help mmregress 
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Title

    mmregress --  MM-robust regression

Syntax

        mmregress depvar [indepvars] [if] [in] [, options]

    options                 Description
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      noconstant            suppress constant term
      eff(#)                fix the desired efficiency
      dummies(dummies)      declare dummy variables
      outlier               generate outlyingness measures
      graph                 generate an outlier identification graphical tool
      label(varname)        label largest outliers according to varname
      replic(#)             set the number of sub-sampling to consider
      init                  return the initial S (or MS) estimator

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Description

    mmregress fits an MM-estimator of regression of depvar on varlist.  An
    MM-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.  The default Guassian efficiency
    is set to 70% but can be changed by calling the eff option.  The
    Breakdown point is 50%.



Options

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

    noconstant; see [R] estimation options.


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

    eff(#); The Gaussian efficiency of the MM-estimator can be changed (it
        can to be set to any value between 0.287 and 0.99). Keep however in
        mind that a higher efficiency is associated to a higher bias.

    dummies(dummies); If several dummy variables are present among the
        explanatory variables, the preliminary S-estimator algorithm could
        fail. An MS-estimator can be used instead by declaring the list of
        dummy variables dummies present in the model.

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

    label(varname); labels the largest outliers using variable varname. This
        option only works jointly with the graph option. If this option is
        not declared, the label will be the observation linenumber.

    outlier; Four outlyingness measures are calculated. The first (S_stdres
        or MS_stdres) contains the robust standardized residuals, the second
        (S_outlier or MS_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.

    init; The initial S (or MS) estimator is returned instead of the final
        MM. This is equivalent to setting the efficiency to 0.287.




Saved results

    mmregress 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)         mmregress
      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{p_end}

    Robust regression with default efficiency
    .  xi: mmregress price mpg headroom trunk weight length turn displacement
    gear_ratio i.rep78 foreign

(click to run)

    .  xi: mmregress price mpg headroom trunk weight length turn displacement
    gear_ratio i.rep78 foreign, initial (click to run) {pstd} {pstd}Same as
    above, but calling the initial S-estimator{p_end} {pstd} {pstd}Same as
    above, but fixing the Gaussian efficiency to 95%{p_end} {phang2}. xi:
    mmregress price mpg headroom trunk weight length turn displacement
    gear_ratio i.rep78 foreign, eff(0.95) {pstd}Same as above, but starting
    the algorithm with an MS-estimator instead of an S-estimator{p_end}
    {phang2}. xi: mmregress price mpg headroom trunk weight length turn
    displacement gear_ratio, dummies(i.rep78 foreign) {pstd}Same as above,
    but calling the initial MS-estimator rather than the more efficient
    MM-estimator{p_end} {phang2}. xi: mmregress price mpg headroom trunk
    weight length turn displacement gear_ratio, dummies(i.rep78 foreign)
    initial {pstd}Robust fixed effects regression{p_end} {phang2}. use
    http://fmwww.bc.edu/ec-p/data/wooldridge2k/CORNWELL, clear {phang2}. gen
    lncrmrte=ln(crmrte) {phang2}. xi: mmregress lncrmrte prbarr prbconv
    prbpris avgsen, dummies(i.county i.year) {pstd} References {pstd}Dehon,
    C., Gassner, M. and Verardi, V. (2008), "Beware of "Good" Outliers and
    Overoptimistic Conclusions", forthcoming in the Oxford Bulletin of
    Economics and Statistics {pstd}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.
    {pstd}Rousseeuw, P. J. and van Zomeren, B. (1990), "Unmasking
    Multivariate Outliers and Leverage Points", Journal of the American
    Statistical Association, 85, pp. 633-639.  {pstd}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 {psee}
    Online:  [R] qreg, [R] regress;{break} [R] rreg, mregress, sregress,