Discrimination index

The Harary index increases with both molecular size and - molecular branching, it is therefore a measure of molecular compactness like the - Wiener index. However, the Harary index seems to be a more discriminating index than the Wiener index. 

This expression is a graph invariant generator. As will be shown later, this topological state expression will be used to develop a family of indexes for the whole graph that is a highly discriminating index of molecular graphs. 

The average relative error is 3.9%, and no observation has a relative error greater than 10%. These results are significantly better than those given by the Hansch model. Hansch and Lien > found it necessary to delete two observations to achieve r - 0.911,5 = 0.22. When the full data set is used, the statistics are even worse r = 0.878, s = 0.24. The potential value of this total topological index x is yet to be explored. Because it is a very highly discriminating index, there may be a useful role for it in QSAR. 

As described previously, AUROC can be useful to quantify a marker s ability to discriminate between samples from animals with and without injury. However, it does not make clear the extent to which the information provided by the candidate marker overlaps with information provided by the standard markers. One way to address this question is to compare the performance of a model that contains the standard markers together with the new candidate marker to a model that contains the standard markers without the new marker. The net reclassification index (NRI) and integrated discrimination index (IDI) (Pencina et al., 2(X)8) are metrics that can be used to quantify and test the difference in performance between binary logistic regression models and thus assess the amount of information added by the new marker. 

The calculation of each index is derived from the usual sum of square decomposition used in ANOVA, but applied to dominance rates. For instance, the discrimination index at panel level is simply the sum of square of the product effect (see the original paper for more details on the other indexes). However, the authors do not follow the F-test approach to test the significance for these indexes, since TDS data (or the residuals from any standard ANOVA model) are not normally distributed. They rather follow the permutation test approach proposed by Meyners and Pineau (2010) and Meyners (2011) and extend it to the scope of their indexes. The reader can refer to the original paper for more details about the testing procedure. 

Figure 3. Distribution curves of discrimination indexes for high-position debris flows.

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