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The SCORE Procedure

Example 57.1: Factor Scoring Coefficients

This example shows how to use PROC SCORE with factor scoring coefficients. First, the FACTOR procedure produces an output data set containing scoring coefficients in observations identified by _TYPE_='SCORE'. These data, together with the original data set Fitness, are supplied to PROC SCORE, resulting in a data set containing scores Factor1 and Factor2. These statements produce Output 57.1.1 through Output 57.1.3: 

   /* This data set contains only the first 12 observations   */
   /* from the full data set used in the chapter on PROC REG. */
   data Fitness;
      input Age Weight Oxygen RunTime RestPulse RunPulse @@;
      datalines;
   44 89.47  44.609 11.37 62 178     40 75.07  45.313 10.07 62 185
   44 85.84  54.297  8.65 45 156     42 68.15  59.571  8.17 40 166
   38 89.02  49.874  9.22 55 178     47 77.45  44.811 11.63 58 176
   40 75.98  45.681 11.95 70 176     43 81.19  49.091 10.85 64 162
   44 81.42  39.442 13.08 63 174     38 81.87  60.055  8.63 48 170
   44 73.03  50.541 10.13 45 168     45 87.66  37.388 14.03 56 186
   ;

   proc factor data=Fitness outstat=FactOut
               method=prin rotate=varimax score;
      var Age Weight RunTime RunPulse RestPulse;
      title 'FACTOR SCORING EXAMPLE';
      run;

   proc print data=FactOut;
      title2 'Data Set from PROC FACTOR';
   run;

   proc score data=Fitness score=FactOut out=FScore;
      var Age Weight RunTime RunPulse RestPulse;
      run;

   proc print data=FScore;
      title2 'Data Set from PROC SCORE';
   run;

Output 57.1.1 shows the PROC FACTOR output. The scoring coefficients for the two factors are shown at the end of the PROC FACTOR output.

Output 57.1.1: Creating an OUTSTAT= Data Set with PROC FACTOR

FACTOR SCORING EXAMPLE

The FACTOR Procedure
Initial Factor Method: Principal Components

Eigenvalues of the Correlation Matrix: Total
= 5 Average = 1
  Eigenvalue Difference Proportion Cumulative
1 2.30930638 1.11710686 0.4619 0.4619
2 1.19219952 0.30997249 0.2384 0.7003
3 0.88222702 0.37965990 0.1764 0.8767
4 0.50256713 0.38886717 0.1005 0.9773
5 0.11369996   0.0227 1.0000

Factor Pattern
  Factor1 Factor2
Age 0.29795 0.93675
Weight 0.43282 -0.17750
RunTime 0.91983 0.28782
RunPulse 0.72671 -0.38191
RestPulse 0.81179 -0.23344

The FACTOR Procedure
Initial Factor Method: Principal Components

Variance Explained by Each
Factor
Factor1 Factor2
2.3093064 1.1921995

Final Communality Estimates: Total = 3.501506
Age Weight RunTime RunPulse RestPulse
0.96628351 0.21883401 0.92893333 0.67396207 0.71349297

 

The FACTOR Procedure
Rotation Method: Varimax

Orthogonal Transformation Matrix
  1 2
1 0.92536 0.37908
2 -0.37908 0.92536

Rotated Factor Pattern
  Factor1 Factor2
Age -0.07939 0.97979
Weight 0.46780 -0.00018
RunTime 0.74207 0.61503
RunPulse 0.81725 -0.07792
RestPulse 0.83969 0.09172


The FACTOR Procedure
Rotation Method: Varimax

Variance Explained by Each
Factor
Factor1 Factor2
2.1487753 1.3527306

Final Communality Estimates: Total = 3.501506
Age Weight RunTime RunPulse RestPulse
0.96628351 0.21883401 0.92893333 0.67396207 0.71349297

 

The FACTOR Procedure
Rotation Method: Varimax

Squared Multiple Correlations
of the Variables with Each
Factor
Factor1 Factor2
1.0000000 1.0000000

Standardized Scoring Coefficients
  Factor1 Factor2
Age -0.17846 0.77600
Weight 0.22987 -0.06672
RunTime 0.27707 0.37440
RunPulse 0.41263 -0.17714
RestPulse 0.39952 -0.04793


Output 57.1.2 lists the OUTSTAT= data set from PROC FACTOR. Note that observations 18 and 19 have _TYPE_='SCORE'. Observations 1 and 2 have _TYPE_='MEAN' and _TYPE_='STD', respectively. These four observations are used by PROC SCORE.

Output 57.1.2: OUTSTAT= Data Set from PROC FACTOR Reproduced with PROC PRINT

FACTOR SCORING EXAMPLE
Data Set from PROC FACTOR

Obs _TYPE_ _NAME_ Age Weight RunTime RunPulse RestPulse
1 MEAN   42.4167 80.5125 10.6483 172.917 55.6667
2 STD   2.8431 6.7660 1.8444 8.918 9.2769
3 N   12.0000 12.0000 12.0000 12.000 12.0000
4 CORR Age 1.0000 0.0128 0.5005 -0.095 -0.0080
5 CORR Weight 0.0128 1.0000 0.2637 0.173 0.2396
6 CORR RunTime 0.5005 0.2637 1.0000 0.556 0.6620
7 CORR RunPulse -0.0953 0.1731 0.5555 1.000 0.4853
8 CORR RestPulse -0.0080 0.2396 0.6620 0.485 1.0000
9 COMMUNAL   0.9663 0.2188 0.9289 0.674 0.7135
10 PRIORS   1.0000 1.0000 1.0000 1.000 1.0000
11 EIGENVAL   2.3093 1.1922 0.8822 0.503 0.1137
12 UNROTATE Factor1 0.2980 0.4328 0.9198 0.727 0.8118
13 UNROTATE Factor2 0.9368 -0.1775 0.2878 -0.382 -0.2334
14 TRANSFOR Factor1 0.9254 -0.3791 . . .
15 TRANSFOR Factor2 0.3791 0.9254 . . .
16 PATTERN Factor1 -0.0794 0.4678 0.7421 0.817 0.8397
17 PATTERN Factor2 0.9798 -0.0002 0.6150 -0.078 0.0917
18 SCORE Factor1 -0.1785 0.2299 0.2771 0.413 0.3995
19 SCORE Factor2 0.7760 -0.0667 0.3744 -0.177 -0.0479


Since the PROC SCORE statement does not contain the NOSTD option, the data in the Fitness data set are standardized before scoring. For each variable specified in the VAR statement, the mean and standard deviation are obtained from the FactOut data set. For each observation in the Fitness data set, the variables are then standardized. For example, for observation 1 in the Fitness data set, the variable Age is standardized to 0.5569 = [(44 - 42.4167)/2.8431].

After the data in the Fitness data set are standardized, the standardized values of the variables in the VAR statement are multiplied by the matching coefficients in the FactOut data set, and the resulting products are summed. This sum is output as a value of the new score variable.

Output 57.1.3 displays the FScore data set produced by PROC SCORE. This data set contains the variables Age, Weight, Oxygen, RunTime, RestPulse, and RunPulse from the Fitness data set. It also contains Factor1 and Factor2, the two new score variables.

Output 57.1.3: OUT= Data Set from PROC SCORE Reproduced with PROC PRINT

FACTOR SCORING EXAMPLE
Data Set from PROC SCORE

Obs Age Weight Oxygen RunTime RestPulse RunPulse Factor1 Factor2
1 44 89.47 44.609 11.37 62 178 0.82129 0.35663
2 40 75.07 45.313 10.07 62 185 0.71173 -0.99605
3 44 85.84 54.297 8.65 45 156 -1.46064 0.36508
4 42 68.15 59.571 8.17 40 166 -1.76087 -0.27657
5 38 89.02 49.874 9.22 55 178 0.55819 -1.67684
6 47 77.45 44.811 11.63 58 176 -0.00113 1.40715
7 40 75.98 45.681 11.95 70 176 0.95318 -0.48598
8 43 81.19 49.091 10.85 64 162 -0.12951 0.36724
9 44 81.42 39.442 13.08 63 174 0.66267 0.85740
10 38 81.87 60.055 8.63 48 170 -0.44496 -1.53103
11 44 73.03 50.541 10.13 45 168 -1.11832 0.55349
12 45 87.66 37.388 14.03 56 186 1.20836 1.05948

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