Multivariate direct models

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 the direct standardization introduced by Wang et al. [42] one finds the transformation needed to transfer spectra from the child instrument to the parent instrument using a multivariate calibration model for the transformation matrix = ZgF. The transformation matrix F (qxq) translates spectra Zg that are actually measured on the child instrument B into spectra Z that appear as if they were measured on instrument A. Predictions are then obtained by applying the old calibration model to these simulated spectra Z ... 

Authors have applied the principles of the electronic tongue to solve a mixture of three components by direct voltammetric analysis. The approach departs from the overlapped voltammogram, and for the resolution of the three components mixture, a multivariate calibration model is built using WNN. The chemical case in the presented study corresponds to the direct multivariate determination of the oxidizable aminoacids tryptophan (Trp), cysteine (Cys) and tyrosine (Tyr), from the differential-pulse voltammetric signal of a platinum electrode. 

One of the proposals [192] combines flow-through diffuse reflectance optosensing with multivariate regression modeling for the simultaneous multiresidue monitoring of nitrophenol derivatives (2-, 4-, and 2,4-dinitrophenol) at trace level concentrations. Improved detectability is assured as a consequence of the direct optical detection onto the sorbent material. 

A large variety of techniques are available to develop predictive models for toxicity. These range from relatively simple techniques to relate quantitative levels of potency with one or more descriptors to more multivariate techniques and ultimately the so-called expert systems that lead the user directly from an input of structure to a prediction. These are outlined briefly below. 

These various covariance models are Inferred directly from the corresponding indicator data i(3 z ), i-l,...,N. The indicator kriging approach is said to be "non-parametric, in the sense that it draws solely from the data, not from any multivariate distribution hypothesis, as was the case for the multi- -normal approach. 

Among nonlocal methods, those based on linear projection are the most widely used for data interpretation. Owing to their limited modeling ability, linear univariate and multivariate methods are used mainly to extract the most relevant features and reduce data dimensionality. Nonlinear methods often are used to directly map the numerical inputs to the symbolic outputs, but require careful attention to avoid arbitrary extrapolation because of their global nature. 

Despite the broad definition of chemometrics, the most important part of it is the application of multivariate data analysis to chemistry-relevant data. Chemistry deals with compounds, their properties, and their transformations into other compounds. Major tasks of chemists are the analysis of complex mixtures, the synthesis of compounds with desired properties, and the construction and operation of chemical technological plants. However, chemical/physical systems of practical interest are often very complicated and cannot be described sufficiently by theory. Actually, a typical chemometrics approach is not based on first principles—that means scientific laws and mles of nature—but is data driven. Multivariate statistical data analysis is a powerful tool for analyzing and structuring data sets that have been obtained from such systems, and for making empirical mathematical models that are for instance capable to predict the values of important properties not directly measurable (Figure 1.1). 

QSPR models have been developed by six multivariate calibration methods as described in the previous sections. We focus on demonstration of the use of these methods but not on GC aspects. Since the number of variables is much larger than the number of observations, OLS and robust regression cannot be applied directly to the original data set. These methods could only be applied to selected variables or to linear combinations of the variables. 

Standardizing the spectral response is mathematically more complex than standardizing the calibration models but provides better results as it allows slight spectral differences - the most common between very similar instruments - to be corrected via simple calculations. More marked differences can be accommodated with more complex and specific algorithms. This approach compares spectra recorded on different instruments, which are used to derive a mathematical equation, allowing their spectral response to be mutually correlated. The equation is then used to correct the new spectra recorded on the slave, which are thus made more similar to those obtained with the master. The simplest methods used in this context are of the univariate type, which correlate each wavelength in two spectra in a direct, simple manner. These methods, however, are only effective with very simple spectral differences. On the other hand, multivariate methods allow the construction of matrices correlating bodies of spectra recorded on different instruments for the above-described purpose. The most frequent choice in this context is piecewise direct standardization... 

Another direction of development of the data set is to strengthen the in vitro-in vivo correlations and develop multivariate models to predict in vivo endpoints, such as therapeutic effects and adverse events. In this respect, it will be interesting to examine which data (among in silico descriptors, in vitro primary and secondary data, in vitro functional data, etc.) are most appropriate to derive robust and predictive models. 

For effective control of crystallizers, multivariable controllers are required. In order to design such controllers, a model in state space representation is required. Therefore the population balance has to be transformed into a set of ordinary differential equations. Two transformation methods were reported in the literature. However, the first method is limited to MSNPR crystallizers with simple size dependent growth rate kinetics whereas the other method results in very high orders of the state space model which causes problems in the control system design. Therefore system identification, which can also be applied directly on experimental data without the intermediate step of calculating the kinetic parameters, is proposed. 

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