# Estimable Functions

In general
linear models and
generalized linear models,
if the X¢
X matrix (where X
is the design matrix)
is less than full rank,
the regression coefficients depend on
the particular generalized
inverse used for solving
the normal equations, and the regression coefficients will not be unique.
When the regression coefficients are not unique, linear functions (f) of the regression coefficients having
the form

f = Lb

where L
is a vector of coefficients, will also in general not be unique.
However, Lb
for an L
which satisfies

L
= L(X'X)-X'X

is invariant for all possible generalized
inverses, and is
therefore called an estimable function.

See also matrix rank. For additional details,
see the General Linear Model (GLM) method
of analysis.