help sregress 


sregress -- S-robust regression


sregress depvar [indepvars] [if] [in] [, option]

options Description -------------------------------------------------------------------------

noconstant suppress constant term outlier generate outlyingness measures graph generate the outlier identification graphical tool replic set the number of sub-sampling to consider



sregress fits an S-estimator of regression of depvar on varlist. An S-estimator of regression is a robust fitting approach which minimizes a (rho) function of the regression residuals which is even, non decreasing for positive values and less increasing than the square function. The function used here is a Tukey Biweight leading to a Guassian efficiency of 28.7%


+-------+ ----+ Model +------------------------------------------------------------

noconstant; see [R] estimation options.

+-----------+ ----+ Algorithm +--------------------------------------------------------

graph; Displays a graphic where outliers are flagged according to their type.

outlier; Four outlyingness measures are calculated. The first (S_stdres) contains the robust standardized residuals, the second (S_outlier) flags outliers in the vertical dimension (i.e. observations associated with robust standardized residual larger than 2.25), the third (Robust_distance) contains robust distances and the fourth (MCD_outlier) flags outliers in the horizontal dimension (i.e. observations associated with robust distances larger than the 97.5th percentile of a Chi-quared).

replic; The number of subsets associated to the underlying algorithm is set by default using the formula replic=log(1-0.99)/log(1-(1-0.2)^(p+1)) where p is the number of explanatory variables. This can be changed using the replic option.

Saved results

sregress saves the following in e():

Scalars e(scale) robust residual scale e(N) number of observations e(df_m) model degrees of freedom e(df_r) residual degrees of freedom

Macros e(cmd) sregress e(properties) b V

Matrices e(b) coefficient vector e(V) variance-covariance matrix of the estimators

Functions e(sample) marks estimation sample


Setup . webuse auto

Robust regression . xi: sregress price mpg headroom trunk weight length turn displacement gear_ratio i.rep78 foreign

Same as above, but asking for outlyingness measures . xi: sregress price mpg headroom trunk weight length turn displacement gear_ratio i.rep78 foreign, outliers


Dehon, C., Gassner, M. and Verardi, V. (2008), "Beware of "Good" Outliers and Overoptimistic Conclusions", forthcoming in the Oxford Bulletin of Economics and Statistics

Rousseeuw, P. J. and Yohai, V. (1987), "Robust Regression by Means of S-estimators", in Robust and Nonlinear Time Series Analysis, edited by J. Franke, W. Härdle and D. Martin, Lecture Notes in Statistics No. 26, Springer Verlag, Berlin, pp. 256-272.

Rousseeuw, P. J. and van Zomeren, B. (1990), "Unmasking Multivariate Outliers and Leverage Points", Journal of the American Statistical Association, 85, pp. 633-639.

Salibian-Barrera, M. and Yohai, V. (2006). "A fast algorithm for S-regression estimates". Journal of Computational and Graphical Statistics, 15, 414-427.

Also see

Online: [R] qreg, [R] regress; [R] rreg, mmregress, mregress, msregress, mcd