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Example 22
Specification Search with Many Optional Arrows
The previous specification search was largely confirmatory in that there were only
three optional arrows. You can take a much more exploratory approach to constructing
a model for the Felson and Bohrnstedt data. Suppose that your only hypothesis about
the six measured variables is that
academic depends on the other five variables, and
attract depends on the other five variables.
The path diagram shown in Figure 22-7 with 11 optional arrows implements this
hypothesis. It specifies which variables are endogenous, and nothing more. Every
observed-variable model that is consistent with the hypothesis is included in the
specification search. The covariances among the observed, exogenous variables could
have been made optional, but doing so would have increased the number of optional
arrows from 11 to 17, increasing the number of candidate models from 2,048 (that is, 2
11
)
to 131,072 (that is, 2
17
). Allowing the covariances among the observed, exogenous
variables to be optional would have been costly, and there would seem to be little interest
in searching for models in which some pairs of those variables are uncorrelated.
Figure 22-7: Highly exploratory model for Felson and Bohrnstedt’s girls’ data
GPA
height
rating
weight
academic
attract
error1
error2
1
1