in proc reg how does sas determine its linear combinations when "model is not of full rank"?

[DAGUTD]

in proc reg how does sas determine its linear combinations when "model is not of full rank"?

[sbxkoenk]

See SAS documentation :

SAS® 9.4 and SAS® Viya® 3.5 Programming Documentation | SAS 9.4 / Viya 3.5
SAS/STAT User's Guide
The REG Procedure
Details --> Models of Less Than Full Rank
https://go.documentation.sas.com/doc/en/pgmsascdc/9.4_3.5/statug/statug_reg_details23.htm

Koen

[DAGUTD]

I had read the suggested material, and went back and reread it. My impression is that the multicollineary subsets come from either the GINV or SWEEP function available in IML. My simple test example is

in which I include r0 for the intercept term when using SWEEP. Setting r1 to Y and r2-r7 to X, PROC REG reports

because the model is not of full rank. I have been unable to replicate this output in IML.

[PGStats]

When colinearities exist, Proc Reg sets certain parameter estimates to zero. Note that which parameter estimate is set to zero (ignored) depends on the order in which it enters the model.

[PaigeMiller]

When a matrix is not full rank, one or more of the eigenvalues of the X'X matrix are zero. So the corresponding eigenvectors determines the linear combinations reported.

[WarrenKuhfeld]

PROC REG internally uses a SWEEP operator to compute the regression coefficients, X'X inverse, and the error sum of squares. PROC REG performs a sequential sweep. That is, it always begins by sweeping the second column of (y X)'(y X), that is the first column corresponding to the first X column. Then it sweeps the next column if the pivot is not zero (if the that column is not a linear function of the preceding column). Then it sweeps the next column if the pivot is not zero (if that column is not a linear combination of preceding columns). ... and so on ....

In contrast, a procedure like TRANSREG does nonsequential sweeps, finding the best column to sweep first, then the second best, and so on. The TRANSREG approach tends to be more accurate, but in linear models, you might prefer sequential sweeps to get Type I sums of squares.

[DAGUTD · Accepted solution]

This solution is closest to my thinking. Nevertheless, I have not yet been able to replicate the reported results. My suspicion is SAS uses more than just SWEEP to determine its results. Nevertheless, thanks to all who responded and offered suggestions. I already had tried other approaches, such as the suggested eigenfunction one.

[DAGUTD]

Also, StatDave_sas (SAS Super FREQ) posted a reply that did not appear in the listing:

In the PROC REG documentation, see "Computational Methods" in the section which explains this. It is controlled by the SINGULAR= option.

These two answers are what I needed. Again, thanks to all.