```help msregress
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Title

msregress --  MS-robust regression

Syntax

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

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

noconstant            suppress constant term
dummies(dummies)      is compulsury and is used to declare dummy
variables
outlier               generate outlyingness measures
graph                 generate the outlier identification graphical
tool
replic                set the number of sub-sampling to consider

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Description

msregress fits an MS-estimator of regression of depvar on varlist.  An
MS-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 which is
appropriate when some dummy variables are among the explanatory.  The
function used here is a Tukey Biweight.

Options

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

noconstant; see [R] estimation options.

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

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

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

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

Saved results

msregress 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)         msregress
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

MS-robust regression
. xi: msregress price mpg headroom trunk weight length turn
displacement gear_ratio, dummies(i.rep78 foreign)

Same as above, but calling the graphical tool
. xi: msregress price mpg headroom trunk weight length turn
displacement gear_ratio, dummies(i.rep78 foreign) graph

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, sregress, mregress, mcd

```