## 4 Results and Discussion
### PLSDA Loading Vectors  
The multivariate data analysis approach utilized in this study outputs a set of loading vectors, which are coefficients that indicate the relative importance that each variable has on the predictive value of the PLSDA model. Before considering the results of individual PLSDA classification success and the relative merit of multianalyzer data fusion for the sample suites examined in this study, it is essential to understand the basis for discrimination. When loading values (in arbitrary units) are plotted against the relevant variables (i.e., energy, wavelength or Raman shift) associated with each analytical technique, the resulting plot has the appearance of a XRFS, LIBS or RS spectrum, except that the magnitude of the peaks or bands specifies how much of an effect it has on explaining the observed variation between the samples. Examination of the loadings allows one to verify that the basis for classification is reasonable based on the anticipated composition of the soil samples. For example, the XRFS spectra for the New Mexico soils (Figure 5A) were classified primarily based on differences in the levels of Ca, Fe, and Sr with smaller contributions from S, K, Ti, Rb, and Ba. These results are consistent with the major and minor elements that can be detected by the XRFS analyzer and are present in the principal soil-forming silicate species, such as the feldspars and aluminosilicate clay minerals as well as various carbonates, oxides, and sulfates. Fe has the largest loading values for the XRFS classification task. This result is in accordance with the broad range of values found for Fe using the internally calibrated quantitation feature of the instrument. For example, the weight percentage of Fe in the New Mexico samples ranges over two orders of magnitude--from \(\sim\)0.030% for the White Sands samples to \(\sim\)3.4% for Sedillo Hill. The XRFS loadings profile for the military installation soil suite (Figure 5B) is similar to that obtained for the New Mexico soils, with some notable exceptions. K, Ca, Fe, Rb, Sr, and Ba are present in each XRFS loadings plot, though their relative significance differs, especially for Ca. Importantly, Pb lines play a major role in discrimination, possibly due to the presence of varying levels of Pb-contaminated soils at these firing range sites. Cu also has a notable impact on this PLSDA model. Figure 4: Principal component score plots of the fusion feature vectors for the two New Hampshire locations (**A**) and at the three Belmont site pits (**B**). It is not surprising that the loadings associated with analysis of the soils from the six New Mexico locations using LIBS, which is especially sensitive to light elements, includes Li, Na, Mg, Al, and Si, in addition to K, Ca, Ti, Fe, and Sr (Figure 6A). Moisture content of the soils appears to also contribute to the discrimination since H and O also have appreciable loading values. While many of the same elements appear in the XRFS and LIBS plots for the New Mexico soils (Figures 5A and 6A), labels for S and Rb are notably absent in the latter since the most intense emission lines for these elements appear at wavelengths greater than the 779 nm cut-off used to exclude argon lines from the chemometric analysis. The loadings plot for the PLSDA model built using the LIBS data for the military installation soil suite has significant values for Pb emission lines, a small contribution for Cu, as well as a similar profile of elements to that found with the New Mexico soils. Only loading values above an arbitrary threshold were labeled in the LIBS plots to simplify the graphical representation, but lines associated with several other elements common to soil such as Mn (403.1 nm) in the New Mexico soils and Cr (425.5 nm) in the military installation soils also have significant loading values.