One simple measure of how badly **S**(**q**) fits **S** is to examine
the sum of squared elements of **E***samp
*= **S** - **S**(**q**). The function is known as
the Ordinary Least Squares (OLS) discrepancy function, and may be written

(52)

where Tr() denotes the trace operator. The
values in **q** which,
for a given **S**, minimize FOLS
are called *Ordinary Least Squares (OLS)* estimates. That is

(53)

The OLS discrepancy function has a number of
difficulties, summarized nicely by Everitt (1984). In particular, it is
not *scale free* — different scalings of the manifest variables can
produce different discrepancy function values. Moreover, when calculated
on sample discrepancies, simple sums of squares may be inappropriate from
a statistical standpoint, because the elements of **S** are not independent
random variables, and because they usually have different sampling variances.