The KDE Procedure |
ODS Graphics |
This section describes the use of ODS for creating graphics with the KDE procedure. To request these graphs, you must specify the ODS GRAPHICS statement in addition to the following options. For more information about the ODS GRAPHICS statement, see Chapter 21, Statistical Graphics Using ODS.
You can specify the PLOTS= option in the BIVAR statement to request graphical displays of bivariate kernel density estimates.
requests one or more plots of the bivariate kernel density estimate. The following table shows the available plot options.
Option |
Description |
ALL |
all available displays |
CONTOUR |
contour plot of bivariate density estimate |
CONTOURSCATTER |
contour plot of bivariate density estimate overlaid with scatter plot of data |
HISTOGRAM |
bivariate histogram of data |
HISTSURFACE |
bivariate histogram overlaid with bivariate kernel density estimate |
NONE |
suppresses all plots |
SCATTER |
scatter plot of data |
SURFACE |
surface plot of bivariate kernel density estimate |
By default, if you enable ODS Graphics and you do not specify the PLOTS= option, then the BIVAR statement creates a contour plot. If you specify the PLOTS= option, you get only the requested plots.
You can specify the PLOTS= option in the UNIVAR statement to request graphical displays of univariate kernel density estimates.
requests one or more plots of the univariate kernel density estimate. The following table shows the available plot options.
Option |
Description |
ALL |
all available displays |
DENSITY |
univariate kernel density estimate curve |
DENSITYOVERLAY |
overlaid univariate kernel density estimate curves |
HISTDENSITY |
univariate histogram of data overlaid with kernel density estimate curve |
HISTOGRAM |
univariate histogram of data |
NONE |
suppresses all plots |
By default, if you enable ODS Graphics and you do not specify the PLOTS= option, then the UNIVAR statement creates a histogram overlaid with a kernel density estimate. If you specify the PLOTS= option, you get only the requested plots.
PROC KDE assigns a name to each graph it creates using the Output Delivery System (ODS). You can use these names to reference the graphs when using ODS. The names are listed in Table 45.2.
To request these graphs you must specify the ODS GRAPHICS statement in addition to the options indicated in Table 45.2. For more information about the ODS GRAPHICS statement, see Chapter 21, Statistical Graphics Using ODS.
ODS Graph Name |
Plot Description |
Statement |
PLOTS= Option |
---|---|---|---|
BivariateHistogram |
Bivariate histogram of data |
BIVAR |
HISTOGRAM |
ContourPlot |
Contour plot of bivariate kernel density estimate |
BIVAR |
CONTOUR |
ContourScatterPlot |
Contour plot of bivariate kernel density estimate overlaid with scatter plot |
BIVAR |
CONTOURSCATTER |
DensityPlot |
Univariate kernel density estimate curve |
UNIVAR |
DENSITY |
DensityOverlayPlot |
Overlaid univariate kernel density estimate curves |
UNIVAR |
DENSITYOVERLAY |
HistogramDensity |
Univariate histogram overlaid with kernel density estimate curve |
UNIVAR |
HISTDENSITY |
Histogram |
Univariate histogram of data |
UNIVAR |
HISTOGRAM |
HistogramSurface |
Bivariate histogram overlaid with surface plot of bivariate kernel density estimate |
BIVAR |
HISTSURFACE |
ScatterPlot |
Scatter plot of data |
BIVAR |
SCATTER |
SurfacePlot |
Surface plot of bivariate kernel density estimate |
BIVAR |
SURFACE |
Let , be a sample of size drawn from a bivariate distribution. For the marginal distribution of , the number of bins () in the bivariate histogram is calculated according to the formula
where denotes the smallest integer greater than or equal to ,
and the optimal bin width is obtained, following Scott (1992, p. 84), as
Here, and are the sample variance and the sample correlation coefficient, respectively. When you specify a WEIGHT variable, PROC KDE uses weighted versions of and in the preceding expressions.
Similar formulas are used to compute the number of bins for the marginal distribution of . Further details can be found in Scott (1992).
Notice that if , then is calculated as in the univariate case (see Terrell and Scott; 1985). In this case .
Copyright © SAS Institute, Inc. All Rights Reserved.