help sregress 
-------------------------------------------------------------------------------

Title

    sregress --   S-robust regression

Syntax

        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


    -------------------------------------------------------------------------

Description

    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%



Options

        +-------+
    ----+ 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


Examples

    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


References


    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