Multivariate calibration models accuracy

A solvent free, fast and environmentally friendly near infrared-based methodology was developed for the determination and quality control of 11 pesticides in commercially available formulations. This methodology was based on the direct measurement of the diffuse reflectance spectra of solid samples inside glass vials and a multivariate calibration model to determine the active principle concentration in agrochemicals. The proposed PLS model was made using 11 known commercial and 22 doped samples (11 under and 11 over dosed) for calibration and 22 different formulations as the validation set. For Buprofezin, Chlorsulfuron, Cyromazine, Daminozide, Diuron and Iprodione determination, the information in the spectral range between 1618 and 2630 nm of the reflectance spectra was employed. On the other hand, for Bensulfuron, Fenoxycarb, Metalaxyl, Procymidone and Tricyclazole determination, the first order derivative spectra in the range between 1618 and 2630 nm was used. In both cases, a linear remove correction was applied. Mean accuracy errors between 0.5 and 3.1% were obtained for the validation set. 

In order to construct a calibration model, the values of the parameters to be determined must be obtained by using a reference method. The optimum choice of reference method will be that providing the highest possible accuracy and precision. The quality of the results obtained with a multivariate calibration model can never exceed that of the method used to obtain the reference values, so the choice should be carefully made as the quality of the model will affect every subsequent prediction. The averaging of random errors inherent in regression methods can help construct models with a higher precision than the reference method. 

In multivariate calibration, accuracy reports the closeness of agreement between the reference value and the value found by the calibration model and is generally expressed as the root mean square error of prediction (RMSEP, as described in section 4.5.6) for a set of validation samples ... 

Luo et al. [83] used an ANN to perform multivariate calibration in the XRF analysis of geological materials and compared its predictive performance with cross-validated PLS. The ANN model yielded the highest accuracy when a nonlinear relationship between the characteristic X-ray line intensity and the concentration existed. As expected, they also found that the prediction accuracy outside the range of the training set was bad. 

An important lesson learned from the study is that there is a trade-off between maximizing prior information utilization and robustness concerning the accuracy of such information. Multivariate calibration methods range from explicit methods with maximum use of prior information (e.g., OLS, least robust when accurate model is not obtainable), hybrid methods with an inflexible constraint (e.g., HLA), hybrid methods with a flexible constraint (e.g., CR), and implicit methods with no prior information (e.g., PLS, most robust, but is prone to be misled by spurious correlations). We believe CR achieves the optimal balance between these ideals in practical situations. 

An independent test set consisting of 13 new samples with RME and/or SME in jet fuel in concentrations ranging from 0 to 10 ppm were made a few weeks later. The regression model was used to predict the concentration of RME and SME with an accuracy of 2.6 and 1.2 ppm, respectively. The predictions confirm that ESI-MS and multivariate calibration can be used to identify and quantify trace amounts of FAME in jet fuel at the 5 ppm level based on recognition of FAME spectra. 

The strengths of the factor-based methods lie in the fact that they are multivariate. The diagnostics are excellent in both the calibration and prediction phases. Improved precision and accuracy over univariate methods can often be realized because of the multivariate advantage. Ultimately, PLS and PCR are able to model complex data and identify when the models are no longer valid. This is an extremely powerful combination. 

CONTENTS 1. Chemometrics and the Analytical Process. 2. Precision and Accuracy. 3. Evaluation of Precision and Accuracy. Comparison of Two Procedures. 4. Evaluation of Sources of Variation in Data. Analysis of Variance. 5. Calibration. 6. Reliability and Drift. 7. Sensitivity and Limit of Detection. 8. Selectivity and Specificity. 9. Information. 10. Costs. 11. The Time Constant. 12. Signals and Data. 13. Regression Methods. 14. Correlation Methods. 15. Signal Processing. 16. Response Surfaces and Models. 17. Exploration of Response Surfaces. 18. Optimization of Analytical Chemical Methods. 19. Optimization of Chromatographic Methods. 20. The Multivariate Approach. 21. Principal Components and Factor Analysis. 22. Clustering Techniques. 23. Supervised Pattern Recognition. 24. Decisions in the Analytical Laboratory. 

Einbu et al. (4) also assessed the use of a combination of FTIR spectroscopy and a multivariate model for composition predictions, but applied to a CO2 absorption process using aqueous MEA. They constructed a model based on a very extensive calibration set of 86 samples, covering MEA concentration of 10 to 80 wt% and CO2 eoneentration of 0.0 to 0.5 mol CO2 per mol amine. Based on these calibration samples, the model was calculated to have a relative predictive uncertainty of 1.4% for MEA and 3.0% for CO2. It has also successfully been use for continuous in-line monitoring of an operating pilot plant, but no quantitative results for the prediction accuracy ate given. 

The importance of validating the multivariate model cannot be over-emphasised. In particular, the data should be checked for outliers , that is, samples whose properties are different from the rest of the calibration set. If outliers are not detected and either removed or corrected, serious errors may be built into the model. Check for outliers by plotting actual compositions (Y data) against predicted compositions. In a good model, all the samples will lie close to the line of best fit. Outliers will be isolated and associated with poor predictive accuracy. 

Often, the use of a fixed reference sample is also used to help improve the precision and accuracy of multivariate models in which many spectra are used together to create a calibration or training set. In these cases, the reference spectrum is the mean of the entire set of Raman spectra used for calibration and it is subtracted from each of the individual calibration spectra as well as any subsequent spectra from which a prediction is to be made. This approach is called mean centering. ... 

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