Application of AIC to Wald and Lagrange Multiplier Tests in Covariance Structure Analysis

The Akaike Information Criterion (AIC) has been proposed as an alternative to the conventional χ(2) goodness-of-fit test. In this article some efficient procedures for the use of AIC in covariance structure analysis are proposed, based on the backward search via the Wald test to impose constraints and the forward search via the Lagrange Multiplier rest to release constraints. An Approximated AIC, AAIC, is developed that is considerably more efficient computationally in providing information on AIC than the conventional approach based on the likelihood ratio test. AAIC can be effectively computed with a stepwise procedure for more general and for more restricted models that do not need to be explicitly estimated. The necessity of a given restriction is shown within the AIC theory not to depend on an a-level cut off in the χ(2) distribution, but on the absolute cutoff value of 2.0. As a consequence, the AIC-based procedure did not yield the simplest model in an example examined in this study. Results also showed that the univariate increment tests, which are products of stepwise procedures in both backward and forward searches, generated the same modifications as the AIC.