Correlation avoiding high

Randomization is another approach to avoiding high correlations among factors. For the example of Section 12.1, randomization is accomplished by mixing up the order in which the experiments are carried out. Any of a number of methods might... 

A stepwise selection procedure is performed to search for QSPR/QSAR models after the preliminary exclusion of - constant and near-constant variables. The - pair correlation cutoff selection of variables is then performed to avoid highly correlated descriptor variables within the model. 

Because variables in models are often highly correlated, when experimental data are collected, the xrx matrix in Equation 2.9 can be badly conditioned (see Appendix A), and thus the estimates of the values of the coefficients in a model can have considerable associated uncertainty. The method of factorial experimental design forces the data to be orthogonal and avoids this problem. This method allows you to determine the relative importance of each input variable and thus to develop a parsimonious model, one that includes only the most important variables and effects. Factorial experiments also represent efficient experimentation. You systematically plan and conduct experiments in which all of the variables are changed simultaneously rather than one at a time, thus reducing the number of experiments needed. 

Including covariates that are highly correlated adds little to the analysis and should be avoided. Knowledge of the nature of the correlation should help to prevent this happening. 

The use of these latent variables provides PLS with a greater capacity than MLR to distill most of the information contained in a large number of descriptors and properties into a smaller number of factors and thereby avoid some of the ravages of the Curse of Dimensionality. It is especially suited to dealing with systems containing many highly correlated descriptors. PLS is related to the methods of principal components analysis (PCA) and maximum redundancy analysis (MRA), in that all three methods augment the raw desaiptors with matrices derived from variance found in the descriptors themselves (PCA), the properties to be modeled (MRA), or a combination of both (PLS). ... 

Although it may well be true that the method of least squares is widely misused because of its apparent objectivity and general availability, it was clearly also true that much of the information obtainable from least squares is not used as completely as it could be. The problem of correlation between model parameters illustrates this clearly. High correlation between parameters amounts only to a statement about the data structure as opposed to the data values. The essential issue is the nature of the dependence of the parameter being determined on the data set. If two parameters have similar dependences, then their estimates are going to be correlated. Measuring more data points or a different set of data points would result in a different correlation matrix. The physical limitations of the experimental method, such as the inability to measure spectral characteristics of weak transitions or transitions that fall in inaccessible frequency regions, make it impractical to avoid correlations. 

Scaling of data is not necessary if the Mahalanobis distance is used. In addition, with this measure distortion occasioned by correlations of features or feature groups is avoided. In contrast, if the Euclidean distance were applied in the case of two highly correlated variables, these variables would be used as two independent features although they provide identical information. 

The VSM-W isotherm equation is a four parameters model, A i, K and C s). The pairwise interaction constants Aj and A j have been found to be highly correlated. To avoid this problem, Cochran et al. (1985) used the Flory-Huggin equation for the activity coefficient instead of the Wilson equation ... 

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