Rites, Wrongs, and Gold in Model Testing

Stimulated by the accompanying articles by Hayduk and Glaser (2000), as well as Mulaik and Millsap (2000), issues related to model evaluation are discussed. Nested model comparisons via sequential chi-square difference tests are supported as meaningful and are consistent with the 4-step approach to model evaluation when models of the factor analytic simultaneous equation type are entertained. Other classes of models, such as generalized Bentler-Weeks or simplex models, can be similarly evaluated by a sequence of nested models, but this sequence may not be the proposed 4-step sequence beginning with a confirmatory factor model. Some problems with the use of a "gold standard" indicator of a factor also are noted.