Saturated Versus Just Identified Models

Abstract

Two concepts of particular relevance for educational and psychological measurement research using the popular structural equation modeling methodology are revisited—saturated model and (just) identified model. The distinction is emphasized between a saturated model on the one hand and an identified model on the other. It is shown that a saturated model need not be identified (and thus need not be just identified). Within that context, it is stressed that for a given set of observed variables there may be more than a single saturated model. To avoid possible confusion, a proposal is made to use the concept of “the saturated model” as referring only to the model with unconstrained variances, covariances, and means for a given set of manifest measures and to make references to “a saturated model” whenever any of the possible set of saturated models for these observed variables is meant.