Introduction to Multivariate Calibration: A Practical Approach

1.1. Chemometrics: what's in a name?

1.2. Univariate and multivariate calibration

1.3. The order and the ways

1.4. Why multivariate calibration?

1.5. Near infrared spectroscopy: the analytical dream

1.6. Multi-way calibration and new advantages

1.7. References

2. First-order multivariate models: CLS

2.1. Direct and inverse models

2.2. Classical least-squares

2.3. The CLS calibration phase

2.4. Why least-squares? Mathematical requirements

2.5. The CLS prediction phase

2.6. The CLS vector of regression coefficients

2.7. A CLS algorithm

2.9. Spectral residuals and sample diagnostic

2.10. The first-order advantage

2.11. A real case

2.12. Advantages and limitations of CLS

2.13. Exercises

2.13. References

3. First-order multivariate models: ILS

3.1. Why calibrating the other way around? A fantastic idea

3.2. The ILS calibration phase

3.3. Mathematical requirements

3.4. The ILS prediction phase

3.5. An ILS algorithm

3.6. The validation of the ILS model

3.7. Advantages and limitations of ILS

3.8. The successive projections algorithm

3.10. How to improve ILS

3.11. Exercises

3.12. References

4. Principal component analysis: PCA

4.2. Real and latent variables

4.3. Principal components

4.4. Significant loadings and scores

4.5. Non-significant loadings and scores

4.6. Sample classification with PCA

4.7. Multivariate calibration with PCA

4.8. Exercises

4.9. References

5. First-order multivariate models: PCR

5.1. Combination of PCA and ILS: another fantastic idea

5.2. Matrix compression and decompression

5.3. The PCR calibration phase

5.4. Mathematical requirements

5.5. The PCR prediction phase

5.6. The PCR vector of regression coefficients

5.8. What is the value of A?

5.9. Advantages and limitations of PCR

5.10. A real case

5.11. What can be better than PCR?

5.12. Exercises

5.13. References

6. The optimum number of latent variables

6.1. The importance of estimating the optimum A

6.2. Explained variance

6.3. Visual inspection of loadings

6.4. Leave-one-out cross validation

6.5. Cross-validation statistics

6.6. Monte Carlo cross-validation

6.7. Other methods

6.8. The principle of parsimony

6.10. Exercises

6.11. References

7. First-order multivariate models: PLS

7.1. The PLS philosophy

7.2. The PLS calibration phase

7.3. Mathematical requirements

7.4. The number of latent variables

7.5. The PLS prediction phase

7.6. The vector of PLS regression coefficients

7.8. Advantages and limitations of PLS

7.9. A real case

7.10. PLS-1 and PLS-2 models

7.11. Discriminant PLS

7.12. Beyond PLS

7.13. References

8. Comparison of models

8.1. Which is the best model?

8.2. The randomization test

8.3. How the test works

8.4. Algorithm for the randomization test

8.5. PCR, PLS-1 and PLS-2: when, how and why

8.6. Linear and non-linear models: when, how and why

8.7. Tests of multivariate non-linearity

8.9. Conclusions

8.10. References

9. Data pre-processing

9.1. Selection of calibration samples

9.3. Selection of wavelengths to build the model

9.4. The vector of regression coefficients as selector

9.5. Interval-PLS

9.6. A real case

9.7. Other selection methods

9.8. Mathematical transformation of spectra

9.9. Mean centering

9.10. Smoothing and derivatives: advantages and hazards

9.11. Multiplicative correction

9.12. Other pre-processing methods

9.14. Is pre-processing always useful?

9.15. Real cases

9.16. A library of MATLAB codes

9.17. Exercises

9.18. References

10. Analytical figures of merit

10.1. Usefulness of figures of merit

10.2. Sensitivity

10.3. Selectivity

10.4. Prediction uncertainty

10.5. Effect of mathematical pre-processing

10.6. Detection limit

10.7. The blank leverage

10.8. Quantitation limit

10.9. Other figures of merit

10.10. A real case

10.11. References

11. MVC1: software for first-order multivariate calibration

11.1. Downloading and installing the software

11.3. Example 1: determination of bromhexine in anti-cough syrups by UV-visible spectrophotometry

11.4. Example 2: determination of I5 in reaction mixtures by UV-visible spectrophotometry

11.5. Example 3: determination of moisture, fat, protein and starch in corn seeds

11.6. More examples

11.7. Other calibration models

11.8. Free and commercial software

11.9. References

12. Non-linearity and artificial neural networks

12.1.      Linear and non-linear problems

12.2.      Artificial neural networks

12.3.      Radial basis functions

12.4.      Neural networks in MVC1

12.5.      A real case

12.6.      References