Univariate approach

Environmental studies are often characterized by large numbers of variables measured on many samples. When poor understanding of the system exists one tends to rely upon the "measure everything and hope that the obvious will appear" approach. The problem is that in complex chemical systems significant patterns in the data are not always obvious when one examines the data one variable at a time. Interactions among the measured chemical variables tend to dominate the data and this useful information is not extracted by univariate approaches. 

Multiv te calibration offers several advantages over univariate approaches ... 

The quality of a model depends on the quality of the samples used to calculate it (or, to say it using the univariate approach, the quality of any traditional univariate calibration cannot be better than the quality of the standards employed to measure the analyte). Although this statement is trivial, the discussion on how many samples and which samples are required to develop a good predictive model is still open, so only general comments will be given. Below, we consider that the quality of the measurement device fits the purpose of the analytical problem. 

Moberg et al. [90] used ICP-MS to determine Cd in fly ash and metal alloys since severe spectral overlaps arose, multivariate regression outperformed other univariate approaches. They also studied whether day-to-day ICP-MS recalibration could be avoided so that the calibration set could be constructed on several runs. 

B. Tyler, Interpretation of TOF-SIMS images multivariate and univariate approaches to image de-noising, image segmentation and compound identification, Appl. Surf. Sci., 203-204, 2003, 825-831. 

Failure of Univariate Optimization. In the univariate approach to optimization, all variables but one are held constant at arbitrary values while the remaining variable is changed until an "optimum" response is found. The process is then repeated for each successive variable, using the "optimum" value for any variables that have now been "optimized" and arbitrary values for all the remaining variables except the one that is presently being investigated. 

Figure 1 illustrates the failure of the conventional univariate approach in finding the optimum conditions for a hypothetical SFC separation in which the temperature and density are to be optimized. The temperature is held constant at some arbitrary value while the density is varied (points A thru F). When the optimum density at that arbitrary temperature is located (point E), the temperature is then varied while holding the density constant at its "optimum" value (points G thru I) until an optimum temperature is found (point H). 

Point H corresponds to the best result obtained by the univariate approach, but it is obviously not the true optimum (point 8). While the univariate approach could be repeated at other initial temperatures in the hope of finding the true optimum, the probability of success is low. Moreover, it takes 9 experiments to find a false... 

Following the establishment of the initial simplex, the simplex begins moving away from the conditions that give the worst result (as described above) and systematically reaches the optimum set of conditions that yield the best separation (vertex 8). In contrast to the false optimum (point H) found by the univariate approach described earlier, the simplex method has located the true optimum density and temperature for this separation. 

The advantage of the GA variable selection approach over the univariate approach discussed earlier is that it is a true search for an optimal multivariate regression solution. One disadvantage of the GA method is that one must enter several parameters before it... 

This chapter constitutes an attempt to demonstrate the utility of multivariate statistics in several stages of the scientific process. As a provocation, it is suggested that the multivariate approach (in experimental design, in data description and in data analysis) will always be more informative and make generalizations more valid than the univariate approach. Finally, the multivariate strategy can be really enjoyable, not the least for its capacity to reveal hidden treasures in data that in a univariate analysis look like a set of random numbers. 

Finally, from Chapter 6, the utility of multivariate statistics in different stages of the scientific process (like design, description and analysis) appears to be more informative and more valuable than the univariate approach. 

Univariate analysis methods have been applied for the quantification of gas mixtures in several systems that we have studied, however, it becomes clear that more advanced techniques must be applied in more complicated systems. An example of this is shown in Fig. 6.9, which shows spectra of a gas mixture of C2H4, NO and H2O. Owing to the significant band overlap present between these components, it is clear that the implementation of a univariate approach will not allow the quantification of... 

The discipline of chemometrics can play an important role in the effective application of infrared imaging to agri-food materials. In a univariate approach, a researcher extracts a specific observable (e.g. frequency or band height) from a set of spectra as a series of scalar quantities. The process is then repeated for additional observables. In many cases, this approach is sufficient to meet the researcher s needs.49 However, the task of extracting the most useful information possible from an infrared image dataset, which may contain thousands of spectra measured at hundreds or even thousands of individual frequencies, often requires a different strategy. It simply may not be possible for the researcher to manually examine and extract information from each of these spectra. The researcher may, therefore, choose to employ a chemometric method instead. Chemometric methods can reduce a large dataset... 

In most multiparameter instrumental techniques, the parameters can be classified into two types independent and dependent. Independent parameters can be optimized independently from all other parameters and can therefore be subjected to a univariate approach i.e., the variable can be adjusted until the largest signal-to-noise ratio (SNR) is obtained and set at that value for the best instrumental performance. This is the simplest situation and can be handled in a very straightforward manner. 

In order to document the key characteristics of the tourist, a number of themes will be explored here. First, the existence and nature of tourist stereotypes will be considered. Then, the role of the tourist as a social position in society will be pursued. This treatment, together with some important conceptual schemes that help organise the stereotypes and role-related studies, will be followed by a consideration of the rich range of univariate approaches frequently used to classify tourists. 

The estimates by this approach are veiy much better titan the univariate approaches in this particular example. Figure 5.9 shows the predicted versus known concentrations for pyrene. The root mean square error of prediction is now... 

By far the simplest are univariate approaches. It is important not to overcomplicate a problem if not justified by the data. Most conventional chromatography software contains methods for estimating ratios between peak intensities. If two spectra are sufficiently dissimilar then this method can work well. The measurements most diagnostic for each compound can be chosen by a number of means. For the data in Table 6.1 we... 

The desirability function (g) that scaled the total analysis time (T) was also a sigmoidal transformation that gave values close to zero for analysis times greater than 45 min and values approaching one for total analysis times close to 6 min. Preliminary experiments, mostly performed by a univariate approach, were used to set these limits. 

Felhofer et al. (46) reported an application describing the separation of five bisphenols (bisphenol E, bisphenol A, bisphenol AP, tetramethyl bisphenol A, and bisphenol P) by MEKC. It has been well established that bisphenols can reach the environment, and also the human body (47). Bisphenols are widely employed in the manufacture of plastics, especially those used in food and beverage packages, baby bottles, and water supply pipes. In this study, a univariate approach was first developed using a BGE composed of borate, SDS, and acetonitrile. The goal was to achieve the best separation of the... 

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