Chapter 11: Nonnormaland Categorical Data in Structural Equation Modeling

Structural equation modeling (SEM) has remained a popular data analytic technique in education, psychology, business, and other disciplines (Austin & Calderön, 1996; MacCallum & Austin, 2000; Tremblay & Gardner, 1996). Given the frequency of its use, it is important to recognize the assumptions associated with different estimation methods, demonstrate the conditions under which results are robust to violations of these assumptions, and specify the procedures that should be employed when assumptions are not met. The importance of attending to assumptions and, consequently, selecting appropriate analysis strategies based on the characteristics of the data and the study’s design, cannot be overstated. Put simply, violating assumptions can produce biased results in terms of data-model fit as well as parameter estimates and their associated significance tests. Biased results, in turn, might result in incorrect decisions about the theory being tested.