A Taxonomy of Path-Related Goodness-of-Fit Indices and Recommended Criterion Values.

Almost all goodness-of-fit indexes (GFIs) for latent variable structural equation models are global GFIs that simultaneously assess the fits of the measurement and structural portions of the model. In one sense, this is an elegant feature of overall model GFIs, but in another sense, it is unfortunate as the fits of the 2 different portions of the model cannot be assessed independently. We (a) review the developing literature on this issue, (b) propose 6 new GFIs that are designed to evaluate the structural portion of latent variable models independently of the measurement model, (c) that are couched within a general taxonomy of James, Mulaik, and Brett's (1982) Conditions 9 and 10 for causal inference from nonexperimental data, (d) conduct a Monte Carlo simulation of the usefulness of these 6 new GFIs for model selection, and (e) on the basis of simulation results provide recommended criteria for 4 of them. Supplemental analyses also compare 2 of the new GFIs to 2 other structural model selection strategies currently in use.