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The VARCLUS Procedure

Getting Started: VARCLUS Procedure

This example demonstrates how you can cluster variables using the VARCLUS procedure.

The following data are job ratings of police officers. The officers were rated by their supervisors on 13 job skills on a scale from 1 to 9. There is also an overall rating that is not used in this analysis. The following DATA step creates the SAS data set JobRat:

   data JobRat;
      input
         (Communication_Skills
          Problem_Solving
          Learning_Ability
          Judgement_under_Pressure
          Observational_Skills
          Willingness_to_Confront_Problems
          Interest_in_People
          Interpersonal_Sensitivity
          Desire_for_Self_Improvement
          Appearance
          Dependability
          Physical_Ability
          Integrity
          Overall_Rating)
         (1.);
   datalines;
   26838853879867
   74758876857667
   56757863775875
   67869777988997
   
   ... more lines ...   

   99997899799799
   99899899899899
   76656399567486
   ;

The following statements cluster the variables:

   proc varclus data=JobRat maxclusters=3;
      var Communication_Skills--Integrity;
   run;

The DATA= option specifies the SAS data set JobRat as input.

The MAXCLUSTERS=3 option specifies that no more than three clusters be computed. By default, PROC VARCLUS splits and optimizes clusters until all clusters have a second eigenvalue less than one. In this example, the default setting would produce only two clusters, but going to three clusters produces a more interesting result.

The VAR statement lists the numeric variables (Communication_Skills–Integrity) to be used in the analysis. The overall rating is omitted from the list of variables.

Although the VARCLUS procedure displays output for one cluster, two clusters, and three clusters, the following figures display only the final analysis for three clusters.

For each cluster, Figure 93.1 displays the number of variables in the cluster, the cluster variation, the total explained variation, and the proportion of the total variance explained by the variables in the cluster. The variance explained by the variables in a cluster is similar to the variance explained by a factor in common factor analysis, but it includes contributions only from the variables in the cluster rather than from all variables.

The line labeled "Total variation explained" in Figure 93.1 gives the sum of the explained variation over all clusters. The final "Proportion" represents the total explained variation divided by the sum of cluster variation. This value, 0.6715, indicates that about 67% of the total variation in the data can be accounted for by the three cluster components.

Figure 93.1 Cluster Summary for Three Clusters from the VARCLUS Procedure

Oblique Principal Component Cluster Analysis

Cluster Summary for 3 Clusters
Cluster	Members	Cluster Variation	Variation Explained	Proportion Explained	Second Eigenvalue
1	6	6	3.771349	0.6286	0.7093
2	5	5	3.575933	0.7152	0.5035
3	2	2	1.382005	0.6910	0.6180

Total variation explained = 8.729286 Proportion = 0.6715

Figure 93.2 shows how the variables are clustered. Figure 93.2 also displays the R-square value of each variable with its own cluster and the R-square value with its nearest cluster. The R-square value for a variable with the nearest cluster should be low if the clusters are well separated. The last column displays the ratio of / for each variable. Small values of this ratio indicate good clustering.

Figure 93.3 displays the standardized scoring coefficients that are used to compute the first principal component of each cluster. Since each variable is assigned to one and only one cluster, each row of the scoring coefficients contains only one nonzero value.

Figure 93.4 displays the cluster structure and the intercluster correlations. The structure table displays the correlation of each variable with each cluster component. The table of intercorrelations contains the correlations between the cluster components.

The VARCLUS procedure next displays the summary table of statistics for the cluster history (Figure 93.5). The first three columns give the number of clusters, the total variation explained by clusters, and the proportion of variation explained by clusters, respectively.

As displayed in the first row of Figure 93.5, the variation explained by the first principal component of all the variables is 6.547402, and the proportion of variation explained is 0.5036.

When the number of clusters is two, the total variation explained is 7.967753, and the proportion of variation explained by the two clusters is 0.6129. The larger second eigenvalue of the clusters is 0.937902, so by default, the VARCLUS procedure would stop splitting clusters at this point. But because the MAXCLUSTERS=3 option was specified in this example, the VARCLUS procedure continues to the three-cluster solution.

When the number of clusters increases to three, the total variation explained is 8.729286, and the proportion of variation explained by the two clusters is 0.6715. The largest second eigenvalue of the clusters is 0.709323. The statistical improvement from increasing the number of clusters from two to three seems modest, but the interpretabilty of the three clusters argues for the three-cluster solution.

Figure 93.5 also displays the minimum proportion of variance explained by a cluster, the minimum R square for a variable, and the maximum () ratio for a variable. The last quantity is the maximum ratio of the value for a variable’s own cluster to the value for its nearest cluster.

Copyright © 2009 by SAS Institute Inc., Cary, NC, USA. All rights reserved.