Statistical procedures use ODS Graphics to create graphs as part of their output. ODS Graphics is described in detail in Chapter 21: Statistical Graphics Using ODS.
Before you create graphs, ODS Graphics must be enabled (for example, by specifying the ODS GRAPHICS ON statement). 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 overall appearance of graphs is controlled by ODS styles. Styles and other aspects of using ODS Graphics are discussed in the section A Primer on ODS Statistical Graphics in Chapter 21: Statistical Graphics Using ODS.
For a single quantile, two plots are particularly useful in revealing outliers and leverage points: a scatter plot of the standardized residuals for the specified quantile against the robust distances and a scatter plot of the robust distances against the classical Mahalanobis distances. You can request these two plots by using the PLOT=RDPLOT and PLOT=DDPLOT options, respectively.
You can also request a normal quantilequantile plot and a histogram of the standardized residuals for the specified quantile by using the PLOT=QQPLOT and PLOT=HISTOGRAM options, respectively.
You can request a plot of fitted conditional quantiles by the single continuous variable that is specified in the model by using the PLOT=FITPLOT option.
All these plots can be requested by specifying corresponding plot options in either the PROC QUANTREG statement or the MODEL statement. If you specify same plot options in both statements, options in the PROC QUANTREG statement override options in the MODEL statement.
You can specify the PLOT=QUANTPLOT option only in the MODEL statement to request a quantile process plot with confidence bands.
The plot options in the PROC QUANTREG statement and the MODEL statement are summarized in Table 95.9. See the PLOT= option in the PROC QUANTREG statement and the PLOT= option in the MODEL statement for details.
Table 95.9: Options for Plots
Keyword 
Plot 


ALL 
All appropriate plots 

DDPLOT 
Robust distance versus Mahalanobis distance 

FITPLOT 
Conditional quantile fit versus independent variable 

HISTOGRAM 
Histogram of standardized robust residuals 

NONE 
No plot 

QUANTPLOT 
Scatter plot of regression quantile 

QQPLOT 
QQ plot of standardized robust residuals 

RDPLOT 
Standardized robust residual versus robust distance 
The following subsections provide information about these graphs.
The QUANTREG procedure assigns a name to each graph it creates. You can use these names to refer to the graphs when you use ODS. The names along with the required statements and options are listed in Table 95.10.
Table 95.10: Graphs Produced by PROC QUANTREG
ODS Graph Name 
Plot Description 
Statement 
Option 

DDPlot 
Robust distance versus Mahalanobis distance 
PROC MODEL 
DDPLOT 
FitPlot 
Quantile fit versus independent variable 
PROC MODEL 
FITPLOT 
Histogram 
Histogram of standardized robust residuals 
PROC MODEL 
HISTOGRAM 
QQPlot 
QQ plot of standardized robust residuals 
PROC MODEL 
QQPLOT 
QuantPanel 
Panel of quantile plots with confidence limits 
MODEL 
QUANTPLOT 
QuantPlot 
Scatter plot for regression quantiles with confidence limits 
MODEL 
QUANTPLOT UNPACK 
RDPlot 
Standardized robust residual versus robust distance 
PROC MODEL 
RDPLOT 
When the model has a single independent continuous variable (with or without the intercept), the QUANTREG procedure automatically creates a plot of fitted conditional quantiles against this independent variable for one or more quantiles that are specified in the MODEL statement.
The following example reuses the trout
data set in the section Analysis of FishHabitat Relationships to show the fit plot for one or several quantiles:
ods graphics on; proc quantreg data=trout ci=resampling; model LnDensity = WDRatio / quantile=0.9 seed=1268; run;
proc quantreg data=trout ci=resampling; model LnDensity = WDRatio / quantile=0.5 0.75 0.9 seed=1268; run;
For a single quantile, the confidence limits for the fitted conditional quantiles are also plotted if you specify the CI=RESAMPLING or CI=SPARSITY option. (See Figure 95.14.) For multiple quantiles, confidence limits are not plotted by default. (See Figure 95.15.) You can add the confidence limits on the plot by specifying the option PLOT=FITPLOT(SHOWLIMITS).
The QUANTREG procedure also provides fit plots for quantile regression splines and polynomials if they are based on a single continuous variable. (See Example 95.4 and Example 95.5 for some examples.)
Figure 95.14: Fit Plot with Confidence Limits
Figure 95.15: Fit Plot for Multiple Quantiles
A quantile process plot is a scatter plot of an estimated regression parameter against a quantile. You can request this plot by specifying the PLOT=QUANTPLOT option in the MODEL statement when multiple regression quantiles are computed or when the entire quantile process is computed. Quantile process plots are often used to check model variations at different quantiles, which is usually called model heterogeneity.
By default, panels are used to hold multiple process plots (up to four in each panel). You can use the UNPACK option to request individual process plots. Figure 95.10 in the section Analysis of FishHabitat Relationships shows a panel that includes two quantile process plots. Output 95.2.9 in Example 95.2 shows a single quantile process plot. Example 95.3 demonstrates more quantile process plots and their usage.
The distancedistance plot (DDPLOT) is mainly used for leveragepoint diagnostics. It is a scatter plot of the robust distances against the classical Mahalanobis distances for the continuous independent variables. For more information about the robust distance, see the section Leverage Point and Outlier Detection. If is a classification variable is specified in the model, this plot is not created.
You can use the PLOT=DDPLOT option to request this plot. The following statements use the growth
data set in Example 95.2 to create a single plot, which is shown in Output 95.2.4 in Example 95.2:
proc quantreg data=growth ci=resampling plot=ddplot; model GDP = lgdp2 mse2 fse2 fhe2 mhe2 lexp2 lintr2 gedy2 Iy2 gcony2 lblakp2 pol2 ttrad2 / quantile=.5 diagnostics leverage(cutoff=8) seed=1268; id Country; run;
The reference lines represent the cutoff values. The diagonal line is also drawn to show the distribution of the distances. By default, all outliers and leverage points are labeled with observation numbers. To change the default, you can use the LABEL= option as described in Table 95.4.
The residualdistance plot (RDPLOT) is used for both outlier and leveragepoint diagnostics. It is a scatter plot of the standardized residuals against the robust distances. For more information about the robust distance, see the section Leverage Point and Outlier Detection. If a classification variable is specified in the model, this plot is not created.
You can use the PLOT=RDPLOT option to request this plot. The following statements use the growth
data set in Example 95.2 to create a single plot, which is shown in Output 95.2.3 in Example 95.2:
proc quantreg data=growth ci=resampling plot=rdplot; model GDP = lgdp2 mse2 fse2 fhe2 mhe2 lexp2 lintr2 gedy2 Iy2 gcony2 lblakp2 pol2 ttrad2 / quantile=.5 diagnostics leverage(cutoff=8) seed=1268; id Country; run;
The reference lines represent the cutoff values. By default, all outliers and leverage points are labeled with observation numbers. To change the default, you can use the LABEL= option as described in Table 95.4.
If you specify ID variables instead of observation numbers in the ID statement, the values of the first ID variable are used as labels.
PROC QUANTREG produces a histogram and a QQ plot for the standardized residuals. The histogram is superimposed with a normal
density curve and a kernel density curve. Using the growth
data set in Example 95.2, the following statements create the plot that is shown in Output 95.2.5 in Example 95.2:
proc quantreg data=growth ci=resampling plot=histogram; model GDP = lgdp2 mse2 fse2 fhe2 mhe2 lexp2 lintr2 gedy2 Iy2 gcony2 lblakp2 pol2 ttrad2 / quantile=.5 diagnostics leverage(cutoff=8) seed=1268; id Country; run;