1996/07/01 by Chih-Ping Chou, Chih‐Ping Chou, P. M. Bentler +1 · 20 citations
Mathematics · #Advanced Statistical Methods and Models #Akaike information criterion #Applied mathematics #Bayesian information criterion #Covariance #Goodness of fit #Lagrange multiplier #Likelihood-ratio test #Mathematical optimization #Mathematics #Model selection #Multivariate statistics #Score test #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistical hypothesis testing #Statistics #Univariate #Wald test
paper · doi:10.1207/s15327906mbr3103_5
published in Multivariate Behavioral Research 31(3), 351-370 (Taylor & Francis)
openalex publication_date 1996/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
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.