A Commentary on the Relationship Between Model Fit and Saturated Path Models in Structural Equation Modeling Applications

The relationship between saturated path-analysis models and their fit to data is revisited. It is demonstrated that a saturated model need not fit perfectly or even well a given data set when fit to the raw data is examined, a criterion currently frequently overlooked by researchers utilizing path analysis modeling techniques. The potential of individual case residuals for saturated model fit assessment is revealed by showing how they can be used to examine local fit, as opposed to overall fit, to sense possible model deficiencies or misspecifications, and to suggest model improvements when needed. The discussion is illustrated with several numerical examples.