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Exploratory Factor Analysis by Specification Search
Limitations of Heuristic Specification Searches
A heuristic specification search can fail to find any of the best models for a given
number of parameters. In fact, the stepwise search in the present example did fail to
find any of the best 11-parameter models. As Figure 23-7 on p. 359 shows, the best
11-parameter model found by the stepwise search had a discrepancy (C) of 97.475. An
exhaustive search, however, turns up two models that have a discrepancy of 55.382. For
every other number of parameters, the stepwise search did find one of the best models.
Of course, it is only when you can perform an exhaustive search to double-check the
result of a heuristic search that you can know whether the heuristic search was
successful. In those problems where a heuristic search is the only available technique,
not only is there no guarantee that it will find one of the best models for each number
of parameters, but there is no way to know whether it has succeeded in doing so.
Even in those cases where a heuristic search finds one of the best models for a given
number of parameters, it does not (as implemented in Amos) give information about
other models that fit equally as well or nearly as well.