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

13Principal Component Analysis forSpecial Types of DataThe viewpoint taken in much of this text is that PCA is mainly a descriptivetool with no need for rigorous distributional or model assumptions.This implies that it can be used on a wide range of data, which can divergeconsiderably from the ‘ideal’ of multivariate normality. There are,however, certain types of data where some modification or special care isdesirable when performing PCA. Some instances of this have been encounteredalready, for example in Chapter 9 where the data are grouped eitherby observations or by variables, and in Chapter 12 where observations arenon-independent. The present chapter describes a number of other specialtypes of data for which standard PCA should be modified in some way, orwhere related techniques may be relevant.Section 13.1 looks at a number of ideas involving PCA for discrete data.In particular, correspondence analysis, which was introduced as a graphicaltechnique in Section 5.4, is discussed further, and procedures for dealingwith data given as ranks are also described.When data consist of measurements on animals or plants it is sometimesof interest to identify ‘components’ of variation that quantify size and variousaspects of shape. Section 13.2 examines modifications of PCA thatattempt to find such components.In Section 13.3, compositional data in which the p elements of x are constrainedto sum to the same constant (usually 1 or 100) for all observationsare discussed, and in Section 13.4 the rôle of PCA in analysing data fromdesigned experiments is described.Section 13.5 looks at a number of ways of defining ‘common’ PCs, orcommon subspaces, when the observations come from several distinct pop-