Factor Analysis Self Assessment
The following data were obtained from 86 plasma donors at a Liverpool hospital. As part of a much larger data set the following variables were analysed.
Descriptive Statistics
| Mean | Std. Deviation | ||
|---|---|---|---|
| HT | Height (inches!) | 67.37 | 3.97 |
| WT | Weight (pounds!) | 166.22 | 26.67 |
| BMI | Body Mass Index | 26.50 | 3.72 |
| AGE | Age (years) | 33.83 | 8.43 |
| MCV | Mean Cell Volume | 90.60 | 4.26 |
| WBC | White Blood Cell Count | 6.35 | 1.58 |
Significant correlations are maked with a *.
| HT | WT | BMI | AGE | MCV | ||
|---|---|---|---|---|---|---|
| Correlation
Coefficient |
||||||
| WT | 0.534* | |||||
| BMI | -0.228 | 0.679* | ||||
| AGE | 0.039 | 0.100 | 0.112 | |||
| MCV | -0.096 | -0.160 | -0.162 | -0.018 | ||
| WBC | -0.181 | -0.056 | 0.028 | -0.006 | 0.318* | |
Make a note of the significant correlations.
A preliminary PCA identified three eigen values > 1.
Eigenvalue 1.9407 1.3174 1.1144 0.9690 0.6439 0.0146 Proportion 0.323 0.220 0.186 0.162 0.107 0.002 Cumulative 0.323 0.543 0.729 0.890 0.998 1.000
Variable PC1 PC2 PC3 PC4 PC5 PC6 ht 0.395 0.403 0.648 -0.021 -0.135 0.493 wt 0.671 -0.178 0.227 0.138 0.067 -0.666 bmi 0.480 -0.532 -0.344 0.154 0.182 0.558 age 0.152 -0.162 -0.020 -0.974 -0.038 -0.015 wbc -0.207 -0.600 0.345 0.087 -0.686 0.018 mcv -0.313 -0.370 0.539 -0.026 0.687 0.031
Factor Analysis (Extract only those factors with eigen values > 1).
Principal Component Factor Analysis of the Correlation Matrix
Variable Factor1 Factor2 Factor3 Communality ht 0.550 0.462 0.684 0.984 wt 0.934 -0.204 0.240 0.972 bmi 0.668 -0.611 -0.363 0.951 age 0.212 -0.186 -0.021 0.080 wbc -0.289 -0.688 0.364 0.690 mcv -0.436 -0.425 0.569 0.695
Variance 1.9407 1.3174 1.1144 4.3725 % Var 0.323 0.220 0.186 0.729 Rotated Factor Loadings and Communalities Varimax Rotation Variable Factor1 Factor2 Factor3 Communality ht -0.015 0.988 0.092 0.984 wt 0.782 0.594 0.083 0.972 bmi 0.958 -0.159 0.088 0.951 age 0.280 0.023 -0.026 0.080 wbc 0.148 -0.153 -0.803 0.690 mcv -0.169 0.026 -0.816 0.695 Variance 1.6593 1.3791 1.3341 4.3725 % Var 0.277 0.230 0.222 0.729
Factor Score Coefficients Variable Factor1 Factor2 Factor3 ht -0.130 0.749 -0.043 wt 0.417 0.355 -0.048 bmi 0.615 -0.245 0.034 age 0.175 -0.012 -0.038 wbc 0.155 -0.041 -0.613 mcv -0.064 0.135 -0.627
Scatter plot of scores on the two components.
The sex of each case is labelled. The solid lines mark the means for the two components (mean values = 0).
Factor Analysis 2 : Extract 4 factors, with rotation
The same data have been re-analysed, but the default extraction rule has been replaced with an option to extract 4 factors (because the eigen value for the fourth factor was 0.969).
Principal Component Factor Analysis of the Correlation Matrix
Unrotated Factor Loadings and Communalities
86 cases used 1 cases contain missing values
Variable Factor1 Factor2 Factor3 Factor4 Communality
ht 0.550 0.462 0.684 -0.021 0.985
wt 0.934 -0.204 0.240 0.135 0.991
bmi 0.668 -0.611 -0.363 0.152 0.974
age 0.212 -0.186 -0.021 -0.959 0.999
wbc -0.289 -0.688 0.364 0.085 0.697
mcv -0.436 -0.425 0.569 -0.025 0.696
Variance 1.9407 1.3174 1.1144 0.9690 5.3416
% Var 0.323 0.220 0.186 0.162 0.890
Rotated Factor Loadings and Communalities
Varimax Rotation
Variable Factor1 Factor2 Factor3 Factor4 Communality
ht -0.028 0.987 0.098 -0.016 0.985
wt 0.788 0.605 0.050 -0.040 0.991
bmi 0.973 -0.146 0.045 -0.060 0.974
age 0.061 0.021 0.006 -0.997 0.999
wbc 0.128 -0.148 -0.811 0.023 0.697
mcv -0.209 0.027 -0.807 -0.016 0.696
Variance 1.6320 1.3848 1.3237 1.0011 5.3416
% Var 0.272 0.231 0.221 0.167 0.890
Factor Score Coefficients
Variable Factor1 Factor2 Factor3 Factor4
ht -0.144 0.748 -0.034 0.005
wt 0.430 0.362 -0.068 0.041
bmi 0.639 -0.236 0.003 0.019
age -0.048 -0.015 -0.002 -1.004
wbc 0.143 -0.037 -0.622 0.030
mcv -0.099 0.137 -0.622 -0.033