Coefficients, factor score

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 ... 

Factor score coefficient, 53 factorial experiment, partial, 27, 28 Fast Fourier transformation, FFT, 89-102... 

From known values of activities, one can calculate the value of the factor (factor score) v La factor score coefficients. 

Means, Standard Deviations, and Factor Score Coefficients for Andrew s 26 Points with Three Factors. (Means and Standard Deviation in Molarities)... 

The factor score coefficients (c ) are not correlation coefficients for independent variableS and the concept of relative weight of the activities of the species does not hold, i.e. the squares of the coefficients do not give the relative importance of the activities in the factor. 

Factor Analysis and Multiple Regression. Factor scores for the 26 and 30 point cases, generated using the factor score coefficients in Tjble IV, were correlated with inverse median survival time, t... 

According to these equations the intensities in a pyrolysis mass spectrum can be divided into a number of contributions from different factors, possibly different chemical components [81, 82]. The intensity of a factor in a particular mass spectrum, called the factor score, can be obtained from rel. (53a or 53b). The coefficients Cj are a measure of the relative contribution of the individual factors to the intensities at a given m/z value. The factor scores of the first factor show the largest variation in the set of spectra [83, 84]. Score plots of one of the factors for each mass h (see rel. 53a) allow sometimes a differentiation of the masses with specific contribution from classes of compounds [85]. Also, scattered score plots of the first two discriminant factors may reveal... 

Only variables with a loading of +0.30 or greater are shown. Exact factor scores were calculated for each subject in the study from the factor scoring coefficients... 

TABLE 3.35 Principal Component Analysis For the Data of Table 3.29 Within Unrotated (UnnormaUzed) Factor Score Coefficients, by Statistica (1995) see (Putz et al., 2009b)... 

A traditional notation in chemometrics for SVD defines scores and loadings by means of the symbols T and P such that X = T P, which is equivalent to X = U A V, where T = U A and P = V. This notation corresponds with the case a = 1 and P = 0, which is the most frequently used combination of factor scaling coefficients in chemometrics. 

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. 

Sometimes, it is not so easy to convince oneself that the solution of the molecular replacement problem has, in fact, been found, even after rigid-body refinement indeed, the first solution is not always well detached and different scores may produce different rankings. The most commonly used scores are correlation coefficients on either intensities or structure-factor amplitudes, and R-factors. Even though these criteria are formally related (Jamrog et ah, 2004), they can produce different rankings, especially if no solution is clearly detached. Some other criterion is then needed to discriminate between the potential solutions. 

Step 7 Note that from eqn (4.8), a coefficient was calculated to relate the scores of the first factor to the property of interest. Similar coefficients are required for each of the A factors included in the PLS model. Hence the prediction of the concentration of the analyte of interest in an unknown sample will go through first calculating the scores of that sample in the model and then applying the estimated -coefficients. 

Sampling theory, 27 Savitsky-Golay coefficients, 41 Savitsky-Golay differentiation, 57 Savitsky-Golay smoothing, 38 Scatter plot, 24 Scores, factor, 74 Scree plot, 75... 

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