Example 26.2: Principal Factor Analysis
The following example uses the data presented in
Example 26.1, and performs
a principal factor analysis with squared multiple
correlations for the prior communality estimates (PRIORS=SMC).
To help determine if the common factor model is appropriate, Kaiser's
measure of sampling adequacy (MSA) is requested, and the residual
correlations and partial correlations are computed (RESIDUAL). To
help determine the number of factors, a scree plot (SCREE)
of the eigenvalues
is displayed, and the PREPLOT option plots the unrotated factor
pattern.
The ROTATE= and REORDER options are specified to enhance factor
interpretability. The ROTATE=PROMAX option produces an orthogonal
varimax prerotation followed by an oblique rotation, and the REORDER
option reorders the variables according to their largest factor
loadings. The PLOT procedure is used to produce a plot of the
reference structure.
An OUTSTAT= data set is created by PROC FACTOR and displayed
in Output 26.2.15.
This example also demonstrates how to define a picture format with the
FORMAT procedure and use the PRINT procedure to produce customized
factor pattern output. Small elements of the Rotated Factor Pattern
matrix are displayed as `.'. Large values are multiplied by 100,
truncated at the decimal, and flagged with an asterisk `*'.
Intermediate values are scaled by 100 and truncated. For more
information on picture formats, refer to "Formats" in SAS
Language Reference: Dictionary.
ods output ObliqueRotFactPat = rotfacpat;
proc factor data=SocioEconomics priors=smc msa scree residual preplot
rotate=promax reorder plot
outstat=fact_all;
title3 'Principal Factor Analysis with Promax Rotation';
proc print;
title3 'Factor Output Data Set';
run;
proc format;
picture FuzzFlag
low - 0.1 = ' . '
0.10 - 0.90 = '009 ' (mult = 100)
0.90 - high = '009 *' (mult = 100);
run;
proc print data = rotfacpat;
format factor1-factor2 FuzzFlag.;
run;
Output 26.2.1: Principal Factor Analysis
|
| Principal Factor Analysis with Promax Rotation |
| The FACTOR Procedure |
| Initial Factor Method: Principal Factors |
| Partial Correlations Controlling all other Variables |
| |
Population |
School |
Employment |
Services |
HouseValue |
| Population |
1.00000 |
-0.54465 |
0.97083 |
0.09612 |
0.15871 |
| School |
-0.54465 |
1.00000 |
0.54373 |
0.04996 |
0.64717 |
| Employment |
0.97083 |
0.54373 |
1.00000 |
0.06689 |
-0.25572 |
| Services |
0.09612 |
0.04996 |
0.06689 |
1.00000 |
0.59415 |
| HouseValue |
0.15871 |
0.64717 |
-0.25572 |
0.59415 |
1.00000 |
| Kaiser's Measure of Sampling Adequacy: Overall MSA = 0.57536759 |
| Population |
School |
Employment |
Services |
HouseValue |
| 0.47207897 |
0.55158839 |
0.48851137 |
0.80664365 |
0.61281377 |
| 2 factors will be retained by the PROPORTION criterion. |
|
|
| Principal Factor Analysis with Promax Rotation |
| The FACTOR Procedure |
| Initial Factor Method: Principal Factors |
| Prior Communality Estimates: SMC |
| Population |
School |
Employment |
Services |
HouseValue |
| 0.96859160 |
0.82228514 |
0.96918082 |
0.78572440 |
0.84701921 |
Eigenvalues of the Reduced Correlation Matrix:
Total = 4.39280116 Average = 0.87856023 |
| |
Eigenvalue |
Difference |
Proportion |
Cumulative |
| 1 |
2.73430084 |
1.01823217 |
0.6225 |
0.6225 |
| 2 |
1.71606867 |
1.67650586 |
0.3907 |
1.0131 |
| 3 |
0.03956281 |
0.06408626 |
0.0090 |
1.0221 |
| 4 |
-.02452345 |
0.04808427 |
-0.0056 |
1.0165 |
| 5 |
-.07260772 |
|
-0.0165 |
1.0000 |
| 2 factors will be retained by the PROPORTION criterion. |
|
Output 26.2.1 displays the results of the principal factor
extraction.
If the data are appropriate for the common factor model, the partial
correlations controlling the other variables should be small compared
to the original correlations. The partial correlation between the
variables School and HouseValue, for example, is 0.65,
slightly less than the original correlation of 0.86. The partial
correlation between Population and School is -0.54,
which is much larger in absolute value than the original correlation;
this is an indication of trouble. Kaiser's MSA is a summary, for each
variable and for all variables together, of how much smaller the
partial correlations are than the original correlations. Values of
0.8 or 0.9 are considered good, while MSAs below 0.5 are
unacceptable. The variables Population, School, and
Employment have very poor MSAs. Only the Services variable has
a good MSA. The overall MSA of 0.58 is sufficiently poor that
additional variables should be included in the analysis to better define the
common factors. A commonly used rule is that there should be
at least three variables per factor. In the following analysis,
there seems to be two common factors in these data, so more variables are
needed for a reliable analysis.
The SMCs are all fairly large; hence, the factor loadings do not
differ greatly from the principal component analysis.
The eigenvalues show clearly that two common factors are present.
There are two large positive eigenvalues that together account for
101.31% of the common variance, which is as close to 100% as you are
ever likely to get without iterating. The scree plot displays a sharp
bend at the third eigenvalue, reinforcing the preceding conclusion.
|
| Principal Factor Analysis with Promax Rotation |
| The FACTOR Procedure |
| Initial Factor Method: Principal Factors |
Scree Plot of Eigenvalues
|
3 +
|
| 1
|
|
|
2 +
E |
i | 2
g |
e |
n |
v 1 +
a |
l |
u |
e |
s |
0 + 3 4 5
|
|
|
|
|
-1 +
|
-------+-----------+-----------+-----------+-----------+-----------+-------
0 1 2 3 4 5
Number
|
|
Output 26.2.2: Factor Pattern Matrix and Communalities
|
| Principal Factor Analysis with Promax Rotation |
| The FACTOR Procedure |
| Initial Factor Method: Principal Factors |
| Factor Pattern |
| |
Factor1 |
Factor2 |
| Services |
0.87899 |
-0.15847 |
| HouseValue |
0.74215 |
-0.57806 |
| Employment |
0.71447 |
0.67936 |
| School |
0.71370 |
-0.55515 |
| Population |
0.62533 |
0.76621 |
Variance Explained by Each
Factor |
| Factor1 |
Factor2 |
| 2.7343008 |
1.7160687 |
| Final Communality Estimates: Total = 4.450370 |
| Population |
School |
Employment |
Services |
HouseValue |
| 0.97811334 |
0.81756387 |
0.97199928 |
0.79774304 |
0.88494998 |
|
As displayed in Output 26.2.2, the principal factor pattern is similar
to the principal component pattern seen in Example 26.1.
For example,
the variable Services has the largest loading on the first
factor, and the Population variable has the smallest. The
variables Population and Employment have large positive
loadings on the second factor, and the HouseValue and
School variables have large negative loadings.
The final communality estimates are all fairly close to the priors.
Only the communality for the variable HouseValue
increased appreciably, from 0.847019 to 0.884950. Nearly 100% of the
common variance is accounted for. The residual correlations
(off-diagonal elements) are low,
the largest being 0.03 (Output 26.2.3).
The partial correlations are not quite as
impressive, since the uniqueness values are also rather small. These
results indicate that the SMCs are good but not quite optimal
communality estimates.
Output 26.2.3: Residual and Partial Correlations
|
| Principal Factor Analysis with Promax Rotation |
| The FACTOR Procedure |
| Initial Factor Method: Principal Factors |
| Residual Correlations With Uniqueness on the Diagonal |
| |
Population |
School |
Employment |
Services |
HouseValue |
| Population |
0.02189 |
-0.01118 |
0.00514 |
0.01063 |
0.00124 |
| School |
-0.01118 |
0.18244 |
0.02151 |
-0.02390 |
0.01248 |
| Employment |
0.00514 |
0.02151 |
0.02800 |
-0.00565 |
-0.01561 |
| Services |
0.01063 |
-0.02390 |
-0.00565 |
0.20226 |
0.03370 |
| HouseValue |
0.00124 |
0.01248 |
-0.01561 |
0.03370 |
0.11505 |
| Root Mean Square Off-Diagonal Residuals: Overall = 0.01693282 |
| Population |
School |
Employment |
Services |
HouseValue |
| 0.00815307 |
0.01813027 |
0.01382764 |
0.02151737 |
0.01960158 |
| Partial Correlations Controlling Factors |
| |
Population |
School |
Employment |
Services |
HouseValue |
| Population |
1.00000 |
-0.17693 |
0.20752 |
0.15975 |
0.02471 |
| School |
-0.17693 |
1.00000 |
0.30097 |
-0.12443 |
0.08614 |
| Employment |
0.20752 |
0.30097 |
1.00000 |
-0.07504 |
-0.27509 |
| Services |
0.15975 |
-0.12443 |
-0.07504 |
1.00000 |
0.22093 |
| HouseValue |
0.02471 |
0.08614 |
-0.27509 |
0.22093 |
1.00000 |
|
Output 26.2.4: Root Mean Square Off-Diagonal Partials
|
| Principal Factor Analysis with Promax Rotation |
| The FACTOR Procedure |
| Initial Factor Method: Principal Factors |
| Root Mean Square Off-Diagonal Partials: Overall = 0.18550132 |
| Population |
School |
Employment |
Services |
HouseValue |
| 0.15850824 |
0.19025867 |
0.23181838 |
0.15447043 |
0.18201538 |
|
Output 26.2.5: Unrotated Factor Pattern Plot
|
| Principal Factor Analysis with Promax Rotation |
| The FACTOR Procedure |
| Initial Factor Method: Principal Factors |
Plot of Factor Pattern for Factor1 and Factor2
Factor1
1
D .9
.8
E
B .7 C
A
.6
.5
.4
.3
.2
F
.1 a
c
-1 -.9-.8-.7-.6-.5-.4-.3-.2-.1 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0t
o
-.1 r
2
-.2
-.3
-.4
-.5
-.6
-.7
-.8
-.9
-1
Population=A School=B Employment=C Services=D HouseValue=E
|
|
As displayed in Output 26.2.5, the unrotated factor pattern
reveals two tight clusters of variables, with the variables
HouseValue and School at the negative
end of Factor2 axis and the variables
Employment and Population at the positive end.
The Services variable
is in between but closer to the HouseValue and School variables.
A good rotation would put the reference axes through the two clusters.
Output 26.2.6: Varimax Rotation: Transform Matrix and Rotated Pattern
|
| Principal Factor Analysis with Promax Rotation |
| The FACTOR Procedure |
| Prerotation Method: Varimax |
| Orthogonal Transformation Matrix |
| |
1 |
2 |
| 1 |
0.78895 |
0.61446 |
| 2 |
-0.61446 |
0.78895 |
| Rotated Factor Pattern |
| |
Factor1 |
Factor2 |
| HouseValue |
0.94072 |
-0.00004 |
| School |
0.90419 |
0.00055 |
| Services |
0.79085 |
0.41509 |
| Population |
0.02255 |
0.98874 |
| Employment |
0.14625 |
0.97499 |
|
Output 26.2.7: Varimax Rotation: Variance Explained and Communalities
|
| Principal Factor Analysis with Promax Rotation |
| The FACTOR Procedure |
| Prerotation Method: Varimax |
Variance Explained by Each
Factor |
| Factor1 |
Factor2 |
| 2.3498567 |
2.1005128 |
| Final Communality Estimates: Total = 4.450370 |
| Population |
School |
Employment |
Services |
HouseValue |
| 0.97811334 |
0.81756387 |
0.97199928 |
0.79774304 |
0.88494998 |
|
Output 26.2.8: Varimax Rotated Factor Pattern Plot
|
| Principal Factor Analysis with Promax Rotation |
| The FACTOR Procedure |
| Prerotation Method: Varimax |
Plot of Factor Pattern for Factor1 and Factor2
Factor1
1
E
.B
.8 D
.7
.6
.5
.4
.3
.2
C F
.1 a
c
-1 -.9-.8-.7-.6-.5-.4-.3-.2-.1 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 A.0t
o
-.1 r
2
-.2
-.3
-.4
-.5
-.6
-.7
-.8
-.9
-1
Population=A School=B Employment=C Services=D HouseValue=E
|
|
Output 26.2.6, Output 26.2.7 and Output 26.2.8 display the results of the varimax rotation.
This rotation puts one axis through the variables HouseValue
and School but misses the Population and Employment
variables slightly.
Output 26.2.9: Promax Rotation: Procrustean Target and Transform Matrix
|
| Principal Factor Analysis with Promax Rotation |
| The FACTOR Procedure |
| Rotation Method: Promax |
| Target Matrix for Procrustean Transformation |
| |
Factor1 |
Factor2 |
| HouseValue |
1.00000 |
-0.00000 |
| School |
1.00000 |
0.00000 |
| Services |
0.69421 |
0.10045 |
| Population |
0.00001 |
1.00000 |
| Employment |
0.00326 |
0.96793 |
| Procrustean Transformation Matrix |
| |
1 |
2 |
| 1 |
1.04116598 |
-0.0986534 |
| 2 |
-0.1057226 |
0.96303019 |
|
Output 26.2.10: Promax Rotation: Oblique Transform Matrix and Correlation
|
| Principal Factor Analysis with Promax Rotation |
| The FACTOR Procedure |
| Rotation Method: Promax |
Normalized Oblique Transformation
Matrix |
| |
1 |
2 |
| 1 |
0.73803 |
0.54202 |
| 2 |
-0.70555 |
0.86528 |
| Inter-Factor Correlations |
| |
Factor1 |
Factor2 |
| Factor1 |
1.00000 |
0.20188 |
| Factor2 |
0.20188 |
1.00000 |
|
Output 26.2.11: Promax Rotation: Rotated Factor Pattern and Correlations
|
| Principal Factor Analysis with Promax Rotation |
| The FACTOR Procedure |
| Rotation Method: Promax |
Rotated Factor Pattern (Standardized
Regression Coefficients) |
| |
Factor1 |
Factor2 |
| HouseValue |
0.95558485 |
-0.0979201 |
| School |
0.91842142 |
-0.0935214 |
| Services |
0.76053238 |
0.33931804 |
| Population |
-0.0790832 |
1.00192402 |
| Employment |
0.04799 |
0.97509085 |
| Reference Axis Correlations |
| |
Factor1 |
Factor2 |
| Factor1 |
1.00000 |
-0.20188 |
| Factor2 |
-0.20188 |
1.00000 |
|
Output 26.2.12: Promax Rotation: Variance Explained and Factor Structure
|
| Principal Factor Analysis with Promax Rotation |
| The FACTOR Procedure |
| Rotation Method: Promax |
| Reference Structure (Semipartial Correlations) |
| |
Factor1 |
Factor2 |
| HouseValue |
0.93591 |
-0.09590 |
| School |
0.89951 |
-0.09160 |
| Services |
0.74487 |
0.33233 |
| Population |
-0.07745 |
0.98129 |
| Employment |
0.04700 |
0.95501 |
Variance Explained by Each
Factor Eliminating Other
Factors |
| Factor1 |
Factor2 |
| 2.2480892 |
2.0030200 |
| Factor Structure (Correlations) |
| |
Factor1 |
Factor2 |
| HouseValue |
0.93582 |
0.09500 |
| School |
0.89954 |
0.09189 |
| Services |
0.82903 |
0.49286 |
| Population |
0.12319 |
0.98596 |
| Employment |
0.24484 |
0.98478 |
|
Output 26.2.13: Promax Rotation: Variance Explained and Final Communalities
|
| Principal Factor Analysis with Promax Rotation |
| The FACTOR Procedure |
| Rotation Method: Promax |
Variance Explained by Each
Factor Ignoring Other Factors |
| Factor1 |
Factor2 |
| 2.4473495 |
2.2022803 |
| Final Communality Estimates: Total = 4.450370 |
| Population |
School |
Employment |
Services |
HouseValue |
| 0.97811334 |
0.81756387 |
0.97199928 |
0.79774304 |
0.88494998 |
|
Output 26.2.14: Promax Rotated Factor Pattern Plot
|
| Principal Factor Analysis with Promax Rotation |
| The FACTOR Procedure |
| Rotation Method: Promax |
Plot of Reference Structure for Factor1 and Factor2
Reference Axis Correlation = -0.2019 Angle = 101.6471
Factor1
1
E
B .9
.8
D
.7
.6
.5
.4
.3
.2
F
.1 a
C c
-1 -.9-.8-.7-.6-.5-.4-.3-.2-.1 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0t
o
-.1 A r
2
-.2
-.3
-.4
-.5
-.6
-.7
-.8
-.9
-1
Population=A School=B Employment=C Services=D HouseValue=E
|
|
The oblique promax rotation (Output 26.2.9 through Output 26.2.14)
places an axis through the variables Population and Employment but misses the
HouseValue and School variables.
Since an independent-cluster solution would be possible
if it were not for the variable Services, a Harris-Kaiser rotation
weighted by the Cureton-Mulaik technique should be used.
Output 26.2.15: Output Data Set
|
| Obs |
_TYPE_ |
_NAME_ |
Population |
School |
Employment |
Services |
HouseValue |
| 1 |
MEAN |
|
6241.67 |
11.4417 |
2333.33 |
120.833 |
17000.00 |
| 2 |
STD |
|
3439.99 |
1.7865 |
1241.21 |
114.928 |
6367.53 |
| 3 |
N |
|
12.00 |
12.0000 |
12.00 |
12.000 |
12.00 |
| 4 |
CORR |
Population |
1.00 |
0.0098 |
0.97 |
0.439 |
0.02 |
| 5 |
CORR |
School |
0.01 |
1.0000 |
0.15 |
0.691 |
0.86 |
| 6 |
CORR |
Employment |
0.97 |
0.1543 |
1.00 |
0.515 |
0.12 |
| 7 |
CORR |
Services |
0.44 |
0.6914 |
0.51 |
1.000 |
0.78 |
| 8 |
CORR |
HouseValue |
0.02 |
0.8631 |
0.12 |
0.778 |
1.00 |
| 9 |
COMMUNAL |
|
0.98 |
0.8176 |
0.97 |
0.798 |
0.88 |
| 10 |
PRIORS |
|
0.97 |
0.8223 |
0.97 |
0.786 |
0.85 |
| 11 |
EIGENVAL |
|
2.73 |
1.7161 |
0.04 |
-0.025 |
-0.07 |
| 12 |
UNROTATE |
Factor1 |
0.63 |
0.7137 |
0.71 |
0.879 |
0.74 |
| 13 |
UNROTATE |
Factor2 |
0.77 |
-0.5552 |
0.68 |
-0.158 |
-0.58 |
| 14 |
RESIDUAL |
Population |
0.02 |
-0.0112 |
0.01 |
0.011 |
0.00 |
| 15 |
RESIDUAL |
School |
-0.01 |
0.1824 |
0.02 |
-0.024 |
0.01 |
| 16 |
RESIDUAL |
Employment |
0.01 |
0.0215 |
0.03 |
-0.006 |
-0.02 |
| 17 |
RESIDUAL |
Services |
0.01 |
-0.0239 |
-0.01 |
0.202 |
0.03 |
| 18 |
RESIDUAL |
HouseValue |
0.00 |
0.0125 |
-0.02 |
0.034 |
0.12 |
| 19 |
PRETRANS |
Factor1 |
0.79 |
-0.6145 |
. |
. |
. |
| 20 |
PRETRANS |
Factor2 |
0.61 |
0.7889 |
. |
. |
. |
| 21 |
PREROTAT |
Factor1 |
0.02 |
0.9042 |
0.15 |
0.791 |
0.94 |
| 22 |
PREROTAT |
Factor2 |
0.99 |
0.0006 |
0.97 |
0.415 |
-0.00 |
| 23 |
TRANSFOR |
Factor1 |
0.74 |
-0.7055 |
. |
. |
. |
| 24 |
TRANSFOR |
Factor2 |
0.54 |
0.8653 |
. |
. |
. |
| 25 |
FCORR |
Factor1 |
1.00 |
0.2019 |
. |
. |
. |
| 26 |
FCORR |
Factor2 |
0.20 |
1.0000 |
. |
. |
. |
| 27 |
PATTERN |
Factor1 |
-0.08 |
0.9184 |
0.05 |
0.761 |
0.96 |
| 28 |
PATTERN |
Factor2 |
1.00 |
-0.0935 |
0.98 |
0.339 |
-0.10 |
| 29 |
RCORR |
Factor1 |
1.00 |
-0.2019 |
. |
. |
. |
| 30 |
RCORR |
Factor2 |
-0.20 |
1.0000 |
. |
. |
. |
| 31 |
REFERENC |
Factor1 |
-0.08 |
0.8995 |
0.05 |
0.745 |
0.94 |
| 32 |
REFERENC |
Factor2 |
0.98 |
-0.0916 |
0.96 |
0.332 |
-0.10 |
| 33 |
STRUCTUR |
Factor1 |
0.12 |
0.8995 |
0.24 |
0.829 |
0.94 |
| 34 |
STRUCTUR |
Factor2 |
0.99 |
0.0919 |
0.98 |
0.493 |
0.09 |
|
The output data set displayed in Output 26.2.15
can be used for Harris-Kaiser rotation by deleting
observations with _TYPE_='PATTERN' and
_TYPE_='FCORR',
which are for the promax-rotated factors, and changing
_TYPE_='UNROTATE' to _TYPE_='PATTERN'.
Output 26.2.16 displays the rotated factor pattern output
formatted with the picture format `FuzzFlag'.
Output 26.2.16: Picture Format Output
|
| Obs |
RowName |
Factor1 |
Factor2 |
| 1 |
HouseValue |
95 * |
. |
| 2 |
School |
91 * |
. |
| 3 |
Services |
76 |
33 |
| 4 |
Population |
. |
100 * |
| 5 |
Employment |
. |
97 * |
|
The following statements produce Output 26.2.17:
data fact2(type=factor);
set fact_all;
if _TYPE_ in('PATTERN' 'FCORR') then delete;
if _TYPE_='UNROTATE' then _TYPE_='PATTERN';
proc factor rotate=hk norm=weight reorder plot;
title3 'Harris-Kaiser Rotation with Cureton-Mulaik Weights';
run;
The results of the Harris-Kaiser rotation are displayed in Output 26.2.17:
Output 26.2.17: Harris-Kaiser Rotation
|
| Harris-Kaiser Rotation with Cureton-Mulaik Weights |
| The FACTOR Procedure |
| Rotation Method: Harris-Kaiser |
| Variable Weights for Rotation |
| Population |
School |
Employment |
Services |
HouseValue |
| 0.95982747 |
0.93945424 |
0.99746396 |
0.12194766 |
0.94007263 |
| Oblique Transformation Matrix |
| |
1 |
2 |
| 1 |
0.73537 |
0.61899 |
| 2 |
-0.68283 |
0.78987 |
| Inter-Factor Correlations |
| |
Factor1 |
Factor2 |
| Factor1 |
1.00000 |
0.08358 |
| Factor2 |
0.08358 |
1.00000 |
|
|
| Harris-Kaiser Rotation with Cureton-Mulaik Weights |
| The FACTOR Procedure |
| Rotation Method: Harris-Kaiser |
Rotated Factor Pattern (Standardized
Regression Coefficients) |
| |
Factor1 |
Factor2 |
| HouseValue |
0.94048 |
0.00279 |
| School |
0.90391 |
0.00327 |
| Services |
0.75459 |
0.41892 |
| Population |
-0.06335 |
0.99227 |
| Employment |
0.06152 |
0.97885 |
| Reference Axis Correlations |
| |
Factor1 |
Factor2 |
| Factor1 |
1.00000 |
-0.08358 |
| Factor2 |
-0.08358 |
1.00000 |
| Reference Structure (Semipartial Correlations) |
| |
Factor1 |
Factor2 |
| HouseValue |
0.93719 |
0.00278 |
| School |
0.90075 |
0.00326 |
| Services |
0.75195 |
0.41745 |
| Population |
-0.06312 |
0.98880 |
| Employment |
0.06130 |
0.97543 |
Variance Explained by Each
Factor Eliminating Other
Factors |
| Factor1 |
Factor2 |
| 2.2628537 |
2.1034731 |
|
|
| Harris-Kaiser Rotation with Cureton-Mulaik Weights |
| The FACTOR Procedure |
| Rotation Method: Harris-Kaiser |
| Factor Structure (Correlations) |
| |
Factor1 |
Factor2 |
| HouseValue |
0.94071 |
0.08139 |
| School |
0.90419 |
0.07882 |
| Services |
0.78960 |
0.48198 |
| Population |
0.01958 |
0.98698 |
| Employment |
0.14332 |
0.98399 |
Variance Explained by Each
Factor Ignoring Other Factors |
| Factor1 |
Factor2 |
| 2.3468965 |
2.1875158 |
| Final Communality Estimates: Total = 4.450370 |
| Population |
School |
Employment |
Services |
HouseValue |
| 0.97811334 |
0.81756387 |
0.97199928 |
0.79774304 |
0.88494998 |
|
|
| Harris-Kaiser Rotation with Cureton-Mulaik Weights |
| The FACTOR Procedure |
| Rotation Method: Harris-Kaiser |
Plot of Reference Structure for Factor1 and Factor2
Reference Axis Correlation = -0.0836 Angle = 94.7941
Factor1
1
E
.B
.8
D
.7
.6
.5
.4
.3
.2
F
.1 a
C c
-1 -.9-.8-.7-.6-.5-.4-.3-.2-.1 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0t
A o
-.1 r
2
-.2
-.3
-.4
-.5
-.6
-.7
-.8
-.9
-1
Population=A School=B Employment=C Services=D HouseValue=E
|
|
In the results of the Harris-Kaiser rotation,
the variable Services receives a small weight,
and the axes are placed as desired.
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.
