help mmregress-------------------------------------------------------------------------------

Title

mmregress-- MM-robust regression

Syntax

mmregressdepvar[indepvars] [if] [in] [,options]

optionsDescription -------------------------------------------------------------------------

noconstantsuppress constant termeff(#)fix the desired efficiencydummies(dummies)declare dummy variablesoutliergenerate outlyingness measuresgraphgenerate an outlier identification graphical toollabel(varname)label largest outliers according tovarnamereplic(#)set the number of sub-sampling to considerinitreturn the initial S (or MS) estimator-------------------------------------------------------------------------

Description

mmregressfits an MM-estimator of regression ofdepvaronvarlist. 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 theeffoption. 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 variablesdummiespresent in the model.

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

label(varname); labels the largest outliers using variablevarname. 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)) wherepis 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

mmregresssaves the following ine():Scalars

e(scale)robust residual scalee(N)number of observationse(df_m)model degrees of freedome(df_r)residual degrees of freedomMacros

e(cmd)mmregresse(properties)b VMatrices

e(b)coefficient vectore(V)variance-covariance matrix of the estimatorsFunctions

e(sample)marks estimation sample

ExamplesSetup

. webuse auto{p_end}Robust regression with default efficiency

. xi: mmregress price mpg headroom trunk weight length turn displacementgear_ratio i.rep78 foreign

(click to run)

. xi: mmregress price mpg headroom trunk weight length turn displacementgear_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 displacementgear_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 turndisplacement 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 trunkweight length turn displacement gear_ratio, dummies(i.rep78 foreign)initial{pstd}Robust fixed effects regression{p_end} {phang2}. usehttp://fmwww.bc.edu/ec-p/data/wooldridge2k/CORNWELL, clear{phang2}. genlncrmrte=ln(crmrte){phang2}. xi: mmregress lncrmrte prbarr prbconvprbpris 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,