Leave-one-out cross-validation methods

As with univariate and multivariate calibration, three-way calibration assumes linear additivity of signals. When the sample matrix influences the spectral profiles or sensitivities, either care must be taken to match the standard matrix to those of the unknown samples, or the method of standard additions must be employed for calibration. Employing the standard addition method with three-way analysis is straightforward only standard additions of known analyte quantity are needed [42], When the standard addition method is applied to nonbilinear data, the lowest predicted analyte concentration that is stable with respect to the leave-one-out cross-validation method is unique to the analyte. 

With their natural logarithm, the data in Table 2 and Table 3 were input to the Eq. (1) to build early-warning models in R environment (Wold, et al., 2001, Mevik Wehrens, 2007), respectively. The model parameters in Chongqing City and Ningbo City were shown in Table 5. One was called Chongqing Model, the other was named Ningbo model. All the models were assessed by Leave-One-Out Cross Validation method (LOOCV), and the maximum model error was less than 15%. 

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