Calibration nonzero intercepts

But the nonzero intercepts also allow an additional degree of freedom when we calculate the calibration matrix, K, . This provides additional opportunity to adjust to the effects of the extraneous absorbances. 

Figure 22. CLS estimates of pure component spectra, nonzero intercept calibration.

Figure 23 contains plots of the expected vs. predicted concentrations for all of the nonzero intercept CLS results. We can easily see that these results are much better than the results of the first calibrations. It is also apparent that when we predict the concentrations from the spectra in A5, the validation set with the... 

Figure 23. Expected concentrations (x-axis) vs. predicted concentrations (y-axis) for nonzero intercept CLS calibrations (see text).

We perform CLS on A6 to produce 2 calibrations. K6 and K6, are the matrices holding the pure component spectra and calibration coefficients, respectively, for CLS with zero intercepts. K6a and K6aMl are the corresponding matrices for CLS with nonzero intercepts. 

Figure 25 contains plots of the pure component spectra for the two calibrations. It is apparent that, in the absence of the extraneous absorbances from Component 4, CLS is now able to do a good job of estimating the pure component spectra. However, even with nonzero intercepts, CLS is unable to remove the sloping baseline from the spectra. Both calibrations distributed most of the baseline effect onto the spectrum for Component 2 and some onto the Component 3 spectrum. 

We can see that the ILS calibrations are noticeably better than the CLS calibrations done with zero intercept. And they are as good or somewhat better that the CLS calibrations with nonzero intercept. This is remarkable when we consider how badly we have degraded the spectra when we condensed them The main reason for the advantage of ILS over CLS can be seen in equation [47],... 

In the absence of mean centering, it is possible to include a nonzero intercept, b0, in a calibration model by expressing the model as... 

Univariate calibration is specific to situations where the instrument response depends only on the target analyte concentration. With multivariate calibration, model parameters can be estimated where responses depend on the target analyte in addition to other chemical or physical variables and, hence, multivariate calibration corrects for these interfering effects. For the ith calibration sample, the model with a nonzero intercept can be written as... 

FIGURE 5.6 Graphical displays for the methanol model at 2274 nm with a nonzero intercept using all 11 calibration samples. The RMSEC is 2.37% methanol, (a) Actual calibration model (-) and measured values ( ). (b) Calibration residual plot, (c) A plot of estimated values against the actual values for the calibration samples the drawn line is the line of equality. 

Summary Statistics for NIR Calibration of Water in Water-Methanol Mixtures Using One Wavelength and a Nonzero Intercept... 

Figure 7.4 Calibration curve for lithium by flame emission using external calibration standards. Note the nonzero intercept for the blank due to background emission from the flame.

These simple one-wavelength calibration models with no intercept term are severely limited. Spectral data is used from only one wavelength, which means a lot of useful data points recorded by the instrument are thrown away. Nonzero baseline offsets cannot be accommodated. Worst of all, because spectral data from only one wavelength is used, absorbance signals from other constituents in the mixtures can interfere with analysis. Some of the problems revealed for models without an intercept term can be reduced when an intercept term is incorporated. 

These authors expand the basic relationship LOD=kiB/5 to include 1) the use of population statistics (vs. sample set statistics) 2) the use of the pooled standard deviation (vs. the blank standard deviation) 3) a consideration of situations where the intercept of the calibration curve is nonzero and 4) a consideration of the errors in cahbration parameters (slope and intercept). 

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