Specification Search (Exploratory SEM)
Structural equation modeling (SEM) is an intrinsically confirmatory technique, but in practice it is often used in an exploratory way. Various tools have been developed for adapting this confirmatory technique to exploratory uses (MacCallum, 1986). These include the use of modification indices and Lagrange multiplier tests for selectively adding parameters to a model, and the use of z statistics (also called critical ratios) and Wald tests for selectively eliminating parameters (Bentler, 1989; Jöreskog & Sörbom, 1996).
Amos provides an alternative approach to exploratory SEM. In this approach, exploratory SEM is treated as a problem in model selection in which the number of candidate models is permitted to be large. Amos's Specification Search provides a method for systematically specifying, fitting and evaluating a large number of candidate models. Tools are provided for choosing among the models on the basis of fit, parsimony, and interpretability.
In a Specification Search, some single- and double- headed arrows in a path diagram are designated as optional. Amos fits the model both with and without each optional arrow, using every possible subset of them. If only one arrow is optional then an exploratory analysis consists of fitting the model with and without that optional arrow. If there are, say, three optional arrows, the program fits the model eight times (that is, 23 times), using every possible subset of the optional arrows.
An analysis can be more or less exploratory, depending on how many arrows are optional. Of course, there is a practical limit to the number of optional arrows since each optional arrow doubles the number of models that need to be fitted.