Other Indices of Fit - Rescaled Akaike Information Criterion

In a number of situations the user must decide among a number of competing nested models of differing dimensionality. (The most typical example is the choice of the number of factors in common factor analysis.) Akaike (1973, 1983) proposed a criterion for selecting the dimension of a model. Steiger and Lind (1980) presented an extensive Monte Carlo study of the performance of the Akaike criterion. Here the criterion is rescaled (without affecting the decisions it indicates) so that it remained more stable across differing sample sizes. The rescaled Akaike criterion is as follows.

Let FML,k be the maximum likelihood discrepancy function and fk be the number of free parameters for the model Mk. Let N be the sample size

Select the model Mk for which


is a minimum.