By virtue of the symmetry between scores and loadings, we can also construct bipolar axes through two columns 1 and 1 - such as is shown in Fig. 31.3f. When we project a row s, upon this bipolar axis we construct a difference between two elements in X. The proof follows readily from eq. (31.22) [Pg.113]

Fig. 31.9. Biplot of chromatographic retention times in Table 31.2, after log double-centering. Two bipolar axes have been drawn through the representation of the methods DMSO, methylenedichloride |

Fig. 32.10. CFA biplot computed from the data in Table 32.10. Factor scaling coefficients were defined as a = P = 0.5. This definition allows us to draw bipolar axes through the four educational categories, showing the contrast between women and men (horizontally) and between chemistry and other fields (vertically). |

The biplot of Fig. 31.9 shows that both the centroids of the compounds and of the methods coincide with the origin (the small cross in the middle of the plot). The first two latent variables account for 83 and 14% of the inertia, respectively. Three percent of the inertia is carried by higher order latent variables. In this biplot we can only make interpretations of the bipolar axes directly in terms of the original data in X. Three prominent poles appear on this biplot DMSO, methylene-dichloride and ethylalcohol. They are called poles because they are at a large distance from the origin and from one another. They are also representative for the three clusters that have been identified already on the column-standardized biplot in Fig. 31.7. [Pg.126]

The distances between compounds in Fig. 31.7 are not notably affected by the transformation in comparison with the previous Fig. 31.6. This biplot allows more easily to perceive the correlations between measurements. Three clusters are now put in evidence, namely (1) DMSO and DMF, (2) ethanol and propanol, (3) octanol, dioxane, THF and methylenedichloride. The line segments drawn from the origin have been added to emphasize these groupings. Unipolar axes could have been defined here in the same way as in Fig. 31.6. Bipolar axes on the column-standardized biplot, however, cannot be interpreted directly in terms of the original data in X. [Pg.123]

The analysis of Table 31.2 by CFA is shown in Fig. 31.11. As can be seen, the result is very similar to that obtained by log double-centering in Figs. 31.9 and 31.10. The first latent variable expresses a contrast between NO2 substituted chalcones and the others. The second latent variable seems to be related to the electronic properties of the substituents. The contributions of the two latent variables to the total inertia is 96%. The double-closed biplot of Fig. 31.11 does not allow a direct interpretation of unipolar and bipolar axes in terms of the original data X. The other rules of interpretation are similar to those of the log double-centered biplot in the previous subsection. Compounds and methods that seem to have moved away from the center and in the same directions possess a positive interaction (attraction). Those that moved in opposite directions show a negative interaction (repulsion). [Pg.132]

© 2019 chempedia.info