Factor Analysis Example -- Harman -- pg 14
12 census tracts
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=prin priors=smc rotate=varimax rotate=promax;
title 'Factor Analysis Example';
run;
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Factor Analysis Example
Initial Factor Method: Principal Factors
Prior Communality Estimates: SMC
Y1 Y2 Y3 Y4 Y5
0.968593 0.822273 0.969182 0.785718 0.847008
Eigenvalues of the Reduced Correlation Matrix:
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.
Initial Factor Method: Principal Factors
Factor Pattern
FACTOR1 FACTOR2
Y1 0.62533* 0.76621* total population
Y2 0.71369* -0.55516* median school years
Y3 0.71448* 0.67935* total employment
Y4 0.87899* -0.15847 misc. profess services
Y5 0.74215* -0.57806* median value house
Variance explained by each factor
FACTOR1 FACTOR2
2.734294 1.716066
Initial Factor Method: Principal Factors
Final Communality Estimates: Total = 4.450360
Y1 Y2 Y3 Y4 Y5
0.978115 0.817560 0.972001 0.797741 0.884943
Prerotation Method: Varimax
Orthogonal Transformation Matrix
1 2
1 0.78894 0.61446
2 -0.61446 0.78894
Rotated Factor Pattern
FACTOR1 FACTOR2
Y1 0.02254 0.98874* total population
Y2 0.90419* 0.00055 median school years
Y3 0.14625 0.97499* total employment
Y4 0.79085* 0.41509 misc. profess services
Y5 0.94071* -0.00004 median value house
Prerotation Method: Varimax
Variance explained by each factor
FACTOR1 FACTOR2
2.349845 2.100515
Final Communality Estimates: Total = 4.450360
Y1 Y2 Y3 Y4 Y5
0.978115 0.817560 0.972001 0.797741 0.884943
Rotation Method: Promax
Target Matrix for Procrustean Transformation
FACTOR1 FACTOR2
Y1 0.00001 1.00000
Y2 1.00000 0.00000
Y3 0.00326 0.96793
Y4 0.69421 0.10045
Y5 1.00000 -0.00000
Procrustean Transformation Matrix
1 2
1 1.04117 -0.09865
2 -0.10572 0.96303
Rotation Method: Promax
Normalized Oblique Transformation Matrix
1 2
1 0.73803 0.54203
2 -0.70555 0.86527
Inter-factor Correlations
FACTOR1 FACTOR2
FACTOR1 1.00000 0.20188
FACTOR2 0.20188 1.00000
Rotation Method: Promax
Rotated Factor Pattern (Std Reg Coefs)
FACTOR1 FACTOR2
Y1 -0.07908 1.00193* total population
Y2 0.91842* -0.09352 median school years
Y3 0.04799 0.97509* total employment
Y4 0.76053* 0.33932 misc. profess services
Y5 0.95558* -0.09792 median value house
Reference Axis Correlations
FACTOR1 FACTOR2
FACTOR1 1.00000 -0.20188
FACTOR2 -0.20188 1.00000
Rotation Method: Promax
Reference Structure (Semipartial Correlations)
FACTOR1 FACTOR2
Y1 -0.07746 0.98129
Y2 0.89951 -0.09160
Y3 0.04700 0.95501
Y4 0.74487 0.33233
Y5 0.93591 -0.09590
Variance explained by each factor eliminating other factors
FACTOR1 FACTOR2
2.248078 2.003022
Rotation Method: Promax
Factor Structure (Correlations)
FACTOR1 FACTOR2
Y1 0.12319 0.98596* total population
Y2 0.89954* 0.09189 median school years
Y3 0.24485 0.98478* total employment
Y4 0.82903* 0.49286 misc. profess services
Y5 0.93581* 0.09500 median value house
Variance explained by each factor ignoring other factors
FACTOR1 FACTOR2
2.447338 2.202282
Rotation Method: Promax
Final Communality Estimates: Total = 4.450360
Y1 Y2 Y3 Y4 Y5
0.978115 0.817560 0.972001 0.797741 0.884943