another city. Particularly noteworthy in this model is that perceived
academic ability depends on perceived attractiveness, and vice versa. A model with
these feedback loops is called nonrecursive (the terms recursive and nonrecursive
were defined earlier in Example 4). The current model is nonrecursive because it is
possible to trace a path from attract to academic and back. This path diagram is saved
in the file Ex07.amw.
Model Identification
We need to establish measurement units for the two unobserved variables, error1 and
error2, for identification purposes. The preceding path diagram shows two regression
weights fixed at 1. These two constraints are enough to make the model identified.
Results of the Analysis
Text Output
The model has two degrees of freedom, and there is no significant evidence that the
model is wrong.
There is, however, some evidence that the model is unnecessarily complicated, as
indicated by some exceptionally small critical ratios in the text output.
Chi-square = 2.761
Degrees of freedom = 2
Probability level = 0.251