Factor Scores
Getting Proper Factor Scores
Using the "Factor Scores" window will allow
you to get proper factor scores for what every
factoring you choose:
• Extraction procedure
• # factors
• rotation
You can also get the "factor score coefficient
matrix -- the weights used to compute the
factor scores
Component Score Coefficient Matrix
1
physical aggression
property damage
theft
extreme verbal abuse
sad
anxious
self-confidence
compliance
.341
.385
.382
.179
-.153
-.063
.061
-.012
Component
2
.053
-.075
-.189
.267
.453
.463
.111
.029
Extraction Method: Principal Component Analysis.
Rotation Method: Varimax with Kaiser Normalization.
Component Scores.
3
.037
-.042
.050
.048
.016
.094
.589
.523
Some have proposed using this matrix as
the basis for interpretation -- since it is the
set of weights used to compute the factor
scores.
Remember, though, that these are βs -they tell the unique contribution of each
variable to the factor score. So, a set of
strongly collinear variables that are highly
correlated with the factor (as shown in the
structure matrix) are likely to have very
low weights in this matrix…
Getting Improper Factor Scores
Improper factor scores can be computed from either raw or Z-score variables. When which?
•
Z-scores are useful when the variables have different means and/or standard deviations.
• Otherwise the score will be dominated by the variables with the largest values
• Imagine forming a composite variable from GRE and GPA scores -- the GPA (M=3.5, S=1) will "get lost"
when combined with the GRE (M=500, S=100)
•
Raw scores "work better" when the variables being combined have similar means and stds
• Individual items -- works best with the same response scale à combining 5-choice and binary items can
lead to "domination" by the multi-response variable
• Set of scores that are "scaled" to the same mean and std
• MMPI scores are all scaled to population values of M=50 and S=10
• GRE Q, A & V are all scaled to M=500 and S = 100
Analyze à Descriptive Statistics à Descriptives
Remember that some of these variables are
frequency-of-occurrence counts (which differ
considerably in likelihood) and others are
ratings.
Notice the variability in means and stds
below.
So, converting to Z-scores is a good idea…
Descriptive Statistics
physical aggression
property damage
theft
extreme verbal abuse
sad
anxious
self-confidence
compliance
Minimum
.00
.00
.00
.00
Maximum
12.00
6.00
4.00
14.00
Mean
1.3617
.7447
.4681
2.9574
Std. Deviation
2.59954
1.49591
1.01833
3.75880
.00
.00
3.00
5.00
6.00
7.00
32.00
32.00
.9574
1.3404
25.6596
24.9787
1.54579
2.09841
5.98286
6.28832
Correlations
Proper varimax
factors
REGR factor score
1 for analysis 1
Pearson Correlation
REGR factor score
2 for analysis 1
Pearson Correlation
Sig. (2-tailed)
N
REGR factor score
3 for analysis 1
Pearson Correlation
Sig. (2-tailed)
Sig. (2-tailed)
N
REGR factor
score 1 for
analysis 1
1
.
REGR factor
score 2 for
analysis 1
.000
1.000
REGR factor
score 3 for
analysis 1
.000
1.000
47
.000
47
1
47
.000
1.000
47
.000
.
47
.000
1.000
47
1
.000
47
-.103
.606
47
-.034
1.000
1.000
.
.490
.821
47
47
47
47
47
N
Proper direct
oblimin factors
(delta = 0)
2 & 3 "flip"
REGR factor score
1 for analysis 2
REGR factor score
2 for analysis 2
REGR factor score
3 for analysis 2
F1
F2
Improper
factors
F3
REGR factor
score 1 for
analysis 2
.091
.542
47
.990**
REGR factor
REGR factor
score 2 for
score 3 for
analysis 2
analysis 2
.996**
-.052
.000
.731
47
.077
47
-.132
.378
47
.990**
F1
.955**
.000
47
.276
F2
.237
.108
47
.953**
.061
47
-.081
.000
47
-.126
.000
.588
.398
47
47
47
F3
-.072
.630
47
-.129
.389
47
.987**
.000
47
Pearson Correlation
Sig. (2-tailed)
.091
.542
.990**
.000
-.103
.490
1
.
.171
.251
-.237
.108
.369*
.011
.979**
.000
-.236
.110
N
Pearson Correlation
47
.996**
.000
47
.077
.606
47
-.034
.821
47
.171
.251
47
1
.
47
-.095
.524
47
.976**
.000
47
.314*
.031
47
-.115
.440
47
-.237
.108
47
-.095
.524
47
1
.
47
-.166
.265
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
47
-.052
.731
47
-.132
.378
47
.990**
.000
47
.955**
47
.276
47
-.081
47
.369*
47
.976**
47
-.166
47
1
.000
47
.237
.061
47
.953**
.588
47
-.126
.011
47
.979**
.000
47
.314*
.265
47
-.263
.
47
.506**
.108
47
.000
47
.000
47
.031
47
.075
47
-.072
.630
47
-.129
.389
47
-.236
.110
47
-.115
.440
47
.398
47
.987**
.000
47
.998**
.000
47
47
-.263
.075
47
.998**
.000
47
.506**
47
-.184
.000
47
1
.214
47
-.269
.000
47
.
47
.067
47
-.184
.214
47
-.269
.067
47
1
.
47
**. Correlation is significant at the 0.01 level (2-tailed).
*. Correlation is significant at the 0.05 level (2-tailed).
Things to notice:
• The two sets of proper factors are highly correlated
• Improper factors are highly correlated with the proper factors
• Much more correlation among the improper factors (especially the two that share
the multivocal item)
• But remember that r = .506 means they share just 25.6% of their variance (r²),
which isn't "excessive"