In chapter 4, we considered the basic building blocks of SEM, namely, model specication, model identication, model estimation, model testing, and model modication. These ve 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 conrmatory approach, a researcher hypothesizes a specic theoretical model, gathers data, and then tests whether the data t the model. In this approach, the theoretical model is either conrmed or disconrmed, based on a chi-square statistical test of signicance and/or meeting acceptable model-t criteria. In the second approach using alternative models, the researcher creates a limited number of theoretically different models to determine which model the data t best. When these models use the same data set, they are referred to as nested models. The alternative approach conducts a chi-square difference test to compare each of the alternative models. The third approach, model generating, species an initial model (theoretical model), but usually the data do not t this initial model at an acceptable model-t criterion level, so modication indices are used to add or delete paths in the model to arrive at a nal best model. The goal in model generating is to nd a model that the data t well statistically, but that also has practical and substantive theoretical meaning. The process of nding the best-tting model is also referred to as a specication search, implying that if an initially specied
model does not t the data, then the model is modied in an effort to improve the t (Marcoulides & Drezner, 2001; 2003). Recent advances in Tabu search algorithms have permitted the generation of a set of models that the data t equally well with a nal determination by the researcher of which model to accept (Marcoulides, Drezner, & Schumacker, 1998).