Stepwise discriminant analysis

Next, supervised-learning pattern recognition methods were applied to the data set. The 111 bonds from these 28 molecules were classified as either breakable (36) or non-breakable (75), and a stepwise discriminant analysis showed that three variables, out of the six mentioned above, were particularly significant resonance effect, R, bond polarity, Qa, and bond dissociation energy, BDE. With these three variables 97.3% of the non-breakable bonds, and 86.1% of the breakable bonds could be correctly classified. This says that chemical reactivity as given by the ease of heterolysis of a bond is well defined in the space determined by just those three parameters. The same conclusion can be drawn from the results of a K-nearest neighbor analysis with k assuming any value between one and ten, 87 to 92% of the bonds could be correctly classified. 

Metronidazole Hierarchical and stepwise classification, stepwise discriminant analysis and PCA Assure the quality of the drug 67... 

Jenrich, R. I. Stepwise Discriminant Analysis, in Statistical Methods for Digital Computers... 

Female adult budworm dry weights and the number of survivors of budworm were analyzed by multivariate analysis of variance to test for the effects of site and sex. Stepwise discriminant analysis was used to determine If tree chemical and physical parameters differed between sites (17). 

Stepwise discriminant analysis was used to determine how tree chemical, phenologlcal, and physical parameters differed between sites (Table VII). Only seven of the 18 variables used were needed to completely differentiate the trees at the 2 sites (F/y ] 93) = 210.36 p < 0.001). The magnitudes of the standardized discriminant function coefficients for the Included variables Indicated that the differences between sites were largely due to terpene chemistry (Table VIII). The discriminant function contrasts primarily the relative concentration of alpha-plnene versus the concentration of several terpenes, particularly bornyl acetate and beta-plnene. Examination of the discriminant scores showed that the stressed trees loaded negatively on the function (x discriminant score = -2.23), while the non-stressed trees loaded positively (x discriminant score = 3.38). In other wards, trees from the stressed site were higher In alpha-plnene vdille the non-stressed trees contained more bornyl acetate, beta-plnene, and other terpenes In their young needles. 

The 76 variables derived from the DEC evaluation were first analyzed using stepwise discriminant analysis to determine the variables that best predicted the presence or absence of each drug. This subset of best-predictor variables was then subjected to a discriminant function analysis that predicted and classified whether subjects were dosed or not dosed with drug. The resulting data were classified as true positive, true negative, false positive, or false negative. These parameters were then used to calculate several measures of predictive accuracy of the DEC evaluation, including sensitivity, specificity, and efficiency. 

In Study 2, the stepwise discriminant analysis resulted in a subset of seven variables that were the best predictors of alprazolam. The model was more accurate in predicting the absence of alprazolam (specificity = 96.7%) than its presence (sensitivity = 78.3%), and predictive efficiency was 90.4%. The analysis resulted in a subset of three variables that were the best predictors of dosing with D-amphetamine. As with alprazolam, the model s predictions had greater specificity (92.5%) than sensitivity (75.0%), and efficiency of the model was high (86.5%). The discriminant analysis resulted in a subset of two variables that were the best predictors of codeine. The model s predictions had much greater specificity (92.4%) than sensitivity (34.8%), and efficiency was moderate (73.2%). The discriminant analysis resulted in a subset of seven variables that were the best predictors of marijuana. The model predicted with greater accuracy the absence (specificity = 93.3%) of marijuana than its presence (sensitivity = 61.4%) predictive efficiency was 82.7%. 

Woo, A.H., Lindsay, R.C. 1983b. Stepwise discriminant analysis of free fatty acid profiles for identifying sources of lipolytic enzymes in rancid butter. J. Dairy Sci. 66, 2070-2075. 

Figure 3. Stepwise discriminant analysis by M. Pollard of all three measured lead isotope ratios for ore samples from Cyprus, Kythnos, and Laurion ore...

Simo, C., Martin-Alvarez, P.J., Barbas, C., Cifuentes, A. (2004). Application of stepwise discriminant analysis to classify commercial orange juices using chiral miceUar electroki-netic chromatography-laser induced fluorescence data of amino acids. Electrophoresis, 25, 2885-2891. 

Costanza, M.C. and A.A. Afifi. 1979. Comparison of stopping rules in forward stepwise discrimination analysis./. Am. Stat. Assoc. 74 777-785. 

The contents of Sr, Cu, Mg and Zn in the serum of patients of the coronary heart diseases and normal persons were determined by using the ICP-AES[19]. The dala were evaluated by using ordinary principal component analysis, cluster analysis and stepwise discrimination analysis. It has been found that ordinary principal component analysis and cluster analysis could not give satisfactory results with four samples misclassified. There were fivo samples misclassified in stepwise discrimination analysis. These data sets were treated by PP PCA and SVD. The PC1-PC2 plot of PP classification shown in Figure 8 has only two samples misclassified. The results further demonstrate that PP PCA is more preferable than the traditional SVD algorithm. 

Discriminant analysis was performed on all 22 compounds. Compounds were assigned to the "active" set if the activity was LC50 = 5 ppm or lower. All others were designated "inactive". Stepwise discriminant analysis BMDP-7M (16) was performed using the following physicochemical descriptors as variables pi, (17)... 

To establish a correlation between the concentrations of different kinds of nucleosides in a complex metabolic system and normal or abnormal states of human bodies, computer-aided pattern recognition methods are required (15, 16). Different kinds of pattern recognition methods based on multivariate data analysis such as principal component analysis (PCA) (8), partial least squares (16), stepwise discriminant analysis, and canonical discriminant analysis (10, 11) have been reported. Linear discriminant analysis (17, 18) and cluster analysis were also investigated (19,20). Artificial neural network (ANN) is a branch of chemometrics that resolves regression or classification problems. The applications of ANN in separation science and chemistry have been reported widely (21-23). For pattern recognition analysis in clinical study, ANN was also proven to be a promising method (8). 

The incidence of aminoglycoside nephrotoxicity rises with advancing age from 7% in patients under age 30 to 15% in patients over 70 years of age [16]. It is likely that dosage may be excessive in older patients based on overestimates of drug excretory capacity by insensitive renal function tests such as the serum urea nitrogen or serum creatinine. This age effect has been confirmed in a retrospective stepwise discriminant analysis of 214 patients in randomized prospective trials [17]. The mechanism of this age effect is unclear since experimental studies show a decrease in drug uptake in older animals compared to similarly dosed younger animals [18]. 

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. 

Then the next step consists on application of multivariate statistical methods to find key features involving molecules, descriptors and anticancer activity. The methods include principal component analysis (PCA), hiererchical cluster analysis (HCA), K-nearest neighbor method (KNN), soft independent modeling of class analogy method (SIMCA) and stepwise discriminant analysis (SDA). The analyses were performed on a data matrix with dimension 25 lines (molecules) x 1700 columns (descriptors), not shown for convenience. For a further study of the methodology apphed there are standard books available such as (Varmuza FUzmoser, 2009) and (Manly, 2004). 

Pilgen E, Pristantz A, Pfeiffer KP, Kostner G (1983) Risk factors for peripheral atherosclerosis retrospective evaluation by stepwise discriminant analysis. Arteriosclerosis 3 57-63... 

Stepwise discriminant analysis (SDA). SDA was run with the BMDP7M program (7). The F-value for selecting a peak to enter in the classification functions or to remove from already classified functions was set as 4.0. The maximum step number was 10, and the precision of classification at every step was tested by the Jackknifed classification method... 

The stepwise discriminant analysis. The stepwise discriminant analysis was run on the basis of eighteen compounds which had a rotated factor loading of more than 0.5 and less than -0.5 on the second factor axis. Furfuryl acetate, 5-methylfurfural, and unknown compound (Peak No. 73) were selected by the stepwise discriminant anlysis. At step 1, furfuryl acetate, with the largest F-value, was entered into the equation as the most discriminative compound. The results of the jackknifed classifi-cation at step 3 showed that the samples could be discriminated in each group with 100% correctness on the basis of the three components. Furfuryl acetate had high F-value, and was extracted as an important index for... 

Discriminant Analysis. Discriminant analysis is used to model a categorical response to a variable, for example, a flavor or treatment grouping, as a linear function of two or more predictors. Powers and Keith (27) published one of the earliest papers on the use of stepwise discriminant analysis (SDA) for gas chromatographic data. They were able to classify coffees using this technique. Other applications include work on wine classification (22) and sweet potato classification (25). 

Powers, J.L Keith, E.S. Stepwise discriminant analysis of gas chromatographic data as an aid in classifying the flavour quality of foods. JFood Sci. 1968, 33 207. 

---