topic Re: Add t-stats to PROC Robustreg in Statistical Procedures

Add t-stats to PROC Robustreg

drip_ — Fri, 01 Jul 2022 14:52:25 GMT

Hi all,

I'm running a robust regression (m estimation) and would like to put out t statistics and (adjusted) r^2 to a dataset similar to the "outest = ... tableout" option when using proc reg.

Is it possible to do this?

Thanks in advance!

Re: Add t-stats to PROC Robustreg

PaigeMiller — Fri, 01 Jul 2022 15:51:59 GMT

I don't see any place where ROBUSTREG produces t-statistics. The R-squared can be obtained by

ods output goodfit=goodfit;

if the estimation method produces R-squared as a standard output (M estimation does).

Re: Add t-stats to PROC Robustreg

sbxkoenk — Fri, 01 Jul 2022 15:55:59 GMT

Hello,

outest= option in PROC ROBUSTREG is like outest= option in PROC REG.
What are you missing in the former that you have in the latter?

data a (drop=i);
   do i=1 to 1000;
      x1=rannor(1234);
      x2=rannor(1234);
      e=rannor(1234);
      if i > 900 then y=100 + e;
      else y=10 + 5*x1 + 3*x2 + .5 * e;
      output;
   end;
run;

proc reg data=a outest=abc;
   model y = x1 x2;
run;

proc robustreg data=a method=m outest=xyz;
   model y = x1 x2;
run;
/* end of program */

Thanks,

Koen

Re: Add t-stats to PROC Robustreg

drip_ — Sat, 02 Jul 2022 08:43:16 GMT

Thanks for your answer! Is it also possible to have the adjusted R-squared as an output?

Re: Add t-stats to PROC Robustreg

drip_ — Sat, 02 Jul 2022 08:43:53 GMT

What I'm missing specifically is the t-stats, so far I have only been able to obtain R-squared

Re: Add t-stats to PROC Robustreg

PaigeMiller — Sat, 02 Jul 2022 10:10:50 GMT

As far as I can see, ROBUSTREG does not produce adjusted R-squared, only R-squared. However, there's nothing stopping you from applying the adjusted R-squared formula to the actual R-squared if you want.

Re: Add t-stats to PROC Robustreg

Rick_SAS — Tue, 05 Jul 2022 13:44:29 GMT

What you are asking for does not make sense, as stated.

For ordinary least-squares regression (OLS), the null hypothesis Beta_i = 0 is tested by using a t test.

But for M estimation, the test statistic for H0 is not t-distributed. Instead, you can test for Beta_i = 0 by using a robust version of the F test. The robust test statistic is distributed as a chi-square statistic. The details are provided in the doc: SAS Help Center: M Estimation

If your goal is to test the null hypothesis that Beta_i=0, then you can use the FWLS option on the PROC ROBUSTREG statement to display a table that shows the parameter estimates for the final weighted least squares fit. The following statements build on the program that @sbxkoenk provided:

proc robustreg data=a method=m outest=xyz FWLS;
   model y = x1 x2;
   ods output ParameterEstimatesF=PEFinal;
run;

proc print data=PEFinal;
run;

The ProbChiSq variable contains the p-values for the test statistic under the null hypothesis.