Estimable Functions

In general linear models and generalized linear models, if the 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.