The QUANTREG Procedure
MODEL Statement
<label:> MODEL response = <effects> </ options>;
You can specify main effects and interaction terms in the MODEL statement, as you can in the GLM procedure (Chapter 52, The GLM Procedure.) Classification variables in the MODEL statement must also be specified in the CLASS statement.
The optional label, which must be a valid SAS name, is used to label output from the matching MODEL statement.
Options
Table 7 summarizes the options available in the MODEL statement.
Table 7: MODEL Statement Options
| Option | Description |
|---|---|
| CORRB | Produces the estimated correlation matrix |
| COVB | Produces the estimated covariance matrix |
| CUTOFF= | Specifies the multiplier of the cutoff value for outlier detection |
| DIAGNOSTICS | Requests the outlier diagnostics |
| ITPRINT | Displays the iteration history |
| LEVERAGE | Requests an analysis of leverage points |
| NODIAG | Suppresses the computation for outlier diagnostics |
| NOINT | Specifies no-intercept regression |
| NOSUMMARY | Suppresses the computation for summary statistics |
| PLOT= | Requests plots |
| QUANTILE= | Specifies the quantile levels |
| SCALE= | Specifies the scale value used to compute the standardized residuals |
| SEED= | Specifies the seed for the random number generator |
| SINGULAR= | Specifies the tolerance for testing singularity |
You can specify the following options for the model fit.
- CORRB
produces the estimated correlation matrix of the parameter estimates. When the resampling method is used to compute the confidence intervals, the QUANTREG procedure computes the bootstrap correlation. When the sparsity method is used to compute the confidence intervals, PROC QUANTREG bases its computation of the asymptotic correlation on an estimator of the sparsity function. The rank method for confidence intervals does not provide a correlation estimate.
- COVB
produces the estimated covariance matrix of the parameter estimates. When the resampling method is used to compute the confidence intervals, the QUANTREG procedure computes the bootstrap covariance. When the sparsity method is used to compute the confidence intervals, PROC QUANTREG bases its computation of the asymptotic covariance on an estimator of the sparsity function. The rank method for confidence intervals does not provide a covariance estimate.
- CUTOFF=value
specifies the multiplier of the cutoff value for outlier detection. By default, CUTOFF=3.
- DIAGNOSTICS<(ALL)>
requests the outlier diagnostics. By default, only observations that are identified as outliers or leverage points are displayed. To request that all observations be displayed, specify the ALL option.
- ITPRINT
displays the iteration history of the interior point algorithm or the smoothing algorithm.
- LEVERAGE<(CUTOFF=value | CUTOFFALPHA=value | H=n)>
requests an analysis of leverage points for the continuous covariates. The results are added to the diagnostics table, which you can request with the DIAGNOSTICS option in the MODEL statement. You can specify the cutoff value for leverage-point detection with the CUTOFF= option. The default cutoff value is , where can be specified with the option. By default, . You can use the H= option to specify the number of points to be minimized for the MCD algorithm used for the leverage-point analysis. By default, H=, where n is the number of observations and p is the number of independent variables. The LEVERAGE option is ignored if the model includes classification variables as covariates.
- NODIAG
suppresses the computation for outlier diagnostics. If you specify the NODIAG option, the diagnostics summary table is not provided.
- NOINT
- NOSUMMARY
suppresses the computation of summary statistics. If you specify the NOSUMMARY option, the summary statistics table is not provided.
-
PLOT=plot-option
PLOTS=(plot-option) You can use the PLOTS= option in the MODEL statement together with ODS Graphics to request the quantile process plot in addition to all that plots that you request in the PLOT= option in the PROC QUANTREG statement.
You can specify the following plot-option in the MODEL statement:
- QUANTPLOT<(EFFECTS) </ <NOLIMITS> <EXTENDCI> <UNPACK> <OLS> > >
plots the regression quantile process. The estimated coefficient of each specified covariate effect is plotted as a function of the quantile. If you do not specify a covariate effect, quantile processes are plotted for all covariate effects in the MODEL statement. You can use the NOLIMITS option to suppress confidence bands for the quantile processes. By default, confidence bands are plotted, and process plots are displayed in panels, each of which can hold up to four plots. By default, the confidence limits are plotted for quantiles in the range between 0.05 and 0.95. You can use the EXTENDCI option to plot the confidence limits even for quantiles outside this range. You can use the UNPACK option to create individual process plots. For an individual process plot, you can superimpose the ordinary least squares estimate by specifying the OLS option.
ODS Graphics must be enabled before you request plots.
For more information about enabling and disabling ODS Graphics, see the section Enabling and Disabling ODS Graphics in Chapter 23, Statistical Graphics Using ODS.
-
QUANTILE=number-list | PROCESS | FQPR<(suboption)>
QUANTLEV=number-list | PROCESS | FQPR<(suboption)> specifies the quantile levels for the quantile regression. A valid quantile level must be a number in the range of (0,1). You can specify the following values for the QUANTILE= option:
- number-list
computes quantile regression for quantile levels that are specified in the number-list.
- PROCESS
computes the entire quantile process regression. If you specify QUANTILE=PROCESS, the value of the ALGORITHM= option in the PROC QUANTREG statement must be SIMPLEX either by default or by specifying it.
The QUANTILE=PROCESS option produces the quantile process estimates table and the quantile process objective function table. The size of these two tables are proportional to the number of the training observations and can be large for a large training data set. You can suppress displaying these two tables by specifying the following ODS EXCLUDE statement:
ods exclude ProcessEst ProcessObj;In addition, you can output these tables to data sets for further processing by specifying the following ODS OUTPUT statement:
ods output ProcessEst=PE ProcessObj=PO;- FQPR<(suboption)>
uses a fast quantile process regression method to approximate quantile process regression on a grid of n equally spaced quantile levels. If you specify QUANTILE=FQPR, the value of the ALGORITHM= option in the PROC QUANTREG statement must be IPM. For more details about the fast quantile process regression method, see the section Fast Quantile Process Regression. You can specify the following suboptions for the FQPR option:
- N=n
specifies the number n of equally spaced quantile levels at which to fit the quantile process regression.
-
OBSRATIO=value
OR=value specifies the number of equally spaced quantile levels as its ratio to the total number of training observations. For example, if the number of training observations is 1,000 and you specify the OR=0.2 suboption, a quantile process regression model is fit for equally spaced quantile levels. The FQPR option ignores the OR= suboption if a valid N= suboption is specified.
- L=value
specifies the starting quantile level of the quantile-level grid. By default, L= if U is not specified, otherwise L=U.
- U=value
specifies the ending quantile level of the quantile-level grid. U= if L is not specified, otherwise U=L.
If you specify neither the N=n nor the OR=value suboption, the FQPR option determines the number of quantile levels as the lesser of 100 and half the number of the training observations.
Unlike the QUANTILE=PROCESS option, the QUANTILE=FQPR option does not display the quantile process estimates table and the quantile process objective function table. Instead the QUANTILE=FQPR option produces the average parameter estimates table and the average objective function table for the specified quantile-level grid. However, you can output the two quantile process tables to data sets by specifying the following ODS OUTPUT statement:
ods output ProcessEst=PE ProcessObj=PO;
By default, QUANTILE=0.5, which fits a median regression.
- SCALE=number
specifies the scale value to use to compute the standardized residuals. By default, the scale is computed as the corrected median of absolute residuals. See the section Leverage Point and Outlier Detection for details.
- SEED=number
specifies the seed for the random number generator used to compute the MCMB confidence intervals. This seed is also used to randomly select the subgroups for preprocessing when you specify the PP option in the PROC QUANTREG statement. If you do not specify a seed, or if you specify a value less than or equal to 0, the seed is generated from reading the time of day from the computer clock.
By default or if you specify SEED=0, the QUANTREG procedure generates a seed between one and one billion.
- SINGULAR=value
sets the tolerance for testing singularity of the information matrix and the crossproducts matrix for the initial least squares estimates. Approximately, the test requires that a pivot be at least this value times the original diagonal value. By default, SINGULAR=1E–12.