Assessing Goodness of Fit

Many mechanistic rules of thumb for evaluating the goodness of fit of structural equation models (SEM) emphasize model parsimony; all other things being equal, a simpler, more parsimonious model with fewer estimated parameters is better than a more complex model Although this is usually good advice, in the present article a heuristic counterexample is demonstrated in which parsimony as typically operationalized in indices of fit may be undesirable. Specifically, in simplex models of longitudinal data, the failure to include correlated uniquenesses relating the same indicators administered on different occasions will typically lead to systematically inflated estimates of stability. Although simplex models with correlated uniquenesses are substantially less parsimonious and may be unacceptable according to mechanistic decision rules that penalize model complexity, it can be argued a priori that these additional parameter estimates should be included. Simulated data . are used to support this claim and to evaluate the behavior of a variety of fit indices and decision rules. The results demonstrate the validity of Bollen and Long’s (1993) conclusion that “test statistics and fit indices are very beneficial, but they are no replacement for sound judgment and substantive expertise” (p. 8).