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The SCORE Procedure

Example 76.1 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. The following statements produce Output 76.1.1 through Output 76.1.3:

      /* 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 76.1.1 shows the PROC FACTOR output. The scoring coefficients for the two factors are shown at the end of the PROC FACTOR output.

Output 76.1.1 Creating an OUTSTAT= Data Set with PROC FACTOR

FACTOR SCORING EXAMPLE

The FACTOR Procedure

Initial Factor Method: Principal Components

Prior Communality Estimates: ONE

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

2 factors will be retained by the MINEIGEN criterion.

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

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

FACTOR SCORING EXAMPLE

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

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

FACTOR SCORING EXAMPLE

The FACTOR Procedure

Rotation Method: Varimax

Scoring Coefficients Estimated by Regression

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 76.1.2 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.

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 .

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 76.1.3 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.

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