Effects of Profile Elevation, Scatter, and Shape on Discriminant Analysis Results

Abstract

Under the heading of "profile analysis" most multivariate statistical textbooks describe the "levels" and the "parallelism" hypotheses, which test group profile differences in elevation and combined scatter/shape, respectively. It is argued that although both tests are very useful tools, they should be incorporated into a strategy allowing for more specific analyses. A detailed profile analysis should be capable of separating the effects of elevation, scatter, and shape on single discriminant functions and contrasts. Procedural steps of such a Multistage Discriminant Analysis are outlined. Emphasis is placed on the geometrical representation of group profile configurations. The procedure is illustrated with an artificial data set.