Jolliffe I. Principal Component Analysis (2ed., Springer, 2002)(518s)

164 7. Principal Component Analysis and Factor AnalysisTable 7.3. Correlations between four direct quartimin factors: children’s intelligencetests.Factor number1 2 3Factor 2 0.349number 3 0.418 0.3064 0.305 0.197 0.112Table 7.4. Factor loadings—three factors, varimax rotation: children’s intelligencetests.Factor number1 2 3⎧1 0.47 0.09 0.142 0.47 0.17 0.053 0.36 0.23 0.244 0.37 0.23 0.00Variable⎪⎨5 0.45 0.08 0.23number 6 0.12 0.55 −0.057 0.17 0.48 0.178 0.05 0.36 0.52⎪⎩ 9 0.13 −0.01 0.6610 0.18 0.43 0.36The first factor in both methods has its highest loadings in variables 1, 2,3 and 5, with the next highest loadings on variables 4 and 7. In factors2, 3, 4 there is the same degree of similarity in the position of the highestloadings: for factor 2, the loadings for variables 7, 8, 10 are highest, with anintermediate value on variable 6; factor 3 has large loadings on variables 4and 6 and an intermediate value on variable 10; and factor 4 is dominated byvariable 9 with intermediate values on variables 8 and 10. The only notabledifference between the results for the two methods is that obliqueness allowsthe second method to achieve slightly higher values on the highest loadingsand correspondingly lower values on the low loadings, as indeed it is meantto.By contrast, the differences between the loadings before and after rotationare more substantial. After rotation, the ‘general factor’ withcoefficients of similar size on all variables disappears, as do most negativecoefficients, and the structure of the loadings is simplified. Again, thisis precisely what rotation is meant to achieve.