Systematic chemometrics

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. 

Under eonstant experimental conditions, the number of Raman seattered photons is proportional to analyte eoneentration. Quantitative methods can be developed with simple peak height measurements [1]. Just as with infrared calibrations, multiple components in eomplex mixtures ean be quantified if a distinet wavelength for each component can be identified. When isolated bands are not readily apparent, advaneed multivariate statistical tools (chemometrics) like partial least squares (PLS) ean help. These work by identifying all of the wavelengths correlated to, or systematically changing with, the eoneentration of a eomponent [2], Raman speetra also can be correlated to other properties, sueh as stress in semieonduetors, polymer erystal-linity, and particle size, because these parameters are refleeted in the loeal moleeular environment. 

From a chemometric point of view, the only constraint is that an appropriate column preprocessing, such as autoscaling, is required in order to eliminate systematic differences between variables of a different nature. Then, when the original variables are very numerous, it is possible to join the PCs computed separately for each variable block. 

Although application of chemometrics in sample preparation is very uncommon, several optimisation techniques may be used to optimise sample preparation systematically. Those techniques can roughly be divided into simultaneous and sequential methods. The main restrictions of a sequential simplex optimisation [6,7] find their origin in the complexity of the optimisation function needed. This function is a predefined function, often composed of several criteria. Such a composite criterion may lead to ambiguous results [8]. Other important disadvantages of simplex optimisation methods are that not seldom local optima are selected instead of global optima and that the number of experiments needed is not known beforehand. 

A. Moreda-Pineiro, P. Bermejo-Barrera and A. Bermejo-Barrera, Chemometric investigation of systematic error in the analysis of biological materials by flame and electrothermal atomic absorption spectrometry. Anal. Chim. Acta, 560(1-2), 2006, 143-152. 

A. Moreda-Pineiro, A. Marcos, A. Fisher and S. J. Hill, Chemometrics approaches for the study of systematic error in inductively coupled plasma atomic emission spectrometry and mass spectrometry, J. Anal. At. Spectrom., 16(4), 2001, 350-359. 

One possibility is to classify the methods used in the various steps of the analytical process (see also Section 1.5). Note that the analytical process usually starts with the definition or selection of the matter to be investigated. Here it is very important to realize that every sample or object of investigation has a history. Because this history may cause severe systematic errors, THIERS [1957] explains Unless the complete history of any sample is known with certainty, the analyst is well advised not to spend his time in analyzing it. Clearly, in such circumstances one should be extremely cautious about drawing conclusions from chemometric interpretations even where data are available. 

A new approach is the application of chemometrics (and neural networks) in modeling [73]. This should allow identification of the parameters of influence in solvent-resistant nanofiltration, which may help in further development of equations. Development of a more systematic model for description and prediction of solute transport in nonaqueous nanofiltration, which is applicable on a wide range of membranes, solvents and solutes, is the next step to be taken. The Maxwell-Stefan approach [74] is one of the most direct methods to attain this. 

To undertake QSRR studies one needs two kinds of input data. One is a set of quantitatively comparable retention data (dependent variable) for a sufficiently large (for statistical reasons) set of analytes. The other is a set of quantities (independent variables) assumed to account for structural differences among the chromatographed analytes. Through the use of chemometric computational techniques, retention parameters are characterized in terms of various descriptors of analytes (or their combinations) or in terms of systematic knowledge extracted (learned) from these descriptors. 

Peters and Moldowan, 1993, p. 137). Illich et al. (1997) found a systematic regional decrease in the DBT/4-methylnaphthalene ratio for many Algerian oil samples, ranging from >0.12 at Hassi Messaoud to <0.06 at Zarzaitine, similar to our observations for DBT/2-MeN. They used chemometric analysis of biomarker and isotope data to conclude that their Hassi Messaoud and Zarzaitine oil samples originated from Silurian and Devonian source rocks, respectively, consistent with our interpretation. The ratio of sums of the methyldibenzothiophenes to methylphenanthrenes also separates the Silurian from Devonian oil samples (MeDBT/MeP = 0.18-0.34 versus 0.07-0.11, respectively. Table 3). These classes of compounds have similar partition coefficients between water and oil and thus, their ratio is not readily affected by water washing. 

Contemporary spectrometers are able to produce huge amounts of data within a very short time. This development continues due to the introduction of array detectors for spectral imaging. The utilization of as much as possible of the enclosed spectral information can only be achieved by chemometric procedures for data analysis. The most commonly used procedures for evaluation of spectra are systematically arranged in Fig. 22.2 with the main emphasis on application, i.e. the variety of procedures was divided into methods for qualitative and quantitative analysis. Another distinctive feature refers to the mathematical algorithms on which the procedures are based. The dominance of multivariate over univariate methods is clearly discernible from Fig. 22.2. 

See also Chemometrics and Statistics Optimization Strategies. Chromatography Overview Principies. Derivatization of Analytes. Extraction Soivent Extraction Principies Solid-Phase Extraction. Forensic Sciences Systematic Drug Identification. Gas Chromatography Mass Spectrometry. Hormones Steroids. Liquid Chromatography Liquid Chromatography-Mass Spectrometry. Mass Spectrometry Atmospheric Pressure Ionization Techniques Forensic Applications. 

In trace analysis it is not sufficient simply to report a level of reproducibility for the actual determination of an analyte. Evaluating the quality of an analysis requires a knowledge of the reproducibility and the uncertainty arising from systematic effects (- Chemometrics). Errors in sampling and/or sample preparation may be orders of magnitude greater than the standard deviation observed in several repetitions of a determination. 

Chemometrics usually applied for the analyses of NIR spectra is described in detail in Chapter 7 and in other literature [4-8]. The most important and essential points remaining in this field seem to be the generalization and the systematic maintenance of calibration... 

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