Scores, factor

Factor scores for each of the n objects with respect to the r computed factors are then defined in the usual way by means of the nxr orthogonal factor score matrix S ... 

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. 

The theory of the non-linear PCA biplot has been developed by Gower [49] and can be described as follows. We first assume that a column-centered measurement table X is decomposed by means of classical (or linear) PCA into a matrix of factor scores S and a matrix of factor loadings L ... 

Using D as input we apply principal coordinates analysis (PCoA) which we discussed in the previous section. This produces the nxn factor score matrix S. The next step is to define a variable point along they th coordinate axis, by means of the coefficient kj and to compute its distance d kj) from all n row-points ... 

The r coordinates of the variable point which traces out the trajectory of the yth column-item in the r-dimensional biplot are compiled in the r-vector Sj. The elements of the latter can be estimated by means of linear regression of the nxr factor scores S upon an n-vector which is defined as ... 

Cluster analysis (which is covered extensively in Chapter 30) can be performed on the factor scores of a data table using a reduced number of factors (Section 31.1.4) rather than on the data table itself. This way, one can apply cluster analysis on the structural information only, while disregarding the noise or artefacts in the data. The number of structural factors may be determined by means of internal... 

Let us now consider a new set of values measured for the various X-variables, collected in a supplementary row vector x. From this we want to derive a row vector y of expected T-values using the predictive PLS model. To do this, the same sequence of operations is followed transforming x into a set of factor scores r, t 2, t A pertaining to this new observation. From these t -scores y can be... 

The suffix in T (nxA) and P (< xA) indicates that only the first A columns of T and P are used, A being much smaller than n and q. In principal component regression we use the PC scores as regressors for the concentrations. Thus, we apply inverse calibration of the property of interest on the selected set of factor scores ... 

The biplot in Fig. 37.3 has been constructed from the factor scores of the 12 compounds and the factor loadings of the five physicochemical and biological variables [42,43]. (The biplot graphic technique is explained in Section 31.2.) It is... 

With an increasing risk factor score, progressively greater benefit is seen with ... 

The principle of FA and PCA consists in an orthogonal decomposition of the original n x m data matrix X into a product of two matrixes, F (nxk matrix of factor scores, common factors) and L (kxm matrix of factor loadings)... 

Direct test particle methods are expected to be inefficient, compared to other possibilities, for molecular systems described with moderate realism. Successful placements of a test particle may be complicated, and placements with favorable Boltzmann factor scores may be rare. Fortunately, the tools noted above are generally available to design more-specific approaches for realistic cases. 

Fig. 2. Distribution of 395 to 470nm factor scores in soils over the Lisbon and Lightning Draw Southeast fields, which correspond to high correlation of 4- to 6-ring aromatic hydrocarbons.

Cd-U-Mo factor scores in soils over the Lisbon and Lightning Draw Southeast fields... 

Devereux Elementary School Behavior Rating Scale. The Devereux Elementary School Behavior Rating Scale is a widely used test incorporating 47 items that have a high test-retest reliability. It uses a checklist format and is easy to use (requires 10 min). There are 11 factor scores and three item scores. 

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. 

The goal of Q-mode FA is to determine the absolute abundance of the dominant components (i.e., physical or chemical properties) for environmental contaminants. It provides a description of the multivariate data set in terms of a few end members (associations or factors, usually orthogonal) that account for the variance within the data set. A factor score represents the importance of each variable in each end member. The set of scores for all factors makes up the factor score matrix. The importance of each variable in each end member is represented by a factor score, which is a unit vector in n (number of variables) dimensional space, with each element having a value between -1 and 1 and the... 

Follow-up cognitive and MMPI testing of the subjects who received EA 3167, at 1 and 6 months (Fig. 45), showed a small residual increase in the paranoid and schizophrenic subscales at 1 month, but at 6 months the profile had essentially returned to the pre-drug values. Differences in the three validity scales that persist may be due to attitudinal factors. Scores for intellectual functions returned to pre-test values during the same period, as shown previously for EA 3443 and EA 3580. ... 

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

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. 

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

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