On the modification and predictive validity of covariance structure models

Abstract

The relationship between model modification and predictive validity in covariance structure models is studied. It is shown that a function of the modification index (MI) (Joreskog and Sorbom, 1986; Sorbom, 1989) is asymptotically equivalent to changes in the predictive validity of the model as measured by Akaike's (1973; 1987) information criterion (AIC). Given this equivalency, it is argued that competing models should be modified independently in substantively plausible directions. The choice among the modified competing models should be made via the AIC. However, given the unreliable nature of the modification index as a specification error search tool, it is argued that a combination of the MI and expected parameter change methodology advocated by Saris, Satorra, and Sorbom (1987) and Kaplan (1990a, 1990b) may be more useful for guiding specification error searches. Implications for modeling practice are discussed.