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Example 23
Heuristic Specification Search
The number of models that must be fitted in an exhaustive specification search grows
rapidly with the number of optional arrows. There are 12 optional arrows in Figure
23-2 on p. 351 so that an exhaustive specification search requires fitting
models. (The number of models will be somewhat smaller if you specify a small
positive number for
Retain only the best___models on the Next search tab of the Options
dialog box.) A number of heuristic search procedures have been proposed for reducing
the number of models that have to be fitted (Salhi, 1998). None of these is guaranteed
to find the best model, but they have the advantage of being computationally feasible
in problems with more than, say, 20 optional arrows where an exhaustive specification
search is impossible.
Amos provides three heuristic search strategies in addition to the option of an
exhaustive search. The heuristic strategies do not attempt to find the overall best model
because this would require choosing a definition of best in terms of the minimum or
maximum of a specific fit measure. Instead, the heuristic strategies attempt to find the
1-parameter model with the smallest discrepancy, the 2-parameter model with the
smallest discrepancy, and so on. By adopting this approach, a search procedure can be
designed that is independent of the choice of fit measure. You can select among the
available search strategies on the
Next search tab of the Options dialog box. The
choices are as follows:
All subsets. An exhaustive search is performed. This is the default.
Forward. The program first fits the model with no optional arrows. Then it adds one
optional arrow at a time, always adding whichever arrow gives the largest
reduction in discrepancy.
Backward. The program first fits the model with all optional arrows in the model.
Then it removes one optional arrow at a time, always removing whichever arrow
gives the smallest increase in discrepancy.
Stepwise. The program alternates between Forward and Backward searches,
beginning with a Forward search. The program keeps track of the best 1-optional-
arrow model encountered, the best 2-optional-arrow model, and so on. After the
first Forward search, the Forward and Backward search algorithms are modified by
the following rule: The program will add an arrow or remove an arrow only if the
resulting model has a smaller discrepancy than any previously encountered model
with the same number of arrows. For example, the program will add an arrow to a
5-optional-arrow model only if the resulting 6-optional-arrow model has a smaller
discrepancy than any previously encountered 6-optional-arrow model. Forward
2
12
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