Iterated Factor Analysis Example -- Harman -- pg 14
Variables:
y1 total population
y2 median school years
y3 total employment
y4 misc. profess services
y5 median value house
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data socfac (type=corr);
_type_='corr';
input _name_ $ y1 y2 y3 y4 y5;
cards;
y1 1.00000 0.00975 0.97245 0.43887 0.02241
y2 0.00975 1.00000 0.15428 0.69141 0.86307
y3 0.97245 0.15428 1.00000 0.51472 0.12193
y4 0.43887 0.69141 0.51472 1.00000 0.77765
y5 0.02241 0.86307 0.12193 0.77765 1.00000
;
proc factor method=prinit priors=smc heywood rotate=varimax rotate=promax;
title 'Iterated Factor Analysis Example';
run;
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Iterated Factor Analysis Example
Initial Factor Method: Iterated Principal Factor Analysis
Prior Communality Estimates: SMC
Y1 Y2 Y3 Y4 Y5
0.968593 0.822273 0.969182 0.785718 0.847008
Preliminary Eigenvalues: Total = 4.3927727 Average = 0.87855454
1 2 3 4 5
Eigenvalue 2.7343 1.7161 0.0395 -0.0245 -0.0726
Difference 1.0182 1.6765 0.0641 0.0481
Proportion 0.6225 0.3907 0.0090 -0.0056 -0.0165
Cumulative 0.6225 1.0131 1.0221 1.0165 1.0000
2 factors will be retained by the PROPORTION criterion.
Iter Change Communalities
1 0.037935 0.97811 0.81756 0.97200 0.79774 0.88494
2 0.023501 0.98398 0.80831 0.97162 0.80096 0.90844
3 0.016081 0.98814 0.79921 0.97003 0.80132 0.92453
4 0.011691 0.99143 0.79156 0.96804 0.80084 0.93622
5 0.008782 0.99421 0.78548 0.96598 0.80021 0.94500
6 0.006706 0.99665 0.78078 0.96397 0.79961 0.95170
7 0.005160 0.99886 0.77718 0.96207 0.79909 0.95686
8 0.003984 1.00000 0.77442 0.96030 0.79866 0.96085
9 0.003089 1.00000 0.77232 0.95885 0.79834 0.96394
10 0.002404 1.00000 0.77072 0.95785 0.79809 0.96634
11 0.001869 1.00000 0.76950 0.95717 0.79791 0.96821
12 0.001452 1.00000 0.76855 0.95671 0.79776 0.96966
13 0.001128 1.00000 0.76782 0.95640 0.79763 0.97079
14 0.000877 1.00000 0.76726 0.95619 0.79753 0.97167
Convergence criterion satisfied.
Initial Factor Method: Iterated Principal Factor Analysis
Eigenvalues of the Reduced Correlation Matrix:
Total = 4.49264752 Average = 0.8985295
1 2 3 4 5
Eigenvalue 2.7559 1.7396 0.0311 -0.0025 -0.0314
Difference 1.0163 1.7085 0.0336 0.0289
Proportion 0.6134 0.3872 0.0069 -0.0006 -0.0070
Cumulative 0.6134 1.0006 1.0076 1.0070 1.0000
Initial Factor Method: Iterated Principal Factor Analysis
Factor Pattern
FACTOR1 FACTOR2
Y1 0.62254* 0.78440* total population
Y2 0.70213* -0.52371* median school years
Y3 0.70144* 0.68130* total employment
Y4 0.88115* -0.14526 misc. profess services
Y5 0.77905* -0.60395* median value house
Variance explained by each factor
FACTOR1 FACTOR2
2.755914 1.739590
Initial Factor Method: Iterated Principal Factor Analysis
Final Communality Estimates: Total = 4.495504
Y1 Y2 Y3 Y4 Y5
1.002851 0.767263 0.956188 0.797534 0.971668
Prerotation Method: Varimax
Orthogonal Transformation Matrix
1 2
1 0.79601 0.60528
2 -0.60528 0.79601
Rotated Factor Pattern
FACTOR1 FACTOR2
Y1 0.02077 1.00121* total population
Y2 0.87590* 0.00810 median school years
Y3 0.14598 0.96689* total employment
Y4 0.78933* 0.41771 misc. profess services
Y5 0.98569* -0.00921 median value house
Prerotation Method: Varimax
Variance explained by each factor
FACTOR1 FACTOR2
2.383571 2.111933
Final Communality Estimates: Total = 4.495504
Y1 Y2 Y3 Y4 Y5
1.002851 0.767263 0.956188 0.797534 0.971668
Rotation Method: Promax
Target Matrix for Procrustean Transformation
FACTOR1 FACTOR2
Y1 0.00001 1.00000
Y2 1.00000 0.00000
Y3 0.00333 0.96738
Y4 0.69058 0.10240
Y5 1.00000 -0.00000
Procrustean Transformation Matrix
1 2
1 1.03073 -0.09520
2 -0.10140 0.95929
Rotation Method: Promax
Normalized Oblique Transformation Matrix
1 2
1 0.74739 0.53403
2 -0.69372 0.86870
Inter-factor Correlations
FACTOR1 FACTOR2
FACTOR1 1.00000 0.19571
FACTOR2 0.19571 1.00000
Rotation Method: Promax
Rotated Factor Pattern (Std Reg Coefs)
FACTOR1 FACTOR2
Y1 -0.07887 1.01387* total population
Y2 0.88807* -0.07999 median school years
Y3 0.05162 0.96644* total employment
Y4 0.75933* 0.34438 misc. profess services
Y5 1.00122* -0.10861 median value house
Reference Axis Correlations
FACTOR1 FACTOR2
FACTOR1 1.00000 -0.19571
FACTOR2 -0.19571 1.00000
Rotation Method: Promax
Reference Structure (Semipartial Correlations)
FACTOR1 FACTOR2
Y1 -0.07735 0.99426
Y2 0.87090 -0.07844
Y3 0.05062 0.94775
Y4 0.74465 0.33772
Y5 0.98186 -0.10651
Variance explained by each factor eliminating other factors
FACTOR1 FACTOR2
2.285550 2.018335
Rotation Method: Promax
Factor Structure (Correlations)
FACTOR1 FACTOR2
Y1 0.11955 0.99843* total population
Y2 0.87242* 0.09381 median school years
Y3 0.24076 0.97654* total employment
Y4 0.82673* 0.49298 misc. profess services
Y5 0.97996* 0.08733 median value house
Variance explained by each factor ignoring other factors
FACTOR1 FACTOR2
2.477169 2.209954
Rotation Method: Promax
Final Communality Estimates: Total = 4.495504
Y1 Y2 Y3 Y4 Y5
1.002851 0.767263 0.956188 0.797534 0.971668