Limitations, chemometrics

Theoretically based correlations (or semitheoretical extensions of them), rooted in thermodynamics or other fundamentals are ordinarily preferred. However, rigorous theoretical understanding of real systems is far from complete, and purely empirical correlations typically have strict limits on apphcabihty. Many correlations result from curve-fitting the desired parameter to an appropriate independent variable. Some fitting exercises are rooted in theory, eg, Antoine s equation for vapor pressure others can be described as being semitheoretical. These distinctions usually do not refer to adherence to the observations of natural systems, but rather to the agreement in form to mathematical models of idealized systems. The advent of readily available computers has revolutionized the development and use of correlation techniques (see Chemometrics Computer technology Dimensional analysis). 

We will explore the two major families of chemometric quantitative calibration techniques that are most commonly employed the Multiple Linear Regression (MLR) techniques, and the Factor-Based Techniques. Within each family, we will review the various methods commonly employed, learn how to develop and test calibrations, and how to use the calibrations to estimate, or predict, the properties of unknown samples. We will consider the advantages and limitations of each method as well as some of the tricks and pitfalls associated with their use. While our emphasis will be on quantitative analysis, we will also touch on how these techniques are used for qualitative analysis, classification, and discriminative analysis. 

A more recently introduced technique, at least in the field of chemometrics, is the use of neural networks. The methodology will be described in detail in Chapter 44. In this chapter, we will only give a short and very introductory description to be able to contrast the technique with the others described earlier. A typical artificial neuron is shown in Fig. 33.19. The isolated neuron of this figure performs a two-stage process to transform a set of inputs in a response or output. In a pattern recognition context, these inputs would be the values for the variables (in this example, limited to only 2, X and x- and the response would be a class variable, for instance y = 1 for class K and y = 0 for class L. 

Workman, J. and Mark, H., Chemometrics in Spectroscopy Comparison of Goodness of Fit Statistics for Linear Regression - Part 3, Computing Confidence Limits for the Correlation Coefficient, Spectroscopy 19(7), 31-33 (2004). 

Sections on matrix algebra, analytic geometry, experimental design, instrument and system calibration, noise, derivatives and their use in data analysis, linearity and nonlinearity are described. Collaborative laboratory studies, using ANOVA, testing for systematic error, ranking tests for collaborative studies, and efficient comparison of two analytical methods are included. Discussion on topics such as the limitations in analytical accuracy and brief introductions to the statistics of spectral searches and the chemometrics of imaging spectroscopy are included. 

A critical attitude towards the results obtained in analysis is necessary in order to appreciate their meaning and limitations. Precision is dependent on the practical method and beyond a certain degree cannot be improved. Inevitably there must be a compromise between the reliability of the results obtained and the use of the analyst s time. To reach this compromise requires an assessment of the nature and origins of errors in measurements relevant statistical tests may be applied in the appraisal of the results. With the development of microcomputers and their ready availability, access to complex statistical methods has been provided. These complex methods of data handling and analysis have become known collectively as chemometrics. 

Besides the mathematical outline, the methods are applied to real data examples from chemometrics for supporting better understanding and applicability of the methods. Prerequisites and limitations for the applicability are discussed, and results from different methods are compared. 

With the appearance of chemometric approach, novel hyphenation instrument configurations and the improvement of limit of detections and quantifycations, analyte description and characterization are usually not the rate-limiting step in bioanalysis. 

Chemometric quality assurance via laboratory and method intercomparisons of standardized test data sets, finally, is becoming recognized as essential for establishing the validity of detection decisions and estimated detection limits, especially when treating multidimensional data with sophisticated algorithms including several chemical components. 

When from initial experiments, conditions that indicate the enantioselectivity of the system towards a given enantiomer pair or towards a limited series of substances are known, one might optimize their separation. To obtain optimal conditions, the different chemometric techniques used for method optimization in classic chromatographic or electrophoretic separations can also be applied for the chiral ones. Different experimental design approaches, using both screening and response surface designs can be In Reference 331, for... 

The use of ultraviolet (UV) spectroscopy for on-line analysis is a relatively recent development. Previously, on-line analysis in the UV-visible (UV-vis) region of the electromagnetic spectrum was limited to visible light applications such as color measurement, or chemical concentration measurements made with filter photometers. Three advances of the past two decades have propelled UV spectroscopy into the realm of on-line measurement and opened up a variety of new applications for both on-line UV and visible spectroscopy. These advances are high-quality UV-grade optical fiber, sensitive and affordable array detectors, and chemometrics. 

The acoustic spectra were recorded simultaneously as other process experiments, in themselves not related to acoustic chemometrics, were carried out. This resulted in many days with stable conditions in the reactor, and no particular variations in the acoustic signals. Therefore there were only a limited number of days (hours) which displayed significant variation in process parameters, which are necessary for successful multivariate analysis and calibration. 

Before selecting a process analytical technology to implement, it is helpful to understand the capabilities and limitations of the technology. Good introductions to NIR spectroscopy and instrumentation can be found in Chapter 5, and to chemometric methods in Chapter 12. NIR pharmaceutical applications are covered in Chapters 13 and 14. Additional information on NIR techniques and applications can be found in Williams, ... 

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