ABSTRACT
In the previous chapter we considered the basic building blocks of SEM, namely model specification, model identification, model estimation, model testing, and model modification. These five steps fall into three main approaches for going from theory to a SEM model in which the covariance structure among variables is analyzed, In the confirmatory approach a researcher hypothesizes a specific theoretical model, gathers data, and then tests whether the data fit the model. In this approach, the theoretical model is either accepted or rejected based on a chi-square statistical test of significance and/or meeting acceptable model fit criteria. In the second approach, using alternative models, the researcher creates a limited number of theoretically different models to determine which model the data fit best. When these models use the same data set, they are referred to as nested models. The alternative approach conducts a chisquare difference test to compare each of the alternative models. The third approach, model generating, specifies an initial model (implied or theoretical model), but usually the data do not fit this initial model at an acceptable model fit criterion level, so modification indices (Lagrange or Wald test in EQS) are used to add or delete paths in the model to arrive at a final best model. The goal in model generating is to find a model that the data fit well statistically, but that also has practical and substantive theoretical meaning. The process of finding the best-fitting model is also referred to as a specification search, implying that if an initially specified model does not fit the data, then the model is modified in an effort to improve the fit (Marcoulides & Drezner, 2001, 2003). Recent advances in Tabu search algorithms have permitted the generation of a set of models that data fit equally well, with a final determination by the researcher of which model to accept (Marcoulides, Drezner, & Schumacker, 1998). Amos has an exploratory SEM specification search, which generates alternative models by specifying optional and/or required paths in a model. A researcher can then explore other substantive meaningful theoretical models and choose from a set of plausible models rather than use modification indices individually to generate and test successive models by adding or deleting paths.
