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

5.3. Biplots 97Figure 5.3. Biplot using α = 0 for artistic qualities data.However, what is gained is the ability to label these axes with values ofthe variables, so that orthogonally projecting an observation onto an axisimmediately gives a prediction of the value of that variable for the chosenobservation. Examples of this type of plot can be found in Gower and Hand(1996, Chapter 2).Other variations of the plot are sometimes used. In one of their examplesin which the data fall into groups, Gabriel and Odoroff (1990) replace the individualpoints by ‘concentration ellipses’ for each group. These ellipses areestimates of equal probability contours, assuming multivariate normality.Jolicoeur and Mosimann (1960) included similar ellipses on their plots.Artistic Qualities of PaintersIn Figure 5.3 a biplot is given for the data set described in Section 5.1.1and consisting of four subjective measurements of artistic qualities for 54painters.The plot given uses the adapted version of α = 0 in preference to α =1, because with α = 1 the points representing the four variables are allvery close to the centre of the plot, leading to difficulties in interpretation.The coordinates of the 54 painters are therefore rescaled versions of those