robust Error Term

[Guest]

Why doesn't Stata provide the information on the total sum of squares, model sum of squares, and residual sum of squares when the –robust- option is specified?

[Carlo Lazzaro]

Guest:
welcome to this forum.
You can retrieve most of this information via -ereturn list-:

. sysuse auto.dta

. regress price mpg, rob

Linear regression                               Number of obs     =         74
                                                F(1, 72)          =      17.28
                                                Prob > F          =     0.0001
                                                R-squared         =     0.2196
                                                Root MSE          =     2623.7

------------------------------------------------------------------------------
             |               Robust
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         mpg |  -238.8943   57.47701    -4.16   0.000    -353.4727    -124.316
       _cons |   11253.06   1376.393     8.18   0.000     8509.272    13996.85
------------------------------------------------------------------------------

. ereturn list

scalars:
                  e(N) =  74
               e(df_m) =  1
               e(df_r) =  72
                  e(F) =  17.27521363224185
                 e(r2) =  .2195828561874971
               e(rmse) =  2623.652888667587
                e(mss) =  139449473.5462299
                e(rss) =  495615922.5753916
               e(r2_a) =  .2087437291901012
                 e(ll) =  -686.5395809065244
               e(ll_0) =  -695.7128688987767
               e(rank) =  2

macros:
            e(cmdline) : "regress price mpg, rob"
              e(title) : "Linear regression"
          e(marginsok) : "XB default"
                e(vce) : "robust"
             e(depvar) : "price"
                e(cmd) : "regress"
         e(properties) : "b V"
            e(predict) : "regres_p"
              e(model) : "ols"
          e(estat_cmd) : "regress_estat"
            e(vcetype) : "Robust"

matrices:
                  e(b) :  1 x 2
                  e(V) :  2 x 2
       e(V_modelbased) :  2 x 2

functions:
             e(sample)  

.

[Guest]

Dear Carlo
I know that but I am wondering why it is not there when I add robust to my reg?

[Carlo Lazzaro]

Guest:
see -regress- entry, Stata .pdf manual, Technical note, page 2246:

Technical note

regress purposefully suppresses displaying the ANOVA table when vce(robust) is specified.

This is done because the sums of squares are no longer appropriate for use in the usual hypothesis

tests, even though computationally the sums of squares remain the same. In the nonrobust setting,

the F statistic reported by regress is defined in terms of the sums of squares, as in ANOVA. When

vce(robust) is specified, the ANOVA test is not valid, and the F statistic corresponds to a Wald test

based on the robustly estimated variance matrix.

Some references give formulas for the F statistic in terms of either R2 or the root MSE. It is not

appropriate to use those formulas for the F statistic with robust standard errors because the R2 and

root MSE are calculated from the sums of squares. Moreover, the root MSE can no longer be used

as an estimate for because there is no longer a single to estimate—the variance of the residual

varies observation by observation. However, regress continues to report the R2 and the root MSE in

the robust setting because those statistics are still usable in other settings. In particular, R2 remains

valid as a goodness-of-fit statistic.