A graphical index of separation (GIOS) in multivariate modeling



We introduce a new measure for the importance of predictor variables, X, for the separation of two groups (classes) of observations. The measure is a Graphical Index of Separation (GIOS), and is, for each predictor, determined from the distribution of all possible pairs of observations with one from each group. GIOS is quantitative, intuitively simple and easy to interpret. The GIOS is straightforward to visualize in bivariate plots, and line or bar plots for larger number of variables. The approach applies both to discriminant analyses such as LDA, SIMCA, PLS-DA, OPLS-DA and to quantitative modeling such as MLR, PLS and OPLS. In the latter case, the observations are first divided into two groups based on their response values, Y. The GIOS approach is illustrated by PLS-DA/OPLS-DA and SIMCA-classification of a number of multivariate data sets with few and many variables relative to the number of observations. Copyright © 2010 John Wiley & Sons, Ltd.