The SURVEYREG Procedure

Regression Coefficients

PROC SURVEYREG solves the normal equations $\mb {X’WX}\bbeta =\mb {X’Wy}$ by using a modified sweep routine that produces a generalized (g2) inverse $(\mb {X’WX})^-$ and a solution (Pringle and Rayner, 1971)

$\hat{\bbeta }=\mb {(X’WX)^-X’Wy}$

where $\mb {W}$ is the diagonal matrix constructed from WEIGHT variable values.

For models with class variables, there are more design matrix columns than there are degrees of freedom (df) for the effect. Thus, there are linear dependencies among the columns. In this case, the parameters are not estimable; there is an infinite number of least squares solutions. PROC SURVEYREG uses a generalized (g2) inverse to obtain values for the estimates. The solution values are not displayed unless you specify the SOLUTION option in the MODEL statement. The solution has the characteristic that estimates are zero whenever the design column for that parameter is a linear combination of previous columns. (In strict terms, the solution values should not be called estimates.) With this full parameterization, hypothesis tests are constructed to test linear functions of the parameters that are estimable.