Multivariate calibration models advantages

The main advantage of multivariate calibration based on CLS with respect to univariate calibration is that CLS does not require selective measurements. Selectivity is obtained mathematically by solving a system of equations, without the requirement for chemical or instrumental separations that are so often needed in univariate calibration. In addition, the model can use a large number of sensors to obtain a signal-averaging effect [4], which is beneficial for the precision of the predicted concentration, making it less susceptible to the noise in the data. Finally, for the case of spectroscopic data, the Lambert Bouguer Beer s law provides a sound foundation for the predictive model. 

The use of NIR spectra on sediment samples to predict certain constituents from calibration models is, by itself, one important development taking advantage of the speed and low cost of the method. This approach, though, only utilises a small proportion of the information on the organic chemical composition contained in the MR spectra. One alternative, then, is to use the whole NIR spectra as a fingerprint , which can be used to evaluate the variation in sediment composition both in time and space. The total variation represented by several hundred absorbance values can normally be compressed to less then 10 latent variables , components, by different multivariate statistical methods. Similar approaches are used in the process industry where hundred or thousand of signals, used to monitor the performance of some production process, are compressed to a finger print and followed over time. 

Multivariate calibration methods offer several advantages over univariate calibration methods. Signal averaging is achieved, since more than one measurement channel is employed in the analysis. Also concentrations of multiple species may be measured if they are present in the calibration samples. A calibration model is built by using responses from calibration standards. The analysis of unknown samples will suffer if a species is present in the sample that is not accounted for in the calibration model.This is mitigated somewhat by the ability to detect whether a sample is an outlier from the calibration set. Multivariate calibration approaches permit selective quantitation of several analytes of interest in complex combinatorial libraries using low-resolution instruments when overlapping responses from different species preclude the use of univariate analysis. Quantitative... 

An important advantage of multivariate calibration over univariate calibration is that, because many measurements are obtained from the same solution, the signal from the analytes and that from the interferences can be separated mathematically, so concentrations can be determined without the need for highly selective measurements for the analyte. This advantage has been termed the first-order advantage, and eqn (4.3) is also called the first-order calibration model. The term first-order means that the response from a test specimen is a vector (a first-order tensor). This nomenclature and the advantages of first-order calibration have been well described in the theory of analytical chemistry. To use this advantage, however, there is one major requirement the multivariate measurements of the calibrators must contain... 

Multivariable calibration permits the simultaneous determination of multicomponent mixtures and it is mainly based on spectroscopy data. Full-spectrum multivariate calibration methods offer the advantage of speed in the determination of the analytes, avoiding separation steps in the analytical procedures. Partial least squares (PLS) has become the usual first-order multivariate tool because of the quality of the calibration models obtained, the ease of its implementation, and the availability of software [27]. However, all first-order methods, of which PLS is no exception, are sensitive to the presence of unmodeled interferents, that is, compounds occurring in new samples that have not been included during the training step of the multivariate model. This situation is encountered... 

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. 

The advantages of these methods are based on their simplicit - tlie number of samples required to construct the models is relatively small, statistics are available that can be used to validate the models, and it is easier to describe these methods to the users of the models. The classical methods are also multivariate in nature and, therefore, have good diagnostics tools that can be used to detect violations of the assumptions both during the calibration and prediction phases. 

The multivariate quantitative spectroscopic analysis of samples with complex matrices can be performed using inverse calibration methods, such as ILS, PCR and PLS. The term "inverse" means that the concentration of the analyte of interest is modelled as a function of the instrumental measurements, using an empirical relationship with no theoretical foundation (as the Lambert Bouguer-Beer s law was for the methods explained in the paragraphs above). Therefore, we can formulate our calibration like eqn (3.3) and, in contrast to the CLS model, it can be calculated without knowing the concentrations of all the constituents in the calibration set. The calibration step requires only the instrumental response and the reference value of the property of interest e.g. concentration) in the calibration samples. An important advantage of this approach is that unknown interferents may be present in the calibration samples. For this reason, inverse models are more suited than CLS for complex samples. 

Multivariate techniques are inverse calibration methods. In normal least-squares methods, often called classical least-squares methods, the system response is modeled as a function of analyte concentration. In inverse methods, the concentrations are treated as functions of the responses. The latter has some advantages in that concentrations can be accurately predicted even in the presence of chemical and physical sources of interference. In classical methods, all components in the system need to be considered in the mathematical model produced (regression equation). 

Inverse least squares in an example of a multivariate method. In this type of model, the dependent variable (concentration) is solved by calculating a solution from multiple independent variables (in this case, the responses at the selected wavelengths). It is not possible to work backwards from the concentration value to the independent spectral response values because an infinite number of possible solutions exist. However, the main advantage of a multivariate method is the ability to calibrate for a constituent of interest without having to account for any interferences in the spectra. 

Most samples used for factor-based multivariate quantitative spectroscopic analysis are not simple mixtures. Otherwise, it would not be necessary to use these models and the calibration could be performed using a much simpler method. These models have the distinct advantage for complex samples because they can find the important information in the spectra and ignore the rest. In order to give the model the best chance to learn to recognize the information for the constituents of interest, it is important to train it using samples that emulate the unknowns as closely as possible. 

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