Discriminant-regression analysis

A systematic study was carried out using in parallel 50 standard solutions for each concentration of three natural colorants (curcumin, carminic acid, and caramel as yellow, red, and brown, respectively). No false positive results for synthetics were obtained up to concentrations of 15 and 20 ng/ml for natural red and yellow colorants, respectively, or 110 ng/ml for natural brown colorant. The concentrations have to be high enough to prove that the screening method is able to accurately discriminate natural and synthetic colorants. To make a clear interpretation of the quantitative UV-Vis spectrum, linear regression analysis was used. Quantitative UV-Vis analysis of a dye ° can be calculated according to the following formula ... 

One of the major uses of multivariate techniques has been the discrimination of samples based on sensory scores, which also has been found to provide information concerning the relative importance of sensory attributes. Techniques used for sensory discrimination include factor analysis, discriminant analysis, regression analysis, and multidimensional scaling (8, 10-15). 

Regression analysis with the dependent class variable y where y = 1 or y = 2 should yield results similar to those from discriminant analysis [LACHENBRUCH, 1975]. Therefore let us first try to predict class memberships by the two variables, x, and x2, without using an intercept in the regression model. 

Patients with good adherence to therapy have a higher incidence of adverse effects (12). Logistic regression analysis identified four factors that discriminate adherent (n = 48) from non-adherent (n = 30) patients the course of the illness, the employment status of a key relative, age at onset of the illness, and the presence or absence of adverse effects. 

Equations (25) are linear with respect to x and this classification technique is referred to as /inear discriminant analysis, with the discriminant function obtained by least squares analysis, analogous to multiple regression analysis. 

Linear discriminant analysis is closely related to multiple regression analysis. Whereas in multiple regression, the dependent variable is assumed to be a continuous function of the independent variables, in discriminant analysis the dependent variable, e.g. Group A or Group B, is nominal and discrete. Given this similarity, it is not surprising that the selection of appropriate variables to perform a discriminant analysis should follow a similar scheme to that employed in multiple regression (see Chapter 6). 

As with multiple regression analysis, the most commonly used selection procedures involve stepwise methods with the F-test being applied at each stage to provide a measure of the value of the variable to be added, or removed, in the discriminant function. The procedure is discussed in detail in Chapter 6. 

Although intravenous anaesthetics can inhibit in-vitro the activity of PMNs, " their in-vivo effect on the phagocyte-dependent immune system is not clearly defined especially in cases of short term anaesthesia. Our study indicates that PMN CL, if analyzed by an appropriate statistical test, seems to be modified also by short term intravenous anaesthesia. In fact, both discriminant analysis (Table 2) and regression analysis between luminol- and lucigenin-dependent CL (Figure 1) indicate that PMN CL is modified also after many hours of a short time intravenous anaesthesia. In... 

Regression analysis is often employed to fit experimental data to a mathematical model. The purpose may be to determine physical properties or constants (e.g., rate constants, transport coefficients), to discriminate between proposed models, to interpolate or extrapolate data, etc. The model should provide estimates of the uncertainty in calculations from the resulting model and, if possible, make use of available error in the data. An initial model (or models) may be empirical, but with advanced knowledge of reactors, distillation columns, other separation devices, heat exchangers, etc., more sophisticated and fundamental models can be employed. As a starting point, a linear equation with a single independent variable may be initially chosen. Of importance, is the mathematical model linear In general, a function,/, of a set of adjustable parameters, 3y, is linear if a derivative of that function with respect to any adjustable parameter is not itself a function of any other adjustable parameter, that is. 

In nonlinear regression analysis, we search for those parameter t alues that minimize the sum of the squares of the differences beiw een the measured values and the calculated values for all the data points.- Not only can nonlinear regression find the best estimates of parameter values, it can al,so be used to discriminate between different rate law models, such as the Langmutr-Hin-shelw ood models discussed in Chapter 10. Many software programs are available to find these parameter values so that all one has to do is enter the data, The Polymath software will be used to illustrate this technique. In order to carry out the search efficiently, in some cases one has to enter initial estimates of the parameter -alues close to the actual values. These estimates can be obtained using Ihe linear-least-squares technique discussed on the CD-ROM Professional Reference Shelf. 

PLS (Partial Least Squares) regression was used for quantification and classification of aristeromycin and neplanocin A (Figure 4). Matlab was used for PCA (Principal Components Analysis) (according to the NIPALS algorithm) to identify correlations amongst the variables from the 882 wavenumbers and reduce the number of inputs for Discriminant Function Analysis (DFA) (first 15 PCA scores used) (Figure 5). 

COMPACT (computer-optimized molecular parametric analysis of chemical toxicity) [582, 583], a discriminant analysis approach, is described to predict carcinogenicity and other forms of toxicity involving the formation of reactive intermediates by determining the structural criteria for substrate specificity towards cytochrome P-450 enzymes it is claimed that the method is about 75% predictive for rodent carcinogenicity [583]. Recently, a discriminant-regression model was described [584]. It applies stepwise discriminant analysis to form clusters of compounds for which quantitative relationships are derived by multiple regression analysis. 

The adaptive least squares (ALS) method [396, 585 — 588] is a modification of discriminant analysis which separates several activity classes e.g. data ordered by a rating score) by a single discriminant function. The method has been compared with ordinary regression analysis, linear discriminant analysis, and other multivariate statistical approaches in most cases the ALS approach was found to be superior to categorize any numbers of classes of ordered data. ORMUCS (ordered multicate-gorial classification using simplex technique) [589] is an ALS-related approach which... 

In order to establish this function, a logical preselection of appropriate data is carried out safeguarding a sufficient representation of the net worth, financial position, and results of the corporation. Here, it should be kept in mind that the financial ratios selected have to show only moderate correlations in order to avoid multicorrelation problems known from regression analysis. With the help of multiple discriminant... 

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