Preface to First Edition - lib

ANALYSIS USING R 293Yuping (CHN) Hagger (GB) Brown (USA)0.232507119 0.659520046 0.756854602Mulliner (GB) Hautenauve (BEL) Kytola (FIN)1.880932819 1.828170404 2.118203163Geremias (BRA) Hui-Ing (TAI) Jeong-Mi (KOR)2.770706272 3.901166920 3.896847898or, more conveniently, by extracting the first from all precomputed principalcomponentsR> predict(heptathlon_pca)[,1]Joyner-Kersee (USA) John (GDR) Behmer (GDR)-4.757530189 -3.147943402 -2.926184760Sablovskaite (URS) Choubenkova (URS) Schulz (GDR)-1.288135516 -1.503450994 -0.958467101Fleming (AUS) Greiner (USA) Lajbnerova (CZE)-0.953445060 -0.633239267 -0.381571974Bouraga (URS) Wijnsma (HOL) Dimitrova (BUL)-0.522322004 -0.217701500 -1.075984276Scheider (SWI) Braun (FRG) Ruotsalainen (FIN)0.003014986 0.109183759 0.208868056Yuping (CHN) Hagger (GB) Brown (USA)0.232507119 0.659520046 0.756854602Mulliner (GB) Hautenauve (BEL) Kytola (FIN)1.880932819 1.828170404 2.118203163Geremias (BRA) Hui-Ing (TAI) Jeong-Mi (KOR)2.770706272 3.901166920 3.896847898The first two components account for 75% of the variance. A barplot of eachcomponent’s variance (see Figure 16.3) shows how the first two componentsdominate. A plot of the data in the space of the first two principal components,with the points labelled by the name of the corresponding competitor,can be produced as shown with Figure 16.4. In addition, the first two loadingsfor the events are given in a second coordinate system, also illustrating thespecial role of the javelin event. This graphical representation is known as biplot(Gabriel, 1971). A biplot is a graphical representation of the informationin an n × p data matrix. The “bi” is a reflection that the technique producesa diagram that gives variance and covariance information about the variablesand information about generalised distances between individuals. The coordinatesused to produce the biplot can all be obtained directly from the principalcomponents analysis of the covariance matrix of the data and so the plots canbe viewed as an alternative representation of the results of such an analysis.Full details of the technical details of the biplot are given in Gabriel (1981)and in Gower and Hand (1996). Here we simply construct the biplot for theheptathlon data (without PNG); the result is shown in Figure 16.4. The plotclearly shows that the winner of the gold medal, Jackie Joyner-Kersee, accumulatesthe majority of her points from the three events long jump, hurdles,and 200m.© 2010 by Taylor and Francis Group, LLC