Potential problems with "well fitting" models

The assessment of model fit is a more complex and indeterminate process than is commonly acknowledged by researchers who use structural equation modeling (SEM) techniques. Even models that are well fitting according to commonly used statistical tests and descriptive fit indices can have significant problems and ambiguities. The authors discuss 7 potential difficulties that can arise and that should temper researchers' conclusions: equivalent models, nonequivalent but well-fitting alternative models, omitted variables, problematic lower-order model components, the failure to parse composite models into meaningful partitions (e.g., measurement vs. structural), inattention to the multiple factors that affect the sensitivity of measures of fit to model misspecifications, and reliance on specification searches. In addition to providing examples of each of these problems, the authors offer recommendations for psychopathologists who conduct SEM analyses.