ROBUSTREG warning message

[Abishekaa]

Hi,

   I would really appreciate it if someone could explain these two warnings for my robust regression analysis. I want to make sure if the output is valid.

Summary: My predictors are highly right skewed, and linear regression of the raw data showed normally distributed residuals, but a large number of outliers and leverage points. Therefore, I decided to carry out robust regression. Below is my SAS log from robust regression:

2188 ods graphics on;
2189 proc robustreg data = new.cov_psmd_models1 PLOTS=all method=MM;
2190 class GENDER51 ELEVEL01 ;
2191 model WFT = msmd GENDER51 ELEVEL01 V5AGE51 / diagnostics leverage;
2192 output out= new.model3_outputROBUSTMM;
2193 title "MODEL3";
2194 run;

WARNING: The design matrix is singular. Some regressors are dropped from the matrix. LEVERAGE is
being computed on the reduced design matrix.
NOTE: The initial LTS estimator has been successfully computed.
NOTE: Algorithm converged for the MM estimates.
WARNING: The reweighted scatter matrix is singular. Projected robust distances and projected
Mahalanobis distances are computed.
NOTE: The projected MCD estimators for covariates have been successfully computed.
NOTE: The initial LTS estimator has been successfully computed.
NOTE: Algorithm converged for the location-scale MM estimates.
NOTE: The data set NEW.MODEL3_OUTPUTROBUSTMM has 200 observations and 13 variables.
NOTE: PROCEDURE ROBUSTREG used (Total process time):
real time 1.50 seconds
cpu time 0.93 seconds

[PaigeMiller]

WARNING: The design matrix is singular. Some regressors are dropped from the matrix. LEVERAGE is being computed on the reduced design matrix.

You have put more terms in the model to fit than the number of records in your data set. OR Some of the terms in the model are perfect linear combinations of other terms in the mode.

Since I haven't seen your data, let me just comment that right-skewed does not imply that you need robust regression. Robust regression generally compensates for outliers, not for skew.

[Abishekaa]

Hi Paige,

             Thank you for the explanation. I did run a regular linear regression and see a lot of outliers and leverage points. That is the reason for using robust regression in my analysis.