The LOESS Procedure

PROC LOESS Statement

Global Plot Options
Specific Plot Options

PROC LOESS <options> ;

The PROC LOESS statement invokes the LOESS procedure. The PROC LOESS statement is required. You can specify the following options in the PROC LOESS statement:

DATA=SAS-data-set

names the SAS data set to be used by PROC LOESS. If the DATA= option is not specified, PROC LOESS uses the most recently created SAS data set.

PLOTS <(global-plot-options)> <= plot-request <(options)>> PLOTS <(global-plot-options)> <= (plot-request <(options)> <... plot-request <(options)>>)>

controls the plots produced through ODS Graphics. When you specify only one plot request, you can omit the parentheses around the plot request. Here are some examples:

plots=none
plots=residuals(smooth)
plots(unpack)=diagnostics
plots(only)=(fit residualHistogram)

ODS Graphics must be enabled before plots can be requested. For example:

ods graphics on; 

proc loess;
   model y = x;
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.

If ODS Graphics is enabled but you but do not specify the PLOTS= option, then PROC LOESS produces a default set of plots. The following table lists the default set of plots produced.

Table 53.1: Default Graphs Produced

Plot	Conditional On
ContourFitPanel	SMOOTH= option specified in the MODEL statement
ContourFit	Model with two regressors
CriterionPlot	Smoothing parameter selection performed
DiagnosticsPanel	Unconditional
ResidualsBySmooth	SMOOTH= option specified in the MODEL statement
ResidualPanel	Unconditional
FitPanel	SMOOTH= option specified in the MODEL statement
FitPlot	Model with one regressor
ScorePlot	One or more SCORE statements and a model with one regressor

For models with multiple dependent variables, separate plots are produced for each dependent variable. For models where multiple smoothing parameters are requested with the SMOOTH= option in the MODEL statement and smoothing parameter value selection is not requested, separate plots are produced for each smoothing parameter. If smoothing parameter value selection is requested with the SELECT= option in the MODEL statement, then the plots are produced for the selected model only. However, if you specify the STEPS suboption of the SELECT= option, then plots are produced for all smoothing parameters examined in the selection process.

The global-plot-options apply to all relevant plots generated by the LOESS procedure, unless they are overridden with a specific-plot-option. The global-plot-options supported by the LOESS procedure follow.

Global Plot Options

MAXPOINTS=NONE | number: specifies that plots with elements that require processing more than number points are suppressed. The default is MAXPOINTS=5000. This cutoff is ignored if you specify MAXPOINTS=NONE.
ONLY: suppresses the default plots. Only the plots specifically requested are produced.
UNPACK: suppresses paneling. By default, multiple plots can appear in some output panels. Specify UNPACK to get each plot individually. You can specify PLOTS(UNPACK) to unpack the default plots. You can also specify UNPACK as a suboption with CONTOURFITPANEL, DIAGNOSTICS, FITPANEL, RESIDUALS and RESIDUALSBYSMOOTH.

Specific Plot Options

The following listing describes the specific plots and their options.

ALL

requests that all plots appropriate for the particular analysis be produced. You can specify other options with ALL; for example, to request all plots and unpack only the residuals, specify PLOTS=(ALL RESIDUALS(UNPACK)).

CONTOURFIT <(contour-options)>

produces a contour plot of the fitted surface overlaid with a scatter plot of the data for models with two regressors. Contour plots are not produced if you specify the DIRECT option in the MODEL statement. You can use the following contour-options to control how the observations are displayed:

OBS=GRADIENT: specifies that observations be displayed as circles colored by the observed response. The same color gradient is used to display the fitted surface and the observations. Observations where the predicted response is close to the observed response have similar colors—the greater the contrast between the color of an observation and the surface, the larger the residual is at that point. OBS=GRADIENT is the default if you do not specify any contour-options.
OBS=NONE: suppresses the observations.
OBS=OUTLINE: specifies that observations be displayed as circles with a border but with a completely transparent fill.
OBS=OUTLINEGRADIENT: is the same as OBS=GRADIENT except that a border is shown around each observation. This option is useful to identify the location of observations where the residuals are small, because at these points the color of the observations and the color of the surface are indistinguishable.

CONTOURFITPANEL <(<UNPACK> <contour-options> )>

produces panels of contour plots overlaid with a scatter plot of the data for each smoothing parameter specified in the SMOOTH= option in the MODEL statement, for models with two regressors. This plot is not produced if you specify the DIRECT option in the MODEL statement. If you do not specify the SMOOTH= option or if the model does not have two regressors, then this plot is not produced. If you specify the SELECT= option in addition to the SMOOTH= option in the MODEL statement, then you need to additionally specify the STEPS suboption of the SELECT= option to obtain this plot. Note that each panel contains at most six plots, and multiple panels are used in the case that there are more than six smoothing parameters in the SMOOTH= option in the MODEL statement. See the CONTOURFIT option for a description of the individual plots in this panel. The UNPACK option suppresses paneling, and the contour-options are the same as for the CONTOURFIT option.

CRITERIONPLOT | CRITERION

displays a scatter plot of the value of the SELECTION= criterion versus the smoothing parameter value for all smoothing parameter values examined in the selection process. This plot is not produced if smoothing parameter selection is not done.

DIAGNOSTICSPANEL | DIAGNOSTICS <(UNPACK)>

produces a summary panel of fit diagnostics consisting of the following:

residuals versus the predicted values
histogram of the residuals
normal quantile plot of the residuals
a “Residual-Fit” (or RF) plot consisting of side-by-side quantile plots of the centered fit and the residuals.
dependent variable values versus the predicted values

You can request the five plots in this panel as individual plots by specifying the UNPACK option. You can also request individual plots in the panel by name without having to unpack the panel. Note that the fit diagnostics panel is produced by default whenever ODS Graphics is enabled.

FITPANEL <(UNPACK)>

produces panels of plots showing the fitted LOESS curve overlaid on a scatter plot of the input data for each smoothing parameter specified in the SMOOTH= option in the MODEL statement. If you do not specify the SMOOTH= option or the model has more than one regressor, then this plot is not produced. If you specify the SELECT= option in addition to the SMOOTH= option in the MODEL statement, then you need to additionally specify the STEPS suboption of the SELECT= option to obtain this plot. Note that each panel contains at most six plots, and multiple panels are used in the case that there are more than six smoothing parameters in the SMOOTH= option in the MODEL statement. If the CLM option is specified in the MODEL statement, then a confidence band at the significance level specified in the ALPHA= option is included in each plot in the panels. If you specify the UNPACK option, then all fit panels are unpacked.

FITPLOT | FIT

produces a scatter plot of the input data with the fitted LOESS curve overlaid for models with a single regressor. If the CLM option is specified in the MODEL statement, then a confidence band at the significance level specified in the ALPHA= option is included in the plot.

NONE

suppresses all plots.

OBSERVEDBYPREDICTED

produces a scatter plot of the dependent variable values by the predicted values.

QQPLOT | QQ

produces a normal quantile plot of the residuals.

RESIDUALSBYSMOOTH <(<UNPACK> <SMOOTH> )>

produces for each regressor panels of plots showing the residuals of the LOESS fit versus the regressor for each smoothing parameter specified in the SMOOTH= option in the MODEL statement. If you do not specify the SMOOTH= option, then this plot is not produced. If you specify the SELECT= option in addition to the SMOOTH= option in the MODEL statement, then you need to additionally specify the STEPS suboption of the SELECT= option to obtain this plot. Note that each panel contains at most six plots, and multiple panels are used in the case that there are more than six smoothing parameters in the SMOOTH= option in the MODEL statement. If you specify the UNPACK option, then all RESIDUALSBYSMOOTH panels are unpacked.

The SMOOTH option requests that a nonparametric fit line be shown in each plot in the panel. The type of nonparametric fit and the options used are controlled by the template that underlies this plot. In the standard template that is provided, the nonparametric smooth is specified to be a loess fit corresponding to the default options of PROC LOESS, except that the PRESEARCH suboption is always used. It is important to note that the loess fit that is shown in each of the residual plots is computed independently of the loess fit that is used to obtain the residuals.

RESIDUALBYPREDICTED

produces a scatter plot of the residuals by the predicted values.

RESIDUALHISTOGRAM

produces a histogram of the residuals.

RESIDUALPANEL | RESIDUALS <(residual-options )>

produces panels of the residuals versus the regressors in the model. Note that each panel contains at most six plots, and multiple panels are used when there are more than six regressors in the model.

The following residual-options are available:

SMOOTH: requests that a nonparametric fit line be shown in each plot in the panel. The type of nonparametric fit and the options used are controlled by the template that underlies this plot. In the standard template that is provided, the nonparametric smooth is specified to be a loess fit corresponding to the default options of PROC LOESS, except that the PRESEARCH suboption is always used. It is important to note that the loess fit that is shown in each of the residual plots is computed independently of the loess fit that is used to obtain the residuals.
UNPACK: suppresses paneling.

RFPLOT | RF

produces a “Residual-Fit” (or RF) plot consisting of side-by-side quantile plots of the centered fit and the residuals. This plot “shows how much variation in the data is explained by the fit and how much remains in the residuals” (Cleveland, 1993).

SCOREPLOT | SCORE

produces a scatter plot of the scored values at the score points for each SCORE statement. SCORE plots are not produced for models with more than one regressor. If the CLM option is specified in the MODEL statement, then confidence bars at the significance level specified in the ALPHA= option are shown at score data points.