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

64 4. Interpreting Principal Components: Examplesof subject areas, of which those illustrated in this book form only a subset.It must be emphasized that although in many examples the PCs can bereadily interpreted, this is by no means universally true. There is no reason,a priori, why a mathematically derived linear function of the originalvariables (which is what the PCs are) should have a simple interpretation.It is remarkable how often it seems to be possible to interpret thefirst few PCs, though it is probable that some interpretations owe a lotto the analyst’s ingenuity and imagination. Careful thought should go intoany interpretation and, at an earlier stage, into the choice of variables andwhether to transform them. In some circumstances, transformation of variablesbefore analysis may improve the chances of a simple interpretation(see Sections 13.2, 13.3, 14.1 and 14.2). Conversely, the arbitrary inclusionof logarithms, powers, ratios, etc., of the original variables can make it unlikelythat any simple interpretation will be found. Further discussion ofthe difficulties of interpretation, and of some alternative approaches, willbe given in Chapter 11.Many interesting applications have appeared since the first edition of thisbook, and some will be discussed in detail later in this edition. However,in the current chapter the original selection of examples, which illustratesa nice range of applications, has been kept. Extra references are given, butno new examples are discussed in detail. Texts such as Jackson (1991), Krzanowski(1988), Krzanowski and Marriott (1994) and Rencher (1995) areuseful sources for additional examples. A non-exhaustive list of disciplinesin which PCA has been applied was given at the end of Chapter 1.4.1 Anatomical MeasurementsOne type of application where PCA has been found useful is identificationof the most important sources of variation in anatomical measurements forvarious species. Typically, a large number of measurements are made onindividuals of a species, and a PCA is done. The first PC almost alwayshas positive coefficients for all variables and simply reflects overall ‘size’ ofthe individuals. Later PCs usually contrast some of the measurements withothers, and can often be interpreted as defining certain aspects of ‘shape’that are important for the species. Blackith and Reyment (1971, Chapter12) mention applications to squirrels, turtles, ammonites, foraminifera(marine microorganisms) and various types of insects. The analysis of sizeand shape is a large topic in its own right, and will discussed in greaterdetail in Section 13.2. Here a small data set is examined in which sevenmeasurements were taken for a class of 28 students (15 women, 13 men).The seven measurements are circumferences of chest, waist, wrist and head,lengths of hand and forearm, and overall height. A similar data set for adifferent group of students was introduced in Chapter 1.