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

(122)

is a minimum.