Bias correction of the Akaike information criterion in factor analysis

The higher-order asymptotic bias for the Akaike information criterion (AIC) in factor analysis or covariance structure analysis is obtained when the parameter estimators are given by the Wishart maximum likelihood. Since the formula of the exact higher-order bias is complicated, simple approximations which do not include unknown parameter values are obtained. Numerical examples with simulations show that the approximations are reasonably similar to their corresponding exact asymptotic values and simulated values. Simulations for model selection give consistently improved results by the approximate correction of the higher-order bias for the AIC over the usual AIC.