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

66 4. Interpreting Principal Components: ExamplesTable 4.2. Simplified version of the coefficients in Table 4.1.Component number 1 2 3WomenHand + +Wrist + +Height + −Forearm + −Head + (−) +Chest + (−)Waist +MenHand + + +Wrist + + −Height + (−)Forearm + − +Head + −Chest +Waist +observations therefore seems appropriate, in order to get better estimatesof the first three PCs. It is, of course, possible that later PCs are differentfor the two sexes, and that combining all 28 observations will obscure suchdifferences. However, if we are interested solely in interpreting the first few,high variance, PCs, then this potential problem is likely to be relativelyunimportant.Before we attempt to interpret the PCs, some explanation of Table 4.2is necessary. Typically, computer packages that produce PCs give the coefficientsto several decimal places. When we interpret PCs, as with othertypes of tabular data, it is usually only the general pattern of the coefficientsthat is really of interest, not values to several decimal places, whichmay give a false impression of precision. Table 4.1 gives only two decimalplaces and Table 4.2 simplifies still further. A + or − in Table 4.2 indicatesa coefficient whose absolute value is greater than half the maximum coefficient(again in absolute value) for the relevant PC; the sign of the coefficientis also indicated. Similarly, a (+) or (−) indicates a coefficient whose absolutevalue is between a quarter and a half of the largest absolute valuefor the PC of interest. There are, of course, many ways of constructing asimplified version of the PC coefficients in Table 4.1. For example, anotherpossibility is to rescale the coefficients in each PC so that the maximumvalue is ±1, and tabulate only the values of the coefficients, rounded toone decimal place whose absolute values are above a certain cut-off, say 0.5or 0.7. Values of coefficients below the cut-off are omitted, leaving blank