THE STRUCTURE-PROPERTY MODELS CAN BE IMPROVED USING THE ORTHOGONALIZED DESCRIPTORS

In this report we describe an approach of how one can with the use of orthogonalized descriptors achieve a better structure-property-activity model. This is illustrated using the truncated connectivity basis (l) chi (l = 0, 1,..., 6). The molecular property used to test the approach was the boiling paints of octanes. We first developed the algorithm which produces absolutely the best models with I descriptors (I = 1-7) in nonorthogonalized basis. These models were always better than the models that most authors achieve by the use of the stepwise/inclusion-exclusion procedure. The next step was the development of the computer program by which we could realize all possible orthogonalization orderings of a given set of I descriptors. In doing that we discovered that the certain orderings of the orthogonalized descriptors lead to models with higher values of the correlation coefficient (R) than the corresponding models with nonorthogonalized descriptors. Because of that we selected among all the possible orthogonalization orderings (there are I! possibilities for I descriptors) that ordering which leads to the descriptor which gives the highest value of R. We call this descriptor the dominant descriptor. After we located the first dominant descriptor, we have chosen the second dominant descriptor among the remaining (I - 1) descriptors following the same procedure. In the identical way are obtained the third, the fourth, etc. dominant descriptor. In this manner the selection of the dominant descriptors necessarily minimize the contributions of those descriptors which contribute small amounts to the total correlation coefficient, because the total R is for any fixed set of I descriptors constant and independent of the orthogonalization order. These descriptors appear to be insignificant and are removed from the consideration. With this act we only negligibly diminished the total R, but the value of S as well as F-test were significantly improved, since we obtained the model with less descriptors.