*! version 1.0 1dec2008
help mmregress

Title

mmregress -- MM-robust
regression

Syntax

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

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

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

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)

Same as above, but calling the initial S-estimator

Same as above, but fixing the Gaussian efficiency to 95%

. xi: mmregress price mpg headroom trunk weight length turn displacement gear_ratio i.rep78 foreign, eff(0.95)

Same as above, but starting the algorithm with an MS-estimator instead of an S-estimator

. xi: mmregress price mpg headroom trunk weight length turn displacement gear_ratio, dummies(i.rep78 foreign)

Same as above, but calling the initial MS-estimator rather than the more efficient MM-estimator

. xi: mmregress price mpg headroom trunk weight length turn displacement gear_ratio, dummies(i.rep78 foreign) initial

Robust fixed effects regression

. use http://fmwww.bc.edu/ec-p/data/wooldridge2k/CORNWELL, clear

. gen lncrmrte=ln(crmrte)

. xi: mmregress lncrmrte prbarr prbconv prbpris avgsen, dummies(i.county i.year)

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, mregress, sregress, msregress, mcd