proc surveyreg

[LLOUKINE]

Hello,

 In my analysis I use proc surveyred  with varmethod=brr  method for the variance estimation and as soon as I declare the categorical variables as  class variables I receive the note in the SAS output that states  ”Matrix X'WX is singular and a generalized inverse was used to solve the normal equations.  Estimates are not unique.” My categorical variables are numeric type and when I use them in the model w/o the class statement that note disappears. I noticed that in one example for this procedure the output has the same note but the estimates are still used and interpreted. PROC SURVEYREG: Variance Estimate Using the Jackknife Method :: SAS/STAT(R) 9.22 User's Guide

In this regards I have 2 questions:

1. Why I am getting that note when I declare the categorical variables using the class statement?
2. Can this note be ignored and the model parameters can be used to make conclusions for the analyses?

Please advise. Thank you!

[YZ11 · Accepted solution]

When your model contains a CLASS statement, then you will get this message any time you run PROC SURVEYREG with the SOLUTION option in the MODEL statement. SURVEYREG is estimating the model correctly, and the message is telling you exactly what technique is being used for the estimation. 
See the following Usage Note for details:
Usage Note 22585: Why is the X'X matrix found to be singular in the PROC GLM Output?
http://support.sas.com/kb/22/585.html
The Usage Note discusses PROC GLM, but the same model parameterization is used in PROC SURVEYREG.

I hope this information is helpful.

[LLOUKINE]

Thank you very much for your reply! I appreciate it! 

[LLOUKINE]

Hi, I looked at the link you provided and it states "The estimates are regarded as biased or not uniquely estimable."  It is sounds as contradictory to your statement that the 'SURVEYREG is estimating the model correctly" . Am I missing something? Can I use a different type of a parametrization in proc surveyreg to avoid Linear dependencies? 

[YZ11]

You can think of “not uniquely estimable” as meaning that there are multiple valid ways to code the CLASS variables, rather than indicating a problem with the model or bias in the results. PROC SURVEYREG (like PROC GLM) uses overparameterized coding for CLASS variables, which leads to non‑unique individual coefficients.

Using different codings can result in different parameter estimates, but those parameters also have different interpretations. 
If you'd like to use a specific reference group, you can use the REF= option in the CLASS statement, and this SAS NOTE 37108.

Also, you may find this note helpful on interpreting CLASS variable coefficients: 

Note 38384: Interpreting the results of the SOLUTION option in the MODEL statement of PROC GLM

[LLOUKINE]

Thank you very much! I will look at that.