The DISCRIM Procedure

(View the complete code for this example.)

In this example, four more discriminant analyses of iris data are run with two quantitative variables: petal width and petal length. The following statements produce Output 36.2.1 through Output 36.2.5:

title 'Discriminant Analysis of Fisher (1936) Iris Data';
proc template;
   define statgraph scatter;
      begingraph;
         entrytitle 'Fisher (1936) Iris Data';
         layout overlayequated / equatetype=fit;
            scatterplot x=petallength y=petalwidth /
                        group=species name='iris';
            layout gridded / autoalign=(topleft);
               discretelegend 'iris' / border=false opaque=false;
            endlayout;
         endlayout;
      endgraph;
   end;
run;

proc sgrender data=sashelp.iris template=scatter;
run;

The scatter plot in Output 36.2.1 shows the joint sample distribution.

Output 36.2.1: Joint Sample Distribution of Petal Width and Petal Length in Three Species

Another data set is created for plotting, containing a grid of points suitable for contour plots. The following statements create the data set:

data plotdata;
   do PetalLength = -2 to 72 by 0.5;
      do PetalWidth= - 5 to 32 by 0.5;
         output;
      end;
   end;
run;

Three macros are defined as follows to make contour plots of density estimates, posterior probabilities, and classification results:

%let close = thresholdmin=0 thresholdmax=0 offsetmin=0 offsetmax=0;
%let close = xaxisopts=(&close) yaxisopts=(&close);

proc template;
   define statgraph contour;
      begingraph;
         layout overlayequated / equatetype=equate &close;
            contourplotparm x=petallength y=petalwidth z=z /
                            contourtype=fill nhint=30;
            scatterplot x=pl y=pw / group=species name='iris'
                        includemissinggroup=false primary=true;
            layout gridded / autoalign=(topleft);
               discretelegend 'iris' / border=false opaque=false;
            endlayout;
         endlayout;
      endgraph;
   end;
run;

%macro contden;
   data contour(keep=PetalWidth PetalLength species z pl pw);
      merge plotd(in=d) sashelp.iris(keep=PetalWidth PetalLength species
                                     rename=(PetalWidth=pw PetalLength=pl));
      if d then z = max(setosa,versicolor,virginica);
   run;

   title3 'Plot of Estimated Densities';

   proc sgrender data=contour template=contour;
   run;
%mend;

%macro contprob;
   data posterior(keep=PetalWidth PetalLength species z pl pw into);
      merge plotp(in=d) sashelp.iris(keep=PetalWidth PetalLength species
                                     rename=(PetalWidth=pw PetalLength=pl));
      if d then z = max(setosa,versicolor,virginica);
      into = 1 * (_into_ =: 'Set') + 2 * (_into_ =: 'Ver') +
             3 * (_into_ =: 'Vir');
   run;

   title3 'Plot of Posterior Probabilities ';

   proc sgrender data=posterior template=contour;
   run;
%mend;

%macro contclass;
   title3 'Plot of Classification Results';

   proc sgrender data=posterior(drop=z rename=(into=z)) template=contour;
   run;
%mend;

A normal-theory analysis (METHOD=NORMAL) assuming equal covariance matrices (POOL=YES) illustrates the linearity of the classification boundaries. These statements produce Output 36.2.2:

title2 'Using Normal Density Estimates with Equal Variance';

proc discrim data=sashelp.iris method=normal pool=yes
   testdata=plotdata testout=plotp testoutd=plotd
   short noclassify crosslisterr;
   class Species;
   var Petal:;
run;

%contden
%contprob
%contclass

A normal-theory analysis assuming unequal covariance matrices (POOL=NO) illustrates quadratic classification boundaries. These statements produce Output 36.2.3:

title2 'Using Normal Density Estimates with Unequal Variance';

proc discrim data=sashelp.iris method=normal pool=no
   testdata=plotdata testout=plotp testoutd=plotd
   short noclassify crosslisterr;
   class Species;
   var Petal:;
run;

%contden
%contprob
%contclass

A nonparametric analysis (METHOD=NPAR) follows, using normal kernels (KERNEL=NORMAL) and equal bandwidths (POOL=YES) in each class. The value of the radius parameter r that, assuming normality, minimizes an approximate mean integrated square error is 0.50 (see the section Nonparametric Methods). These statements produce Output 36.2.4:

title2 'Using Kernel Density Estimates with Equal Bandwidth';

proc discrim data=sashelp.iris method=npar kernel=normal
   r=.5 pool=yes testoutd=plotd testdata=plotdata testout=plotp
   short noclassify crosslisterr;
   class Species;
   var Petal:;
run;

%contden
%contprob
%contclass

Another nonparametric analysis is run with unequal bandwidths (POOL=NO). These statements produce Output 36.2.5:

title2 'Using Kernel Density Estimates with Unequal Bandwidth';

proc discrim data=sashelp.iris method=npar kernel=normal
   r=.5 pool=no testoutd=plotd testdata=plotdata testout=plotp
   short noclassify crosslisterr;
   class Species;
   var Petal:;
run;

%contden
%contprob
%contclass