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

11.2. Alternatives to Rotation 291• SCoT, SCoTLASS and Vines’ (2000) simple components all havetuning parameters which must be chosen. At present there is no procedurefor choosing the tuning parameters automatically, and it isadvisable to try more than one value and judge subjectively when asuitable compromise between simplicity and variance retention hasbeen achieved. For simple components c = 0 is often a good choice.The sudden switching between solutions as ψ varies, noted for SCoT,seems not to be a problem with respect to t or c for SCoTLASS orsimple components.• Principal components have the special property that the vectorsof loadings are orthogonal and the component scores are uncorrelated.It was noted in Section 11.1 that rotated PCs lose atleast one of these properties, depending on which normalizationconstraint is used. None of the new techniques is able to retainboth properties either. SCoT and SCoTLASS, as defined aboveand implemented in the examples, retain orthogonality of the vectorsof loadings but sacrifice uncorrelatedness of the components.It is straightforward, though a little more complicated computationally,to implement versions of SCoT and SCoTLASS that keepuncorrelatedness rather than orthogonality. All that is required is tosubstitute the conditions c ′ h Sc k =0,h