Browne and Cudeck (1989) proposed a single
sample cross-validation index as a follow-up to their earlier (Cudeck
& Browne, 1983) paper on cross-validation. Cudeck and Browne had proposed
a cross-validation index which, for model *Mk*
in a set of competing models is of the form FML(Sn,Sk(q)).
In this case, *F *is the maximum likelihood discrepancy function,
Sn
is the covariance matrix calculated on a cross-validation sample, and
Sk(q)
the reproduced covariance matrix obtained by fitting model *Mk*
to the original calibration sample. In general, better models will have
smaller cross-validation indices.

The drawback of the original procedure is that it requires two samples, i.e., the calibration sample for fitting the models, and the cross-validation sample. The new measure estimates the original cross-validation index from a single sample.

The measure is

(124)

where nk is the number
of free parameters in model *k*,**
***p* is the number of manifest variables, and *N*
is the sample size.