Variable selection using pair-correlation method. Environmental applications

Pair-correlation method (PCM) has been developed for selecting between two, correlated descriptor variables. PCM utilizes systematic information present in the scatter of QSAR applications. The data are suitably ordered in a 2 x 2 contingency table. Statistical tests are used to discriminate between the descriptor variables. We have developed, adapted, investigated and compared the following test statistics to each other: Conditional Fisher's exact test (CE), McNemar's test (MN), Chi-square test and Williams' t-test (Wt). If a test indicates significant difference between the descriptors, we use the terms superior-inferior or winner-loser for the overwhelming and subordinate descriptors, respectively. If more than two variables are to be compared, the discrimination can be made pair-wise and then the variables have to be ordered. Three ways of ordering have been used: simple ordering (number of wins), ordering according to the differences between wins and losses, and ordering according to probability-weighted differences between wins and losses. The basic algorithm of PCM has been described in this paper, the various selection criteria and the ordering methods were compared on suitable model systems. These case studies involved description of cAMP phospodiesterase inhibition by flavons, toxicity of chlorobenzenes and mutagenic character of aromatic and heteroaromatic amines.