Interpreting Discriminant Functions: A Data Analytic Approach

The article focuses on the interpretation of discriminant functions following a significant MANOVA test. Based on a geometric interpretation of MANOVA, new indices called discriminant ratio coefficients are derived which will aid in the identification and interpretation of that subset of variables that essentially contribute to a significant group discrimination. They will also aid in identifying situations where the relative importance of individual response variables can be simply quantified. In such cases, discriminant ratio coefficients provide natural measures of relative importance. Their efficacy as data analytic tools will be compared to several commonly used techniques, both theoretically and through examples. A modified approach for dealing with cases of coefficient instability is also described.