Multivariable statistical techniques

Joback, K. G., A Unified Appr oach to Physical Pr operiy Estimation Using Multivariate Statistical Techniques, M.S. Thesis, Massachusetts Institute of Technology, Cambridge, MA, 1984. 

PPR is a linear projection-based method with nonlinear basis functions and can be described with the same three-layer network representation as a BPN (see Fig. 16). Originally proposed by Friedman and Stuetzle (1981), it is a nonlinear multivariate statistical technique suitable for analyzing high-dimensional data, Again, the general input-output relationship is again given by Eq. (22). In PPR, the basis functions 9m can adapt their shape to provide the best fit to the available data. 

This example (Kosanovich et al., 1995) builds on the previous example and illustrates how multivariate statistical techniques can be used in a variety of ways to understand and compare process behavior. The charge to the reactor is an aqueous solution that is first boiled in an evaporator until the water content is reduced to approximately 20% by weight. The evaporator s contents are then discharged into a reactor in which 10 to 20 pounds of polymer residue can be present from the processing of the previous batch. 

However, there is a mathematical method for selecting those variables that best distinguish between formulations—those variables that change most drastically from one formulation to another and that should be the criteria on which one selects constraints. A multivariate statistical technique called principal component analysis (PCA) can effectively be used to answer these questions. PCA utilizes a variance-covariance matrix for the responses involved to determine their interrelationships. It has been applied successfully to this same tablet system by Bohidar et al. [18]. 

Shanmukh, S. Jones, L. Zhao, Y. P. Driskell, J. D. Tripp, R. A. Dluhy, R. A., Identifica tion and classification of respiratory syncytial virus (RSV) strains by surface enhanced Raman spectroscopy and multivariate statistical techniques, Anal. Bioanal. Chem. 2008, 390, 1551 1555... 

Summarizing, sequence comparison allows us to compute the quantitative distance between any two linguistic assertions. In this research, the assertions are those derived from the procedures described above. Once distances (similarity data) are computed that satisfy the metric axioms, the matrix of inter-assertion distances can be analyzed using a variety of multivariate statistical techniques. 

Data have been collected since 1970 on the prevalence and levels of various chemicals in human adipose (fat) tissue. These data are stored on a mainframe computer and have undergone routine quality assurance/quality control checks using univariate statistical methods. Upon completion of the development of a new analysis file, multivariate statistical techniques are applied to the data. The purpose of this analysis is to determine the utility of pattern recognition techniques in assessing the quality of the data and its ability to assist in their interpretation. 

Exploratory data analysis (3 ) is performed on the data base using multivariate statistical techniques. The objectives of... 

In the past few years, PLS, a multiblock, multivariate regression model solved by partial least squares found its application in various fields of chemistry (1-7). This method can be viewed as an extension and generalization of other commonly used multivariate statistical techniques, like regression solved by least squares and principal component analysis. PLS has several advantages over the ordinary least squares solution therefore, it becomes more and more popular in solving regression models in chemical problems. 

Among the multivariate statistical techniques that have been used as source-receptor models, factor analysis is the most widely employed. The basic objective of factor analysis is to allow the variation within a set of data to determine the number of independent causalities, i.e. sources of particles. It also permits the combination of the measured variables into new axes for the system that can be related to specific particle sources. The principles of factor analysis are reviewed and the principal components method is illustrated by the reanalysis of aerosol composition results from Charleston, West Virginia. An alternative approach to factor analysis. Target Transformation Factor Analysis, is introduced and its application to a subset of particle composition data from the Regional Air Pollution Study (RAPS) of St. Louis, Missouri is presented. 

Human perception of flavor occurs from the combined sensory responses elicited by the proteins, lipids, carbohydrates, and Maillard reaction products in the food. Proteins Chapters 6, 10, 11, 12) and their constituents and sugars Chapter 12) are the primary effects of taste, whereas the lipids Chapters 5, 9) and Maillard products Chapter 4) effect primarily the sense of smell (olfaction). Therefore, when studying a particular food or when designing a new food, it is important to understand the structure-activity relationship of all the variables in the food. To this end, several powerful multivariate statistical techniques have been developed such as factor analysis Chapter 6) and partial least squares regression analysis Chapter 7), to relate a set of independent or "causative" variables to a set of dependent or "effect" variables. Statistical results obtained via these methods are valuable, since they will permit the food... 

For phenolics in fruit by-products such as apple seed, peel, cortex, and pomace, an HPLC method was also utilized. Apple waste is considered a potential source of specialty chemicals (58,62), and its quantitative polyphenol profile may be useful in apple cultivars for classification and identification. Chlorogenic acid and coumaroylquinic acids and phloridzin are known to be major phenolics in apple juice (53). However, in contrast to apple polyphenolics, HPLC with a 70% aqueous acetone extract of apple seeds showed that phloridzin alone accounts for ca. 75% of the total apple seed polyphenolics (62). Besides phloridzin, 13 other phenolics were identified by gradient HPLC/PDA on LiChrospher 100 RP-18 from apple seed (62). The HPLC technique was also able to provide polyphenol profiles in the peel and cortex of the apple to be used to characterize apple cultivars by multivariate statistical techniques (63). Phenolic compounds in the epidermis zone, parenchyma zone, core zone, and seeds of French cider apple varieties are also determined by HPLC (56). Three successive solvent extractions (hexane, methanol, aqueous acetone), binary HPLC gradient using (a) aqueous acetic acid, 2.5%, v/v, and (b) acetonitrile fol-... 

It must be pointed out that the electronic nose and the electronic tongue methodology are able to show the authenticity of the product only if supported by the multivariate statistical techniques useful not only to classify but also to validate and predict unknown samples. 

Jobak, K.G. 1984. A unified approach to physical property estimation using multivariate statistical techniques. SM Thesis, Chem. Eng., Mass. Inst. Technol., Cambridge, MA. 

In addition to univariate statistical analysis, the data were also examined by means of multivariate statistical techniques. In particular, R-mode factor analysis was used, which is a very effective tool to interpret anomalies and to help identify their sources. Factor analysis allows grouping of anomalies by compatible geochemical associations from a geologic-mineralogical point of view, the presence of mineralizing processes, or processes connected to the surface environment. Based on this analysis, six meaningful chemical associations were identified (Fig. 15.8). 

Multivariate statistical techniques can be used to combine data from several classical analytical methods. In this way Simoneau et al. (2000) tested the quantification of CBEs in mixtures with cocoa butter by analysis of fatty acids by GC and triacyglycerols with both GC and HPLC. 

Quantitative structure-activity/pharmacokinetic relationships (QSAR/ QSPKR) for a series of synthesized DHPs and pyridines as Pgp (type I (100) II (101)) inhibitors was generated by 3D molecular modelling using SYBYL and KowWin programs. A multivariate statistical technique, partial least square (PLS) regression, was applied to derive a QSAR model for Pgp inhibition and QSPKR models. Cross-validation using the leave-one-out method was performed to evaluate the predictive performance of models. For Pgp reversal, the model obtained by PLS could account for most of the variation in Pgp inhibition (R2 = 0.76) with fair predictive performance (Q2 = 0.62). Nine structurally related 1,4-DHPs drugs were used for QSPKR analysis. The models could explain the majority of the variation in clearance (R2 = 0.90), and cross-validation confirmed the prediction ability (Q2 = 0.69) [ 129]. 

Differentiation between the stereoisomeric dexamethasone and betamethasone (Figure 13.2) has been investigated in detail [47-49]. While De Wasch et al. [47] differentiated from differences in relative abundances, Antignac et al. [48] proposed the use of multivariate statistical techniques, based on principal component analysis. Baseline separation between betamethasone, dexamethasone, and various related esters was reported by Arthur et al. [49] using a Cg column and a step gradient. 

Multivariate statistical techniques are commonly employed in near-IR quantitative and qualitative analysis because these approaches have been proven useful for extracting desired information from near-IR spectra, which often contain up to 1200 wavelengths of observation per spectrum. Principal component analysis/principal component regression (PCA/ PCR) is one such multivariate approach. Descriptions of this... 

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