Getting Started


The following example uses the PRINCOMP procedure to analyze job performance. Police officers were rated by their supervisors in 14 categories as part of standard police departmental administrative procedure.

The following statements create the Jobratings data set:

  options validvarname=any;   data Jobratings;   input ('Communication Skills'n   'Problem Solving'n   'Learning Ability'n   'Judgment Under Pressure'n   'Observational Skills'n   'Willingness to Confront Problems'n   'Interest in People'n   'Interpersonal Sensitivity'n   'Desire for Self-Improvement'n   'Appearance'n   'Dependability'n   'Physical Ability'n   'Integrity'n   'Overall Rating'n) (1.);   datalines;   26838853879867   74758876857667   56757863775875   67869777988997   . . .   99899899899899   76656399567486   ;  

The data set Jobratings contains 14 variables . Each variable contains the job ratings using a scale measurement from 1 to 10 (1=fail to comply , 10=exceptional). The last variable Overall Rating contains a score as an overall index on how each officer performs .

The following statement requests a principal component analysis on the Jobratings data set and outputs the scores to the Scores data set (OUT= Scores ). Note that variable Overall Rating is excluded from the analysis.

  proc princomp data=Jobratings(drop='Overall Rating'n) out=scores;   run;  

Figure 58.1 to Figure 58.3 display the PROC PRINCOMP output, beginning with simple statistics followed by the correlation matrix. The PROC PRINCOMP statement requests by default principal components computed from the correlation matrix, so the total variance is equal to the number of variables, 13. In this example, it would also be reasonable to use the COV option, which would cause variables with a high variance (such as Dependability )tohavemoreinfluence on the results than variables with a low variance (such as Learning Ability ). If you used the COV option, scores would be computed from centered rather than standardized variables.

start figure
  The PRINCOMP Procedure   Observations         103   Variables             13   Simple Statistics   Judgment   Communication       Problem      Learning         Under  Observational   Skills       Solving       Ability      Pressure         Skills   Mean    6.650485437   6.631067961   6.990291262   6.737864078    6.932038835   StD     1.764068036   1.590352602   1.339411238   1.731830976    1.761584269   Simple Statistics   Willingness   to Confront      Interest  Interpersonal       Desire for   Problems     in People    Sensitivity Self-Improvement     Appearance   Mean   7.291262136   6.708737864    6.621359223       6.572815534   7.000000000   StD    1.525155524   1.892353385    1.760773587       1.729796212   1.798692335   Simple Statistics   Physical   Dependability           Ability         Integrity   Mean    6.825242718       7.203883495       7.213592233   StD     1.917040123       1.555251845       1.845240223  
end figure

Figure 58.1: Number of Observations and Simple Statistics from the PRINCOMP Procedure
start figure
  The PRINCOMP Procedure   Correlation Matrix   Judgment   Communication   Problem   Learning      Under   Skills   Solving    Ability   Pressure   Communication Skills                     1.0000    0.6280     0.5546     0.5538   Problem Solving                          0.6280    1.0000     0.5690     0.6195   Learning Ability                         0.5546    0.5690     1.0000     0.4892   Judgment Under Pressure                  0.5538    0.6195     0.4892     1.0000   Observational Skills                     0.5381    0.4284     0.6230     0.3733   Willingness to Confront Problems         0.5265    0.5015     0.5245     0.4004   Interest in People                       0.4391    0.3972     0.2735     0.6226   Interpersonal Sensitivity                0.5030    0.4398     0.1855     0.6134   Desire for Self-Improvement              0.5642    0.4090     0.5737     0.4826   Appearance                               0.4913    0.3873     0.3988     0.2266   Dependability                            0.5471    0.4546     0.5110     0.5471   Physical Ability                         0.2192    0.3201     0.2269     0.3476   Integrity                                0.5081    0.3846     0.3142     0.5883   Correlation Matrix   Willingness     Interest   Observational     to Confront           in   Skills        Problems       People   Communication Skills                     0.5381          0.5265       0.4391   Problem Solving                          0.4284          0.5015       0.3972   Learning Ability                         0.6230          0.5245       0.2735   Judgment Under Pressure                  0.3733          0.4004       0.6226   Observational Skills                     1.0000          0.7300       0.2616   Willingness to Confront Problems         0.7300          1.0000       0.2233   Interest in People                       0.2616          0.2233       1.0000   Interpersonal Sensitivity                0.1655          0.1291       0.8051   Desire for Self-Improvement              0.5985          0.5307       0.4857   Appearance                               0.4177          0.4825       0.2679   Dependability                            0.5626          0.4870       0.6074   Physical Ability                         0.4274          0.4872       0.3768   Integrity                                0.3906          0.3260       0.7452  
end figure

Figure 58.2: Correlation Matrix from the PRINCOMP Procedure
start figure
  Correlation Matrix   Interpersonal         Desire for   Sensitivity   Self-Improvement   Appearance   Communication Skills                     0.5030             0.5642       0.4913   Problem Solving                          0.4398             0.4090       0.3873   Learning Ability                         0.1855             0.5737       0.3988   Judgment Under Pressure                  0.6134             0.4826       0.2266   Observational Skills                     0.1655             0.5985       0.4177   Willingness to Confront Problems         0.1291             0.5307       0.4825   Interest in People                       0.8051             0.4857       0.2679   Interpersonal Sensitivity                1.0000             0.3713       0.2600   Desire for Self-Improvement              0.3713             1.0000       0.4474   Appearance                               0.2600             0.4474       1.0000   Dependability                            0.5408             0.5981       0.5089   Physical Ability                         0.2182             0.3752       0.3820   Integrity                                0.6920             0.5664       0.4135   Correlation Matrix   Physical   Dependability       Ability      Integrity   Communication Skills                     0.5471        0.2192         0.5081   Problem Solving                          0.4546        0.3201         0.3846   Learning Ability                         0.5110        0.2269         0.3142   Judgment Under Pressure                  0.5471        0.3476         0.5883   Observational Skills                     0.5626        0.4274         0.3906   Willingness to Confront Problems         0.4870        0.4872         0.3260   Interest in People                       0.6074        0.3768         0.7452   Interpersonal Sensitivity                0.5408        0.2182         0.6920   Desire for Self-Improvement              0.5981        0.3752         0.5664   Appearance                               0.5089        0.3820         0.4135   Dependability                            1.0000        0.4461         0.6536   Physical Ability                         0.4461        1.0000         0.3810   Integrity                                0.6536        0.3810         1.0000  
end figure

Figure 58.3: Correlation Matrix from the PRINCOMP Procedure

Figure 58.4 displays the eigenvalues. The first principal component explains about 50% of the total variance, the second principal component explains about 13.6%, and the third principal component explains about 7.7%. Note that the eigenvalues sum to the total variance. The eigenvalues indicate that three to five components provide a good summary of the data, with three components accounting for about 71.7% of the total variance and five components explaining about 82.7%. Subsequent components contribute less than 5% each.

start figure
  The PRINCOMP Procedure   Eigenvalues of the Correlation Matrix   Eigenvalue    Difference    Proportion    Cumulative   1   6.54740242    4.77468744        0.5036        0.5036   2   1.77271499    0.76747933        0.1364        0.6400   3   1.00523565    0.26209665        0.0773        0.7173   4   0.74313901    0.06479499        0.0572        0.7745   5   0.67834402    0.22696368        0.0522        0.8267   6   0.45138034    0.06922167        0.0347        0.8614   7   0.38215866    0.08432613        0.0294        0.8908   8   0.29783254    0.02340663        0.0229        0.9137   9   0.27442591    0.01208809        0.0211        0.9348   10   0.26233782    0.01778332        0.0202        0.9550   11   0.24455450    0.04677622        0.0188        0.9738   12   0.19777828    0.05508241        0.0152        0.9890   13   0.14269586                      0.0110        1.0000  
end figure

Figure 58.4: Eigenvalues from the PRINCOMP Procedure

Figure 58.5 and Figure 58.6 display the eigenvectors. From the eigenvectors matrix, you can represent the first principal component Prin1 as a linear combination of the original variables

start figure
  The PRINCOMP Procedure   Eigenvectors   Prin1       Prin2       Prin3       Prin4   Communication Skills                0.303548    0.052039   .329181   .227039   Problem Solving                     0.278034    0.057046   .400112    0.300476   Learning Ability                    0.266521    0.288152   .354591   .020735   Judgment Under Pressure             0.294376   .199458   .255164    0.397306   Observational Skills                0.276641    0.366979    0.065959    0.035711   Willingness to Confront Problems    0.267580    0.392989    0.098723    0.184409   Interest in People                  0.278060   .432916    0.118113    0.046047   Interpersonal Sensitivity           0.253814   .495662   .064547   .060000   Desire for Self-Improvement         0.299833    0.099077    0.061097   .211279   Appearance                          0.237358    0.190065    0.248353   .544587   Dependability                       0.319480   .049742    0.169476   .156070   Physical Ability                    0.213868    0.097499    0.614959    0.514519   Integrity                           0.298246   .301812    0.190222   .169062   Eigenvectors   Prin5       Prin6       Prin7       Prin8   Communication Skills                0.181087   .416563    0.143543    0.333846   Problem Solving                     0.453604    0.096750    0.048904    0.199259   Learning Ability   .219329    0.578388   .114808    0.064088   Judgment Under Pressure   .030188    0.102087    0.068204   .591822   Observational Skills   .325257   .301254   .297894    0.163484   Willingness to Confront Problems    0.038278   .458585   .044796   .365684   Interest in People   .111279    0.030870   .011105    0.154829   Interpersonal Sensitivity           0.107807   .170305   .088194    0.192725   Desire for Self-Improvement   .427477    0.105369    0.689011    0.087453   Appearance                          0.568044    0.221643    0.049267   .257497   Dependability   .130575    0.202301   .594850    0.081242   Physical Ability                    0.203995    0.173168    0.169247    0.302536   Integrity   .130757   .100039    0.029456   .317545  
end figure

Figure 58.5: Eigenvectors from the PRINCOMP Procedure
start figure
  Eigenvectors   Prin9      Prin10      Prin11      Prin12   Communication Skills   .430955    0.375983    0.028370   .252778   Problem Solving                     0.256098   .372914   .434417    0.069863   Learning Ability                    0.224706    0.287031    0.210540   .284355   Judgment Under Pressure   .358618    0.178270    0.118318    0.306490   Observational Skills                0.258377    0.223793   .079692    0.565290   Willingness to Confront Problems    0.129976   .330710    0.275249   .386151   Interest in People                  0.321200   .081470    0.393841   .210915   Interpersonal Sensitivity           0.137468   .074821    0.285447    0.276824   Desire for Self-Improvement   .121474   .363854   .052085    0.151436   Appearance                           0.087395    0.061890    0.168369    0.236655   Dependability   .495598   .377561   .164909   .090904   Physical Ability   .149625    0.258321   .006202   .055828   Integrity                           0.271060    0.297010   .612497   .276273   Eigenvectors   Prin13   Communication Skills   .122809   Problem Solving   .116642   Learning Ability                    0.248555   Judgment Under Pressure   .126636   Observational Skills   .168555   Willingness to Confront Problems    0.177688   Interest in People   .610215   Interpersonal Sensitivity           0.643410   Desire for Self-Improvement         0.053834   Appearance   .113705   Dependability   .018094   Physical Ability                    0.133430   Integrity                           0.114965  
end figure

Figure 58.6: Eigenvectors from the PRINCOMP Procedure
  • Prin1 =0 . 303548 — ( Communication Skills )

    • +0 . 278034 — ( Problem Solving )

    • +0 . 266521 — ( Learning Ability )

    • .

    • .

    • .

    • +0 . 298246 — ( Integrity )

and, similarly, the second principal component Prin2 is

  • Prin2 =0 . 052039 — ( Communication Skills )

    • +0 . 057046 — ( Problem Solving )

    • +0 . 288152 — ( Learning Ability )

    • .

    • .

    • .

    • ˆ’ . 301812 — ( Integrity )

where the variables are standardized.

The first component reflects overall performance since the first eigenvector shows approximately equal loadings on all variables. The second eigenvector has high positive loadings on the variables Observational Skills and Willingness to Confront Problems but even higher negative loadings on the variables Interest in People and Interpersonal Sensitivity. This component seems to reflect the ability to take action, but it also reflects a lack of interpersonal skills. The third eigenvector has a very high positive loading on the variable Physical Ability and high negative loadings on the variables Problem Solving and Learning Ability. This component seems to reflect physical strength, but also shows poor learning and problem-solving skills.

In short, the three components represent:

First Component: overall performance

Second Component: smart, tough, and introverted

Third Component: superior strength and average intellect




SAS.STAT 9.1 Users Guide (Vol. 5)
SAS.STAT 9.1 Users Guide (Vol. 5)
ISBN: N/A
EAN: N/A
Year: 2004
Pages: 98

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