Factor score plots

Figure 2. Factor two (hardness) vs. Factor one (salinity) factor score plot for 679 samples. Data entry errors identified.

Figure 4. Factor score plots of sludge treated and untreated garden soil.

Figure T Factor score plots of 100 bright (A,a), 100 hurley (B,h), 100 oriental (C,c), 33.3 /33.3 /33.3 (D,d), and G0%/ OfolVdio (E,e). Uppercase vere cased. Lowercase were uncased samples. Top, factor 1 vs. factor 2 and bottom, factor 3 vs. factor 5.

Figure 10. Factor score plots of analytical/sensory data. Labels are as in Figure T-...

Factor analysis was performed on the IR spectra of subfractions 1 to 13 using 28 nonzero wavenumber variables. Five of the orginal 33 variables were unique to spectrum 15 and were not used in the factor analysis of samples 1-13. Figure 4b shows the factor score plots of the IR data on subfractions 1-13 in the FI vs. F2 factor space. Samples 1-7 are very close together, implying that infrared spectroscopy does not detect much difference between these dominantly aliphatic mixutres in this space. Analysis of the underlying correlation between variables by means of the variance diagram method showed that component (a) (350 ) represents methyl and methylene absorptions such as 2870, 2850, 2920, 1460 and 720 cm". Component axes (b) (120 ) with peak 1516 cm l and (c) (160 ) with 3050,... 

In Fig. 31.1a these scores are used as the coordinates of the four wind directions in 2-dimensional factor-space. From this so-called score plot one observes a large degree of association between the wind directions of 90, 180 and 270 degrees, while the one at 0 degrees stemds out from the others. 

Fig. 31.1. (a) Score plot in which the distances between representations of rows (wind directions) are reproduced. The factor scaling coefficient a equals 1. Data are listed in Table 31.1. (b) Loading plot in which the distances between representations of columns (trace elements) are preserved. The factor scaling coefficient P equals 1. Data are defined in Table 31.1. 

Fig. 31.2. Geometrical example of the duality of data space and the concept of a common factor space, (a) Representation of n rows (circles) of a data table X in a space Sf spanned by p columns. The pattern P" is shown in the form of an equiprobabi lity ellipse. The latent vectors V define the orientations of the principal axes of inertia of the row-pattern, (b) Representation of p columns (squares) of a data table X in a space y spanned by n rows. The pattern / is shown in the form of an equiprobability ellipse. The latent vectors U define the orientations of the principal axes of inertia of the column-pattern, (c) Result of rotation of the original column-space S toward the factor-space S spanned by r latent vectors. The original data table X is transformed into the score matrix S and the geometric representation is called a score plot, (d) Result of rotation of the original row-space S toward the factor-space S spanned by r latent vectors. The original data table X is transformed into the loading table L and the geometric representation is referred to as a loading plot, (e) Superposition of the score and loading plot into a biplot.

Fig. 31.3. (a,b) Reproduction of distances D and angular distances 0 in a score plot (a = 1) or loading plot (p = 1) in the common factor-space (c,d) Unipolar axis through the representation of a row or column and through the origin 0 of space. Reproduction of the data X is obtained by perpendicular projection of the column- or row-pattern upon the unipolar axis (a + P = 1). (e,0 Bipolar axis through the representation of two rows or two columns. Reproduction of differences (contrasts) in the data X is obtained by perpendicular projection of the column- or row-pattern upon the bipolar axis (a + P = 1). 

These factor scores can be used for the construction of a score plot in which each object is represented as a point in the plane of the first two dominant factors. 

Fig. 32.6. (a) Generalized score plot derived by correspondence factor analysis (CFA) from Table 32.4. The figure shows the distance of Triazolam from the origin, and the distance between Triazolam and Lorazepam. (b) Generalized loading plot derived by CFA from Table 32.4. The figure shows the distance of epilepsy from the origin, and the distance between epilepsy and anxiety. 

Factor analysis with the extraction of two factors and varimax rotation can be carried out in R as described below. The factor scores are estimated with a regression method. The resulting score and loading plots can be used as in PCA. 

Then using these 91 peaks only, the original data set was reexamined by principal components analysis. Eigenvalues greater than one were plotted to determine how many factors should be retained. After variraax rotation, the factor scores were plotted and interpreted. 

Scores Plot (Sa nple Diagnostic) The score plots show the relationship of the samples in LS row space and are examined for consistency with what is known about dse data set. Look for unusual or inconsistent patterns which can indicate potential problems with the model and/or samples (see also PCA, Section 4.2.2). 1b the PCA discussion the scores are referred to as PCs, but in PLS they are referred to as factors. 

FIGURE 5.98. Factor 2 versus Factor 1 PLS scores plot for component A. 

Scores Plot (Sample Diagnostic) Figure 5.105 displays Factor 2 versus Factor l, describing 99-4% of the spectral variance for the corrected data. 

Scores Plot (Sample Diagnostic) The Factor 2 versus Factor l plot is shown in Figure 5.119 with the points labeled by run order. The samples in this score space form multiple lines with similar slopes. Each line contains the spectra from a single standard (design point) at var ing temperatures. For example, samples 49-54 correspond to spectra collected from a single standard... 

Scores Plot (Sample Diagnostic) Figure 5-132 displays the Factor 2 versus Factor l scores for the MCB model (showing 98.41% of the spectral variance). The experimental design for this data set is not readily discernible because this plot shows only two dimensions. However, samples 1-4 define the extremes, which makes sense because these are the pure spectra. As expected, the center-point replicates lie very near each other and are in the middle of the plot. 

With the molecular descriptors as the X-block, and the senso scores for sweet as the Y-block, PLS was used to calculate a predictive model using the Unscrambler program version 3.1 (CAMO A/S, Jarleveien 4, N-7041 Trondheim, Norway). When the full set of 17 phenols was us, optimal prediction of sweet odour was shown with 1 factor. Loadings of variables and scores of compounds on the first two factors are shown in Fig es 1 and 2 respectively. Figure 3 shows predicted sweet odour score plotted against that provid by the sensory panel. Vanillin, with a sensory score of 3.3, was an obvious outlier in this set, and so the model was recalculated without it. Again 1 factor was r uired for optimal prediction, shown in Figure 4. 

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