PROC ROBUSTREG Statement 
The PROC ROBUSTREG statement invokes the procedure. You can specify the following options in the PROC ROBUSTREG statement.
saves the estimated covariance matrix in the OUTEST= data set. This option is not supported for LTS estimation.
specifies the input SAS data set used by PROC ROBUSTREG. By default, the most recently created SAS data set is used.
requests that final weighted least squares estimates be computed. These estimates are equivalent to the least squares estimates after the detected outliers are deleted.
specifies an input SAS data set that contains initial estimates for all the parameters in the model. See the section INEST= Data Set for a detailed description of the contents of the INEST= data set.
displays the iteration history for the iteratively reweighted least squares algorithm used by M and MM estimation. You can also use this option in the MODEL statement.
specifies the length of effect names in tables and output data sets to be n characters, where n is a value between 20 and 200. The default length is 20 characters.
specifies the order in which to sort the levels of the classification variables (which are specified in the CLASS statement). This option applies to the levels for all classification variables, except when you use the (default) ORDER=FORMATTED option with numeric classification variables that have no explicit format. With this option, the levels of such variables are ordered by their internal value.
The ORDER= option can take the following values:
Value of ORDER= 
Levels Sorted By 

DATA 
Order of appearance in the input data set 
FORMATTED 
External formatted value, except for numeric variables with no explicit format, which are sorted by their unformatted (internal) value 
FREQ 
Descending frequency count; levels with the most observations come first in the order 
INTERNAL 
Unformatted value 
By default, ORDER=FORMATTED. For ORDER=FORMATTED and ORDER=INTERNAL, the sort order is machinedependent. For more information about sorting order, see the chapter on the SORT procedure in the Base SAS Procedures Guide and the discussion of BYgroup processing in SAS Language Reference: Concepts.
specifies an output SAS data set that contains the parameter estimates, and, if the COVOUT option is specified, the estimated covariance matrix. See the section OUTEST= Data Set for a detailed description of the contents of the OUTEST= data set.
specifies options that control details of the plots. If ODS Graphics is enabled but you do not specify the PLOTS= option, then PROC ROBUSTREG produces the robust fit plot by default when the model includes a single continuous independent variable.
ODS Graphics must be enabled before requesting plots. For example:
ods graphics on; proc robustreg data=stack plots=all; model y = x1 x2 x3; run; ods graphics off;
For more information about enabling and disabling ODS Graphics, see the section Enabling and Disabling ODS Graphics in Chapter 21, Statistical Graphics Using ODS.
The globalplotoptions apply to all plots generated by the ROBUSTREG procedure. The following globalplotoption is available:
suppresses the default robust fit plot. Only plots specifically requested are displayed.
You can specify more than one plotrequest within the parentheses after PLOTS=. For a single plot request, you can omit the parentheses. The following plotrequests are available.
creates all appropriate plots.
creates a plot of robust distance against Mahalanobis distance. See the section Leverage Point and Outlier Detection for details about robust distance. The LABEL= option specifies how the points on this plot are to be labeled, as summarized by the following table.
Value of LABEL= 
Label Method 

ALL 
Label all points 
LEVERAGE 
Label leverage points 
NONE 
No labels 
OUTLIERS 
Label outliers 
By default, the ROBUSTREG procedure labels both outliers and leverage points.
If you specify ID variables in the ID statement, the values of the first ID variable are used as labels; otherwise, observation numbers are used as labels.
creates a plot of robust fit against the single independent continuous variable specified in the model. You can request this plot when only a single independent continuous variable is specified in the model. Confidence limits are added on the plot by default. The NOLIMITS option suppresses these limits.
creates a histogram for the standardized robust residuals. The histogram is superimposed with a normal density curve and a kernel density curve.
suppresses all plots.
creates the normal quantilequantile plot for the standardized robust residuals.
creates the plot of standardized robust residual against robust distance. See the section Leverage Point and Outlier Detection for details about robust distance. The LABEL= option specifies a label method for points on this plot. These label methods are described in Table 77.1.
If you specify ID variables in the ID statement, the values of the first ID variable are used as labels; otherwise, observation numbers are used as labels.
specifies the seed for the random number generator used to randomly select the subgroups and subsets for LTS and S estimation. By default or if you specify zero, the ROBUSTREG procedure generates a random seed.
specifies the estimation method and some additional options for the estimation method. PROC ROBUSTREG provides four estimation methods: M estimation, LTS estimation, S estimation, and MM estimation. The default method is M estimation.
Note: Since the LTS and S methods use subsampling algorithms, these methods are not suitable in an analysis with variables that have only a few unequal values or a few unequal values within one BY group. For example, indicator variables that correspond to a classification variable often fall into this type. The same issue also applies to the initial LTS and S estimates in the MM method. In case of a model that includes classification independent variables or continuous independent variables with a few unequal values, the M method is recommended.
With METHOD=M, you can specify the following additional options:
specifies the type of asymptotic covariance computed for the M estimate. The three types are described in the section Asymptotic Covariance and Confidence Intervals. By default, ASYMPCOV= H1.
specifies a convergence criterion for the M estimate. The three criteria listed in the following table are available.
Type 
Option 
Coefficient 
CONVERGENCE=COEF 
Residual 
CONVERGENCE=RESID 
Weight 
CONVERGENCE=WEIGHT 
By default, CONVERGENCE = COEF. You can specify the precision of the convergence criterion with the EPS= option. By default, EPS=1.E8.
sets the maximum number of iterations during the parameter estimation. By default, MAXITER=1,000.
specifies the scale parameter or a method for estimating the scale parameter. These methods and options are summarized in the following table.
Scale 
Option 
Default d 
Fixed constant 
SCALE=value 

Huber estimate 
SCALE=HUBER<(D=d)> 
2.5 
Median estimate 
SCALE=MED 

Tukey estimate 
SCALE=TUKEY<(D=d)> 
2.5 
By default, SCALE = MED.
specifies the weight function used for the M estimate. The ROBUSTREG procedure provides 10 weight functions, which are listed in the following table. You can specify the parameters in these functions with the A=, B=, and C= options. These functions are described in the section M Estimation. The default weight function is bisquare.
Weight Function 
Option 
Default a, b, c 
Andrews 
WF=ANDREWS<(C=c)> 

Bisquare 
WF=BISQUARE<(C=c)> 

Cauchy 
WF=CAUCHY<(C=c)> 

Fair 
WF=FAIR<(C=c)> 

Hampel 
WF=HAMPEL<( <A=a> <B=b> <C=c>)> 

Huber 
WF=HUBER<(C=c)> 

Logistic 
WF=LOGISTIC<(C=c)> 

Median 
WF=MEDIAN<(C=c)> 

Talworth 
WF=TALWORTH<(C=c)> 

Welsch 
WF=WELSCH<(C=c)> 

With METHOD=LTS, you can specify the following additional options:
specifies the number of concentration steps (Csteps) for the LTS estimate. See the section LTS Estimate for information about how the default value is determined.
specifies the quantile for the LTS estimate. See the section LTS Estimate for information about how the default value is determined.
requests (IADJUST=ALL) or suppresses (IADJUST=NONE) the intercept adjustment for all estimates in the LTS algorithm. By default, the intercept adjustment is used for data sets with fewer than 10,000 observations. See the section Algorithm for details.
specifies the number of best solutions kept for each subgroup during the computation of the LTS estimate. The default number is 10, which is the maximum number allowed.
specifies the number of times to repeat least squares fit in subgroups during the computation of the LTS estimate. See the section LTS Estimate for information about how the default number is determined.
requests a display of the subgrouping information and parameter estimates within subgroups. This option generates the ODS tables shown in Table 77.5.
ODS Table Name 
Description 

BestEstimates 
Best final estimates for LTS 

BestSubEstimates 
Best estimates for each subgroup 

CStep 
Cstep information for LTS 

Groups 
Grouping information for LTS 
specifies the data set size of the subgroups in the computation of the LTS estimate. The default number is 300.
With METHOD=S, you can specify the following additional options:
specifies the type of asymptotic covariance computed for the S estimate. The four types are described in the section Asymptotic Covariance and Confidence Intervals. By default, ASYMPCOV= H4.
specifies the function for the S estimate. PROC ROBUSTREG provides two functions, Tukey’s bisquare function and Yohai’s optimal function, which you can request with CHIF=TUKEY and CHIF=YOHAI, respectively. The default is Tukey’s bisquare function.
specifies the efficiency (as a fraction) for the S estimate. The parameter in the function is determined by this efficiency. The default efficiency is determined such that the consistent S estimate has the breakdown value of . This option is overwritten by the K0= option if both of them are used.
specifies the parameter in the function of the S estimate. For CHIF=TUKEY, the default is 1.548. For CHIF=YOHAI, the default is 0.66. These default values correspond to a breakdown value of the consistent S estimate.
sets the maximum number of iterations for computing the scale parameter of the S estimate. By default, MAXITER=1000.
specifies the number of repeats of subsampling in the computation of the S estimate. See the section Algorithm for information about how the default number of repeats is determined.
suppresses the refinement for the S estimate. See the section Algorithm for details.
specifies the size of the subset for the S estimate. See the section Algorithm for information about how the default value is determined.
specifies the tolerance for the S estimate of the scale. The default value is 0.001.
With METHOD=MM, you can specify the following additional options:
specifies the type of asymptotic covariance computed for the MM estimate. The four types are described in the section Details: ROBUSTREG Procedure. By default, ASYMPCOV= H4.
requests the bias test for the final MM estimate. See the section Bias Test for details about this test.
selects the function for the MM estimate. PROC ROBUSTREG provides two functions: Tukey’s bisquare function and Yohai’s optimal function, which you can request with CHIF=TUKEY and CHIF=YOHAI, respectively. The default is Tukey’s bisquare function. This function is also used by the initial S estimate if you specify the INITEST=S option.
specifies a convergence criterion for the MM estimate. The three criteria listed in Table 77.6 are available.
Type 
Option 
Coefficient 
CONVERGENCE=COEF 
Residual 
CONVERGENCE=RESID 
Weight 
CONVERGENCE=WEIGHT 
By default, CONVERGENCE = COEF. You can specify the precision of the convergence criterion with the EPS= option. By default, EPS=1.E8.
specifies the efficiency (as a fraction) for the MM estimate. The parameter in the function is determined by this efficiency. The default efficiency is set to 0.85, which corresponds to for CHIF=TUKEY or for CHIF=YOHAI.
specifies the integer h for the initial LTS estimate used by the MM estimator. See the section Algorithm for how to specify h and how the default is determined.
specifies the initial estimator for the MM estimator. By default, the LTS estimator with its default settings is used as the initial estimator for the MM estimator.
specifies the parameter in the function for the MM estimate. For CHIF=TUKEY, the default is . For CHIF=YOHAI, the default is . These default values correspond to the breakdown value of the MM estimator.
sets the maximum number of iterations during the parameter estimation. By default, MAXITER=1,000.